%PDF-1.3 1 0 obj << /Type /Catalog /Outlines 2 0 R /Pages 3 0 R >> endobj 2 0 obj << /Type /Outlines /Count 0 >> endobj 3 0 obj << /Type /Pages /Kids [6 0 R 146 0 R 240 0 R 368 0 R 424 0 R 440 0 R 456 0 R 488 0 R 490 0 R ] /Count 9 /Resources << /ProcSet 4 0 R /Font << /F1 8 0 R /F2 9 0 R /F3 10 0 R /F4 11 0 R /F5 148 0 R /F6 149 0 R >> /XObject << /I1 12 0 R /I2 13 0 R /I3 242 0 R /I4 243 0 R /I5 244 0 R /I6 245 0 R /I7 246 0 R /I8 247 0 R /I9 284 0 R /I10 285 0 R /I11 286 0 R /I12 287 0 R /I13 288 0 R /I14 289 0 R /I15 326 0 R /I16 327 0 R /I17 328 0 R /I18 329 0 R /I19 330 0 R /I20 331 0 R /I21 376 0 R /I22 377 0 R /I23 378 0 R /I24 379 0 R /I25 380 0 R /I26 381 0 R /I27 382 0 R /I28 383 0 R /I29 384 0 R /I30 385 0 R /I31 394 0 R /I32 395 0 R /I33 396 0 R /I34 397 0 R /I35 398 0 R /I36 399 0 R /I37 400 0 R /I38 401 0 R /I39 402 0 R /I40 403 0 R /I41 412 0 R /I42 413 0 R /I43 414 0 R /I44 415 0 R /I45 416 0 R /I46 417 0 R /I47 418 0 R /I48 419 0 R /I49 420 0 R /I50 421 0 R /I51 428 0 R /I52 431 0 R /I53 444 0 R /I54 447 0 R >> >> /MediaBox [0.000 0.000 612.000 792.000] >> endobj 4 0 obj [/PDF /Text /ImageC ] endobj 5 0 obj << /Creator (DOMPDF) /CreationDate (D:20170829201643+00'00') /ModDate (D:20170829201643+00'00') /Title (Forecasting Peaks of Seasonal Influenza Epidemics PLOS Currents Outbreaks) >> endobj 6 0 obj << /Type /Page /Parent 3 0 R /Annots [ 14 0 R 16 0 R 18 0 R 20 0 R 22 0 R 24 0 R 26 0 R 28 0 R 30 0 R 32 0 R 34 0 R 36 0 R 38 0 R 40 0 R 42 0 R 44 0 R 46 0 R 48 0 R 50 0 R 52 0 R 54 0 R 56 0 R 58 0 R 60 0 R 62 0 R 64 0 R 66 0 R 68 0 R 70 0 R 72 0 R 74 0 R 76 0 R 78 0 R 80 0 R 82 0 R 84 0 R 86 0 R 88 0 R 90 0 R 92 0 R 94 0 R 96 0 R 98 0 R 100 0 R 102 0 R 104 0 R 106 0 R 108 0 R 110 0 R 112 0 R 114 0 R 116 0 R 118 0 R 120 0 R 122 0 R 124 0 R 126 0 R 128 0 R 130 0 R 132 0 R 134 0 R 136 0 R 138 0 R 140 0 R 142 0 R 144 0 R ] /Contents 7 0 R >> endobj 7 0 obj << /Length 28994 >> stream q 375.000 0 0 39.000 222.000 738.000 cm /I2 Do Q q 15.000 709.302 577.500 28.698 re W n 0.267 0.267 0.267 rg BT 15.000 718.042 Td /F2 21.0 Tf [(Forecasting Peaks of Seasonal Influenza Epidemics)] TJ ET Q 0.271 0.267 0.267 rg BT 15.000 700.036 Td /F3 9.8 Tf [(June 21, 2013)] TJ ET BT 74.846 700.036 Td /F3 9.8 Tf [()] TJ ET 0.267 0.267 0.267 rg BT 79.721 700.036 Td /F3 9.8 Tf [(Research Article)] TJ ET BT 26.250 688.195 Td /F1 9.8 Tf [(Elaine O. Nsoesie)] TJ ET 0.271 0.267 0.267 rg BT 104.279 688.195 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 109.700 688.195 Td /F1 9.8 Tf [(Madhav Marathe)] TJ ET 0.271 0.267 0.267 rg BT 182.855 692.083 Td /F1 8.7 Tf [(1)] TJ ET BT 187.673 688.195 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 193.094 688.195 Td /F1 9.8 Tf [(John S. Brownstein)] TJ ET 0.271 0.267 0.267 rg BT 26.250 677.023 Td /F4 9.0 Tf [(1)] TJ ET BT 31.254 677.023 Td /F1 9.0 Tf [( Virginia Tech)] TJ ET BT 26.250 665.301 Td /F1 9.8 Tf [(Nsoesie EO, Marathe M, Brownstein JS. Forecasting Peaks of Seasonal Influenza Epidemics. PLOS Currents Outbreaks. 2013 )] TJ ET BT 26.250 653.397 Td /F1 9.8 Tf [(Jun 21 . Edition 1. doi: 10.1371/currents.outbreaks.bb1e879a23137022ea79a8c508b030bc.)] TJ ET q 15.000 28.965 577.500 622.051 re W n 0.271 0.267 0.267 rg BT 26.250 624.294 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 604.340 Td /F1 9.8 Tf [(We present a framework for near real-time forecast of influenza epidemics using a simulation optimization approach. The )] TJ ET BT 26.250 592.435 Td /F1 9.8 Tf [(method combines an individual-based model and a simple root finding optimization method for parameter estimation and )] TJ ET BT 26.250 580.530 Td /F1 9.8 Tf [(forecasting. In this study, retrospective forecasts were generated for seasonal influenza epidemics using web-based estimates )] TJ ET BT 26.250 568.626 Td /F1 9.8 Tf [(of influenza activity from Google Flu Trends for 2004-2005, 2007-2008 and 2012-2013 flu seasons. In some cases, the peak )] TJ ET BT 26.250 556.721 Td /F1 9.8 Tf [(could be forecasted 5-6 weeks ahead. This study adds to existing resources for influenza forecasting and the proposed method )] TJ ET BT 26.250 544.816 Td /F1 9.8 Tf [(can be used in conjunction with other approaches in an ensemble framework.)] TJ ET BT 26.250 508.214 Td /F4 12.0 Tf [(Funding Statement)] TJ ET BT 26.250 488.259 Td /F1 9.8 Tf [(This work is supported by research grants from the National Library of Medicine, the National Institutes of Health )] TJ ET BT 26.250 476.355 Td /F1 9.8 Tf [(\(5R01LM010812-03\) and the Intelligence Advanced Research Projects Activity \(IARPA\) via Department of Interior National )] TJ ET BT 26.250 464.450 Td /F1 9.8 Tf [(Business Center \(DoI/NBC\) contract number D12PC000337. The US Government is authorized to reproduce and distribute )] TJ ET BT 26.250 452.545 Td /F1 9.8 Tf [(reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions )] TJ ET BT 26.250 440.640 Td /F1 9.8 Tf [(contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or )] TJ ET BT 26.250 428.736 Td /F1 9.8 Tf [(endorsements, either expressed or implied, of IARPA, DoI/NBC, or the US Government.)] TJ ET BT 26.250 399.633 Td /F4 12.0 Tf [(Introduction)] TJ ET BT 26.250 379.679 Td /F1 9.8 Tf [(In a paper published in 1986, Longini et al.)] TJ ET 0.267 0.267 0.267 rg BT 209.989 381.186 Td /F4 8.7 Tf [(1)] TJ ET 0.271 0.267 0.267 rg BT 214.807 379.679 Td /F1 9.8 Tf [( discussed the usefulness of developing approaches to infectious disease )] TJ ET BT 26.250 367.774 Td /F1 9.8 Tf [(forecasting for minimizing the public health impacts of an epidemic. The computational model presented was developed by )] TJ ET BT 26.250 355.869 Td /F1 9.8 Tf [(scientists in the Soviet Union for predicting the spatio-temporal spread of influenza between and within 126 cities and centers in )] TJ ET BT 26.250 343.965 Td /F1 9.8 Tf [(the Soviet Union. The model was based on a system of integro-differential equations with partial derivatives, which were later )] TJ ET BT 26.250 332.060 Td /F1 9.8 Tf [(translated to a set of difference equations for computer analysis. Cities were connected through a transportation matrix with )] TJ ET BT 26.250 320.155 Td /F1 9.8 Tf [(elements representing daily passenger movement between cities. An extension of the model to a global scale was applied to )] TJ ET BT 26.250 308.250 Td /F1 9.8 Tf [(forecasting the worldwide spread of the 1968-1969 Hong Kong influenza A \(H3N2\) pandemic. Longini et al. )] TJ ET 0.267 0.267 0.267 rg BT 490.145 309.758 Td /F4 8.7 Tf [(1)] TJ ET 0.271 0.267 0.267 rg BT 494.964 308.250 Td /F1 9.8 Tf [( concluded that the )] TJ ET BT 26.250 296.346 Td /F1 9.8 Tf [(performance of the model was promising in the forecast of the temporal-geographic spread of influenza over the forecast period, )] TJ ET BT 26.250 284.441 Td /F1 9.8 Tf [(which consisted of 425 days.)] TJ ET BT 26.250 265.036 Td /F1 9.8 Tf [(Since then several approaches have been proposed for forecasting influenza with varying degree of success. These range from )] TJ ET BT 26.250 253.131 Td /F1 9.8 Tf [(simple compartmental models )] TJ ET 0.267 0.267 0.267 rg BT 158.450 254.639 Td /F4 8.7 Tf [(2)] TJ ET BT 163.269 254.639 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 168.088 253.131 Td /F1 9.8 Tf [( to complex large-scale approaches )] TJ ET 0.267 0.267 0.267 rg BT 324.692 254.639 Td /F4 8.7 Tf [(4)] TJ ET BT 329.511 254.639 Td /F4 8.7 Tf [(5)] TJ ET 0.271 0.267 0.267 rg BT 334.329 253.131 Td /F1 9.8 Tf [(. Statistical methods based on the Box-Jenkins )] TJ ET BT 26.250 241.227 Td /F1 9.8 Tf [(approach to time-series analysis and state-space models have also been proposed )] TJ ET 0.267 0.267 0.267 rg BT 387.166 242.734 Td /F4 8.7 Tf [(6)] TJ ET BT 391.984 242.734 Td /F4 8.7 Tf [(7)] TJ ET BT 396.803 242.734 Td /F4 8.7 Tf [(8)] TJ ET BT 401.622 242.734 Td /F4 8.7 Tf [(9)] TJ ET 0.271 0.267 0.267 rg BT 406.440 241.227 Td /F1 9.8 Tf [(. Several of these approaches aim to )] TJ ET BT 26.250 229.322 Td /F1 9.8 Tf [(forecast different aspects of the influenza epidemic. Predicted measures typically include peak time and height, magnitude and )] TJ ET BT 26.250 217.417 Td /F1 9.8 Tf [(spread. Comparing approaches can be challenging since the gold standard varies and successful prediction is not always )] TJ ET BT 26.250 205.512 Td /F1 9.8 Tf [(clearly defined. However, there have been several achievements in near real-time and retrospective forecasts of peak time, )] TJ ET BT 26.250 193.608 Td /F1 9.8 Tf [(trend and magnitude. These include studies by Towers and Feng )] TJ ET 0.267 0.267 0.267 rg BT 309.683 195.115 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 314.501 193.608 Td /F1 9.8 Tf [(, which forecasted the 2009 pandemic to peak near the end )] TJ ET BT 26.250 181.703 Td /F1 9.8 Tf [(of October with 95% confidence. Reports from the Center for Disease Control and Prevention \(CDC\) indicated that the H1N1 )] TJ ET BT 26.250 169.798 Td /F1 9.8 Tf [(peak was observed in the second week of October in the US. Retrospective forecasts by Shaman and Karspeck )] TJ ET 0.267 0.267 0.267 rg BT 511.810 171.305 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 521.447 169.798 Td /F1 9.8 Tf [( suggested )] TJ ET BT 26.250 157.893 Td /F1 9.8 Tf [(seasonal influenza peaks could be forecasted in some cases as prompt as 7 weeks before the true peak.)] TJ ET BT 26.250 138.489 Td /F1 9.8 Tf [(Although, these accomplishments are promising, there are several limitations that impede influenza forecasting. These include )] TJ ET BT 26.250 126.584 Td /F1 9.8 Tf [(limitations inherent in the model assumptions, in addition to challenges incurred in data availability and estimation of disease )] TJ ET BT 26.250 114.679 Td /F1 9.8 Tf [(model parameters during an outbreak. Challenges due to the lack of data for near real-time forecasting are being tackled by the )] TJ ET BT 26.250 102.774 Td /F1 9.8 Tf [(proposal of alternative data sources to augment traditional methods to disease surveillance. One alternative data source is the )] TJ ET BT 26.250 90.870 Td /F1 9.8 Tf [(estimation of influenza activity using search query data. Google Flu Trends \(GFT\) estimates influenza activity based on a )] TJ ET BT 26.250 78.965 Td /F1 9.8 Tf [(modeling of search queries on terms, which appear to be good indicators of influenza activity. Shaman and Karspeck )] TJ ET 0.267 0.267 0.267 rg BT 532.402 80.472 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 542.039 78.965 Td /F1 9.8 Tf [(, in )] TJ ET BT 26.250 67.060 Td /F1 9.8 Tf [(addition, to other studies )] TJ ET 0.267 0.267 0.267 rg BT 135.187 68.567 Td /F4 8.7 Tf [(6)] TJ ET BT 140.005 68.567 Td /F4 8.7 Tf [(9)] TJ ET 0.271 0.267 0.267 rg BT 144.824 67.060 Td /F1 9.8 Tf [( have used GFT in influenza forecasting. The method presented by Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 499.256 68.567 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 508.893 67.060 Td /F1 9.8 Tf [( is more closely )] TJ ET BT 26.250 55.155 Td /F1 9.8 Tf [(related to that presented in this study. However, differences exist in the underlying epidemiology model and the process of )] TJ ET BT 26.250 43.251 Td /F1 9.8 Tf [(parameter estimation. Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 186.111 44.758 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 195.748 43.251 Td /F1 9.8 Tf [( combine a data assimilation technique \(ensemble adjustment Kalman filter\) and a )] TJ ET Q q 15.000 709.302 577.500 28.698 re W n 0.267 0.267 0.267 rg BT 15.000 718.042 Td /F2 21.0 Tf [(Forecasting Peaks of Seasonal Influenza Epidemics)] TJ ET Q 0.271 0.267 0.267 rg BT 15.000 700.036 Td /F3 9.8 Tf [(June 21, 2013)] TJ ET BT 74.846 700.036 Td /F3 9.8 Tf [()] TJ ET 0.267 0.267 0.267 rg BT 79.721 700.036 Td /F3 9.8 Tf [(Research Article)] TJ ET BT 26.250 688.195 Td /F1 9.8 Tf [(Elaine O. Nsoesie)] TJ ET 0.271 0.267 0.267 rg BT 104.279 688.195 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 109.700 688.195 Td /F1 9.8 Tf [(Madhav Marathe)] TJ ET 0.271 0.267 0.267 rg BT 182.855 692.083 Td /F1 8.7 Tf [(1)] TJ ET BT 187.673 688.195 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 193.094 688.195 Td /F1 9.8 Tf [(John S. Brownstein)] TJ ET 0.271 0.267 0.267 rg BT 26.250 677.023 Td /F4 9.0 Tf [(1)] TJ ET BT 31.254 677.023 Td /F1 9.0 Tf [( Virginia Tech)] TJ ET BT 26.250 665.301 Td /F1 9.8 Tf [(Nsoesie EO, Marathe M, Brownstein JS. Forecasting Peaks of Seasonal Influenza Epidemics. PLOS Currents Outbreaks. 2013 )] TJ ET BT 26.250 653.397 Td /F1 9.8 Tf [(Jun 21 . Edition 1. doi: 10.1371/currents.outbreaks.bb1e879a23137022ea79a8c508b030bc.)] TJ ET q 15.000 28.965 577.500 622.051 re W n 0.271 0.267 0.267 rg BT 26.250 624.294 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 604.340 Td /F1 9.8 Tf [(We present a framework for near real-time forecast of influenza epidemics using a simulation optimization approach. The )] TJ ET BT 26.250 592.435 Td /F1 9.8 Tf [(method combines an individual-based model and a simple root finding optimization method for parameter estimation and )] TJ ET BT 26.250 580.530 Td /F1 9.8 Tf [(forecasting. In this study, retrospective forecasts were generated for seasonal influenza epidemics using web-based estimates )] TJ ET BT 26.250 568.626 Td /F1 9.8 Tf [(of influenza activity from Google Flu Trends for 2004-2005, 2007-2008 and 2012-2013 flu seasons. In some cases, the peak )] TJ ET BT 26.250 556.721 Td /F1 9.8 Tf [(could be forecasted 5-6 weeks ahead. This study adds to existing resources for influenza forecasting and the proposed method )] TJ ET BT 26.250 544.816 Td /F1 9.8 Tf [(can be used in conjunction with other approaches in an ensemble framework.)] TJ ET BT 26.250 508.214 Td /F4 12.0 Tf [(Funding Statement)] TJ ET BT 26.250 488.259 Td /F1 9.8 Tf [(This work is supported by research grants from the National Library of Medicine, the National Institutes of Health )] TJ ET BT 26.250 476.355 Td /F1 9.8 Tf [(\(5R01LM010812-03\) and the Intelligence Advanced Research Projects Activity \(IARPA\) via Department of Interior National )] TJ ET BT 26.250 464.450 Td /F1 9.8 Tf [(Business Center \(DoI/NBC\) contract number D12PC000337. The US Government is authorized to reproduce and distribute )] TJ ET BT 26.250 452.545 Td /F1 9.8 Tf [(reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions )] TJ ET BT 26.250 440.640 Td /F1 9.8 Tf [(contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or )] TJ ET BT 26.250 428.736 Td /F1 9.8 Tf [(endorsements, either expressed or implied, of IARPA, DoI/NBC, or the US Government.)] TJ ET BT 26.250 399.633 Td /F4 12.0 Tf [(Introduction)] TJ ET BT 26.250 379.679 Td /F1 9.8 Tf [(In a paper published in 1986, Longini et al.)] TJ ET 0.267 0.267 0.267 rg BT 209.989 381.186 Td /F4 8.7 Tf [(1)] TJ ET 0.271 0.267 0.267 rg BT 214.807 379.679 Td /F1 9.8 Tf [( discussed the usefulness of developing approaches to infectious disease )] TJ ET BT 26.250 367.774 Td /F1 9.8 Tf [(forecasting for minimizing the public health impacts of an epidemic. The computational model presented was developed by )] TJ ET BT 26.250 355.869 Td /F1 9.8 Tf [(scientists in the Soviet Union for predicting the spatio-temporal spread of influenza between and within 126 cities and centers in )] TJ ET BT 26.250 343.965 Td /F1 9.8 Tf [(the Soviet Union. The model was based on a system of integro-differential equations with partial derivatives, which were later )] TJ ET BT 26.250 332.060 Td /F1 9.8 Tf [(translated to a set of difference equations for computer analysis. Cities were connected through a transportation matrix with )] TJ ET BT 26.250 320.155 Td /F1 9.8 Tf [(elements representing daily passenger movement between cities. An extension of the model to a global scale was applied to )] TJ ET BT 26.250 308.250 Td /F1 9.8 Tf [(forecasting the worldwide spread of the 1968-1969 Hong Kong influenza A \(H3N2\) pandemic. Longini et al. )] TJ ET 0.267 0.267 0.267 rg BT 490.145 309.758 Td /F4 8.7 Tf [(1)] TJ ET 0.271 0.267 0.267 rg BT 494.964 308.250 Td /F1 9.8 Tf [( concluded that the )] TJ ET BT 26.250 296.346 Td /F1 9.8 Tf [(performance of the model was promising in the forecast of the temporal-geographic spread of influenza over the forecast period, )] TJ ET BT 26.250 284.441 Td /F1 9.8 Tf [(which consisted of 425 days.)] TJ ET BT 26.250 265.036 Td /F1 9.8 Tf [(Since then several approaches have been proposed for forecasting influenza with varying degree of success. These range from )] TJ ET BT 26.250 253.131 Td /F1 9.8 Tf [(simple compartmental models )] TJ ET 0.267 0.267 0.267 rg BT 158.450 254.639 Td /F4 8.7 Tf [(2)] TJ ET BT 163.269 254.639 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 168.088 253.131 Td /F1 9.8 Tf [( to complex large-scale approaches )] TJ ET 0.267 0.267 0.267 rg BT 324.692 254.639 Td /F4 8.7 Tf [(4)] TJ ET BT 329.511 254.639 Td /F4 8.7 Tf [(5)] TJ ET 0.271 0.267 0.267 rg BT 334.329 253.131 Td /F1 9.8 Tf [(. Statistical methods based on the Box-Jenkins )] TJ ET BT 26.250 241.227 Td /F1 9.8 Tf [(approach to time-series analysis and state-space models have also been proposed )] TJ ET 0.267 0.267 0.267 rg BT 387.166 242.734 Td /F4 8.7 Tf [(6)] TJ ET BT 391.984 242.734 Td /F4 8.7 Tf [(7)] TJ ET BT 396.803 242.734 Td /F4 8.7 Tf [(8)] TJ ET BT 401.622 242.734 Td /F4 8.7 Tf [(9)] TJ ET 0.271 0.267 0.267 rg BT 406.440 241.227 Td /F1 9.8 Tf [(. Several of these approaches aim to )] TJ ET BT 26.250 229.322 Td /F1 9.8 Tf [(forecast different aspects of the influenza epidemic. Predicted measures typically include peak time and height, magnitude and )] TJ ET BT 26.250 217.417 Td /F1 9.8 Tf [(spread. Comparing approaches can be challenging since the gold standard varies and successful prediction is not always )] TJ ET BT 26.250 205.512 Td /F1 9.8 Tf [(clearly defined. However, there have been several achievements in near real-time and retrospective forecasts of peak time, )] TJ ET BT 26.250 193.608 Td /F1 9.8 Tf [(trend and magnitude. These include studies by Towers and Feng )] TJ ET 0.267 0.267 0.267 rg BT 309.683 195.115 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 314.501 193.608 Td /F1 9.8 Tf [(, which forecasted the 2009 pandemic to peak near the end )] TJ ET BT 26.250 181.703 Td /F1 9.8 Tf [(of October with 95% confidence. Reports from the Center for Disease Control and Prevention \(CDC\) indicated that the H1N1 )] TJ ET BT 26.250 169.798 Td /F1 9.8 Tf [(peak was observed in the second week of October in the US. Retrospective forecasts by Shaman and Karspeck )] TJ ET 0.267 0.267 0.267 rg BT 511.810 171.305 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 521.447 169.798 Td /F1 9.8 Tf [( suggested )] TJ ET BT 26.250 157.893 Td /F1 9.8 Tf [(seasonal influenza peaks could be forecasted in some cases as prompt as 7 weeks before the true peak.)] TJ ET BT 26.250 138.489 Td /F1 9.8 Tf [(Although, these accomplishments are promising, there are several limitations that impede influenza forecasting. These include )] TJ ET BT 26.250 126.584 Td /F1 9.8 Tf [(limitations inherent in the model assumptions, in addition to challenges incurred in data availability and estimation of disease )] TJ ET BT 26.250 114.679 Td /F1 9.8 Tf [(model parameters during an outbreak. Challenges due to the lack of data for near real-time forecasting are being tackled by the )] TJ ET BT 26.250 102.774 Td /F1 9.8 Tf [(proposal of alternative data sources to augment traditional methods to disease surveillance. One alternative data source is the )] TJ ET BT 26.250 90.870 Td /F1 9.8 Tf [(estimation of influenza activity using search query data. Google Flu Trends \(GFT\) estimates influenza activity based on a )] TJ ET BT 26.250 78.965 Td /F1 9.8 Tf [(modeling of search queries on terms, which appear to be good indicators of influenza activity. Shaman and Karspeck )] TJ ET 0.267 0.267 0.267 rg BT 532.402 80.472 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 542.039 78.965 Td /F1 9.8 Tf [(, in )] TJ ET BT 26.250 67.060 Td /F1 9.8 Tf [(addition, to other studies )] TJ ET 0.267 0.267 0.267 rg BT 135.187 68.567 Td /F4 8.7 Tf [(6)] TJ ET BT 140.005 68.567 Td /F4 8.7 Tf [(9)] TJ ET 0.271 0.267 0.267 rg BT 144.824 67.060 Td /F1 9.8 Tf [( have used GFT in influenza forecasting. The method presented by Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 499.256 68.567 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 508.893 67.060 Td /F1 9.8 Tf [( is more closely )] TJ ET BT 26.250 55.155 Td /F1 9.8 Tf [(related to that presented in this study. However, differences exist in the underlying epidemiology model and the process of )] TJ ET BT 26.250 43.251 Td /F1 9.8 Tf [(parameter estimation. Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 186.111 44.758 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 195.748 43.251 Td /F1 9.8 Tf [( combine a data assimilation technique \(ensemble adjustment Kalman filter\) and a )] TJ ET Q q 15.000 709.302 577.500 28.698 re W n 0.267 0.267 0.267 rg BT 15.000 718.042 Td /F2 21.0 Tf [(Forecasting Peaks of Seasonal Influenza Epidemics)] TJ ET Q 0.271 0.267 0.267 rg BT 15.000 700.036 Td /F3 9.8 Tf [(June 21, 2013)] TJ ET BT 74.846 700.036 Td /F3 9.8 Tf [()] TJ ET 0.267 0.267 0.267 rg BT 79.721 700.036 Td /F3 9.8 Tf [(Research Article)] TJ ET BT 26.250 688.195 Td /F1 9.8 Tf [(Elaine O. Nsoesie)] TJ ET 0.271 0.267 0.267 rg BT 104.279 688.195 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 109.700 688.195 Td /F1 9.8 Tf [(Madhav Marathe)] TJ ET 0.271 0.267 0.267 rg BT 182.855 692.083 Td /F1 8.7 Tf [(1)] TJ ET BT 187.673 688.195 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 193.094 688.195 Td /F1 9.8 Tf [(John S. Brownstein)] TJ ET 0.271 0.267 0.267 rg BT 26.250 677.023 Td /F4 9.0 Tf [(1)] TJ ET BT 31.254 677.023 Td /F1 9.0 Tf [( Virginia Tech)] TJ ET BT 26.250 665.301 Td /F1 9.8 Tf [(Nsoesie EO, Marathe M, Brownstein JS. Forecasting Peaks of Seasonal Influenza Epidemics. PLOS Currents Outbreaks. 2013 )] TJ ET BT 26.250 653.397 Td /F1 9.8 Tf [(Jun 21 . Edition 1. doi: 10.1371/currents.outbreaks.bb1e879a23137022ea79a8c508b030bc.)] TJ ET q 15.000 28.965 577.500 622.051 re W n 0.271 0.267 0.267 rg BT 26.250 624.294 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 604.340 Td /F1 9.8 Tf [(We present a framework for near real-time forecast of influenza epidemics using a simulation optimization approach. The )] TJ ET BT 26.250 592.435 Td /F1 9.8 Tf [(method combines an individual-based model and a simple root finding optimization method for parameter estimation and )] TJ ET BT 26.250 580.530 Td /F1 9.8 Tf [(forecasting. In this study, retrospective forecasts were generated for seasonal influenza epidemics using web-based estimates )] TJ ET BT 26.250 568.626 Td /F1 9.8 Tf [(of influenza activity from Google Flu Trends for 2004-2005, 2007-2008 and 2012-2013 flu seasons. In some cases, the peak )] TJ ET BT 26.250 556.721 Td /F1 9.8 Tf [(could be forecasted 5-6 weeks ahead. This study adds to existing resources for influenza forecasting and the proposed method )] TJ ET BT 26.250 544.816 Td /F1 9.8 Tf [(can be used in conjunction with other approaches in an ensemble framework.)] TJ ET BT 26.250 508.214 Td /F4 12.0 Tf [(Funding Statement)] TJ ET BT 26.250 488.259 Td /F1 9.8 Tf [(This work is supported by research grants from the National Library of Medicine, the National Institutes of Health )] TJ ET BT 26.250 476.355 Td /F1 9.8 Tf [(\(5R01LM010812-03\) and the Intelligence Advanced Research Projects Activity \(IARPA\) via Department of Interior National )] TJ ET BT 26.250 464.450 Td /F1 9.8 Tf [(Business Center \(DoI/NBC\) contract number D12PC000337. The US Government is authorized to reproduce and distribute )] TJ ET BT 26.250 452.545 Td /F1 9.8 Tf [(reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions )] TJ ET BT 26.250 440.640 Td /F1 9.8 Tf [(contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or )] TJ ET BT 26.250 428.736 Td /F1 9.8 Tf [(endorsements, either expressed or implied, of IARPA, DoI/NBC, or the US Government.)] TJ ET BT 26.250 399.633 Td /F4 12.0 Tf [(Introduction)] TJ ET BT 26.250 379.679 Td /F1 9.8 Tf [(In a paper published in 1986, Longini et al.)] TJ ET 0.267 0.267 0.267 rg BT 209.989 381.186 Td /F4 8.7 Tf [(1)] TJ ET 0.271 0.267 0.267 rg BT 214.807 379.679 Td /F1 9.8 Tf [( discussed the usefulness of developing approaches to infectious disease )] TJ ET BT 26.250 367.774 Td /F1 9.8 Tf [(forecasting for minimizing the public health impacts of an epidemic. The computational model presented was developed by )] TJ ET BT 26.250 355.869 Td /F1 9.8 Tf [(scientists in the Soviet Union for predicting the spatio-temporal spread of influenza between and within 126 cities and centers in )] TJ ET BT 26.250 343.965 Td /F1 9.8 Tf [(the Soviet Union. The model was based on a system of integro-differential equations with partial derivatives, which were later )] TJ ET BT 26.250 332.060 Td /F1 9.8 Tf [(translated to a set of difference equations for computer analysis. Cities were connected through a transportation matrix with )] TJ ET BT 26.250 320.155 Td /F1 9.8 Tf [(elements representing daily passenger movement between cities. An extension of the model to a global scale was applied to )] TJ ET BT 26.250 308.250 Td /F1 9.8 Tf [(forecasting the worldwide spread of the 1968-1969 Hong Kong influenza A \(H3N2\) pandemic. Longini et al. )] TJ ET 0.267 0.267 0.267 rg BT 490.145 309.758 Td /F4 8.7 Tf [(1)] TJ ET 0.271 0.267 0.267 rg BT 494.964 308.250 Td /F1 9.8 Tf [( concluded that the )] TJ ET BT 26.250 296.346 Td /F1 9.8 Tf [(performance of the model was promising in the forecast of the temporal-geographic spread of influenza over the forecast period, )] TJ ET BT 26.250 284.441 Td /F1 9.8 Tf [(which consisted of 425 days.)] TJ ET BT 26.250 265.036 Td /F1 9.8 Tf [(Since then several approaches have been proposed for forecasting influenza with varying degree of success. These range from )] TJ ET BT 26.250 253.131 Td /F1 9.8 Tf [(simple compartmental models )] TJ ET 0.267 0.267 0.267 rg BT 158.450 254.639 Td /F4 8.7 Tf [(2)] TJ ET BT 163.269 254.639 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 168.088 253.131 Td /F1 9.8 Tf [( to complex large-scale approaches )] TJ ET 0.267 0.267 0.267 rg BT 324.692 254.639 Td /F4 8.7 Tf [(4)] TJ ET BT 329.511 254.639 Td /F4 8.7 Tf [(5)] TJ ET 0.271 0.267 0.267 rg BT 334.329 253.131 Td /F1 9.8 Tf [(. Statistical methods based on the Box-Jenkins )] TJ ET BT 26.250 241.227 Td /F1 9.8 Tf [(approach to time-series analysis and state-space models have also been proposed )] TJ ET 0.267 0.267 0.267 rg BT 387.166 242.734 Td /F4 8.7 Tf [(6)] TJ ET BT 391.984 242.734 Td /F4 8.7 Tf [(7)] TJ ET BT 396.803 242.734 Td /F4 8.7 Tf [(8)] TJ ET BT 401.622 242.734 Td /F4 8.7 Tf [(9)] TJ ET 0.271 0.267 0.267 rg BT 406.440 241.227 Td /F1 9.8 Tf [(. Several of these approaches aim to )] TJ ET BT 26.250 229.322 Td /F1 9.8 Tf [(forecast different aspects of the influenza epidemic. Predicted measures typically include peak time and height, magnitude and )] TJ ET BT 26.250 217.417 Td /F1 9.8 Tf [(spread. Comparing approaches can be challenging since the gold standard varies and successful prediction is not always )] TJ ET BT 26.250 205.512 Td /F1 9.8 Tf [(clearly defined. However, there have been several achievements in near real-time and retrospective forecasts of peak time, )] TJ ET BT 26.250 193.608 Td /F1 9.8 Tf [(trend and magnitude. These include studies by Towers and Feng )] TJ ET 0.267 0.267 0.267 rg BT 309.683 195.115 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 314.501 193.608 Td /F1 9.8 Tf [(, which forecasted the 2009 pandemic to peak near the end )] TJ ET BT 26.250 181.703 Td /F1 9.8 Tf [(of October with 95% confidence. Reports from the Center for Disease Control and Prevention \(CDC\) indicated that the H1N1 )] TJ ET BT 26.250 169.798 Td /F1 9.8 Tf [(peak was observed in the second week of October in the US. Retrospective forecasts by Shaman and Karspeck )] TJ ET 0.267 0.267 0.267 rg BT 511.810 171.305 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 521.447 169.798 Td /F1 9.8 Tf [( suggested )] TJ ET BT 26.250 157.893 Td /F1 9.8 Tf [(seasonal influenza peaks could be forecasted in some cases as prompt as 7 weeks before the true peak.)] TJ ET BT 26.250 138.489 Td /F1 9.8 Tf [(Although, these accomplishments are promising, there are several limitations that impede influenza forecasting. These include )] TJ ET BT 26.250 126.584 Td /F1 9.8 Tf [(limitations inherent in the model assumptions, in addition to challenges incurred in data availability and estimation of disease )] TJ ET BT 26.250 114.679 Td /F1 9.8 Tf [(model parameters during an outbreak. Challenges due to the lack of data for near real-time forecasting are being tackled by the )] TJ ET BT 26.250 102.774 Td /F1 9.8 Tf [(proposal of alternative data sources to augment traditional methods to disease surveillance. One alternative data source is the )] TJ ET BT 26.250 90.870 Td /F1 9.8 Tf [(estimation of influenza activity using search query data. Google Flu Trends \(GFT\) estimates influenza activity based on a )] TJ ET BT 26.250 78.965 Td /F1 9.8 Tf [(modeling of search queries on terms, which appear to be good indicators of influenza activity. Shaman and Karspeck )] TJ ET 0.267 0.267 0.267 rg BT 532.402 80.472 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 542.039 78.965 Td /F1 9.8 Tf [(, in )] TJ ET BT 26.250 67.060 Td /F1 9.8 Tf [(addition, to other studies )] TJ ET 0.267 0.267 0.267 rg BT 135.187 68.567 Td /F4 8.7 Tf [(6)] TJ ET BT 140.005 68.567 Td /F4 8.7 Tf [(9)] TJ ET 0.271 0.267 0.267 rg BT 144.824 67.060 Td /F1 9.8 Tf [( have used GFT in influenza forecasting. The method presented by Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 499.256 68.567 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 508.893 67.060 Td /F1 9.8 Tf [( is more closely )] TJ ET BT 26.250 55.155 Td /F1 9.8 Tf [(related to that presented in this study. However, differences exist in the underlying epidemiology model and the process of )] TJ ET BT 26.250 43.251 Td /F1 9.8 Tf [(parameter estimation. 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The humidity-driven model is )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(due to findings suggesting that changes in susceptibility and population-contact patterns are not the sole drivers of influenza )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(outbreaks, but also changes in environmental variables such as absolute humidity )] TJ ET 0.267 0.267 0.267 rg BT 381.745 745.174 Td /F4 8.7 Tf [(11)] TJ ET 0.271 0.267 0.267 rg BT 391.382 743.667 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(In contrast, we present a method, which combines an individual-based model and an optimization approach for influenza )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(forecasting. The individual-based model aims to capture the underlying process of disease transmission based on population )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(contact patterns, which characterizes the dynamics in the observed epidemic time series curve. Individual-based models and )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(other large-scale computational models have been widely used for evaluating control measures for public policy and pandemic )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(planning )] TJ ET 0.267 0.267 0.267 rg BT 65.816 678.150 Td /F4 8.7 Tf [(12)] TJ ET BT 75.453 678.150 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 85.090 676.643 Td /F1 9.8 Tf [(. The optimization approach is used to produce possible parameters, which capture the trend observed in the )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(data. Since the process is stochastic, several possible realizations of the epidemic are produced enabling the estimation of )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(confidence bounds for the predicted measures, which are essential for forecasting. For simplicity, we focus on forecasting the )] TJ ET BT 26.250 640.929 Td /F1 9.8 Tf [(peak time. However, preliminary validation of the methods functionality was applied to forecasting of the peak time, in addition )] TJ ET BT 26.250 629.024 Td /F1 9.8 Tf [(to peak height and magnitude using synthetic, model-generated epidemic time series curves )] TJ ET 0.267 0.267 0.267 rg BT 426.721 630.531 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 436.359 629.024 Td /F1 9.8 Tf [(. Here, we forecast and update )] TJ ET BT 26.250 617.119 Td /F1 9.8 Tf [(parameters on a weekly basis. Although applied to forecasting influenza-like illness \(ILI\), the method is not exclusive to )] TJ ET BT 26.250 605.214 Td /F1 9.8 Tf [(influenza but can be applied to other infectious diseases with similar modes of transmission.)] TJ ET BT 26.250 568.612 Td /F4 12.0 Tf [(Materials and Methods)] TJ ET BT 26.250 548.658 Td /F4 9.8 Tf [(Data )] TJ ET BT 55.510 548.658 Td /F5 9.8 Tf [(Google Flu Trends)] TJ ET BT 26.250 529.253 Td /F1 9.8 Tf [(ILI data or data from syndromic surveillance systems, which accurately capture influenza activity at a specific population level, )] TJ ET BT 26.250 517.348 Td /F1 9.8 Tf [(can be used in forecasting the epidemic peak. Typically, data from the U.S. Outpatient Influenza-like Illness Surveillance )] TJ ET BT 26.250 505.443 Td /F1 9.8 Tf [(Network \(ILINet\) provided by the Centers for Disease Control and Prevention \(CDC\) is considered the gold standard. However, )] TJ ET BT 26.250 493.539 Td /F1 9.8 Tf [(limitations exist in the availability of the data in near real-time. The data is usually subject to retrospective revisions as reports )] TJ ET BT 26.250 481.634 Td /F1 9.8 Tf [(on ILI cases are updated and also publicly released with a time delay. In addition, data is currently not available at the )] TJ ET BT 26.250 469.729 Td /F1 9.8 Tf [(necessary resolution \(city and surrounding metropolitan regions\) needed for the individual-based model. We therefore opt to )] TJ ET BT 26.250 457.824 Td /F1 9.8 Tf [(use GFT data, which is one of several alternative data sources shown to provide reasonable estimates of influenza activity. The )] TJ ET BT 26.250 445.920 Td /F1 9.8 Tf [(data is provided at a weekly resolution, is openly available in near real-time for several major cities in the US and is usually not )] TJ ET BT 26.250 434.015 Td /F1 9.8 Tf [(retrospectively updated. The process of constructing GFT is formally described in )] TJ ET 0.267 0.267 0.267 rg BT 379.005 435.522 Td /F4 8.7 Tf [(15)] TJ ET 0.271 0.267 0.267 rg BT 388.642 434.015 Td /F1 9.8 Tf [(. Similar to Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 500.270 435.522 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 509.907 434.015 Td /F1 9.8 Tf [(, we use GFT )] TJ ET BT 26.250 422.110 Td /F1 9.8 Tf [(data for the 2004-2005, and 2007-2008 influenza seasons. We also attempt to forecast the peak of the 2012-2013 influenza )] TJ ET BT 26.250 410.205 Td /F1 9.8 Tf [(epidemic. Peak times for these three epidemics are forecasted for Seattle, Washington.)] TJ ET BT 26.250 390.801 Td /F4 9.8 Tf [(Simulation Optimization Approach)] TJ ET BT 26.250 371.396 Td /F1 9.8 Tf [(The simulation optimization approach consists of two parts: a stochastic individual-based epidemiology model for simulating )] TJ ET BT 26.250 359.491 Td /F1 9.8 Tf [(influenza-like disease transmission and an optimization procedure for finding optimal parameters, which capture ongoing )] TJ ET BT 26.250 347.586 Td /F1 9.8 Tf [(disease activity. The optimization approach is used to recursively propose new parameter values, which are evaluated based on )] TJ ET BT 26.250 335.682 Td /F1 9.8 Tf [(simulated outcomes from the individual-based model. We separately describe the individual-based model and optimization )] TJ ET BT 26.250 323.777 Td /F1 9.8 Tf [(method.)] TJ ET BT 26.250 304.372 Td /F4 9.8 Tf [(Synthetic Networks and Individual-based Networked Model)] TJ ET BT 26.250 284.967 Td /F1 9.8 Tf [(The study of infectious disease dynamics has made significant strides due to factors such as improved computational )] TJ ET BT 26.250 273.063 Td /F1 9.8 Tf [(resources, novel surveillance methods, and improved technological devices for rapid tests and diagnostics. Individual-based )] TJ ET BT 26.250 261.158 Td /F1 9.8 Tf [(models requiring large computational resources have benefited from these advances. These methods have been applied to the )] TJ ET BT 26.250 249.253 Td /F1 9.8 Tf [(study of the socio-temporal transmission and the evaluation of measures for controlling the propagation of infectious disease )] TJ ET BT 26.250 237.348 Td /F1 9.8 Tf [(outbreaks in large populations )] TJ ET 0.267 0.267 0.267 rg BT 159.025 238.856 Td /F4 8.7 Tf [(12)] TJ ET 0.271 0.267 0.267 rg BT 168.663 237.348 Td /F1 9.8 Tf [(. The overall approach comprises of two parts: \(i\) synthesizing a social contact network that )] TJ ET BT 26.250 225.444 Td /F1 9.8 Tf [(captures detailed and time varying interactions between individuals comprising the urban region under consideration and \(ii\) a )] TJ ET BT 26.250 213.539 Td /F1 9.8 Tf [(high performance computing oriented dynamical model that simulates the spatial disease propagation and efficacy of )] TJ ET BT 26.250 201.634 Td /F1 9.8 Tf [(interventions. The process of synthesizing a social contact network for an urban region is based on our earlier work and can be )] TJ ET BT 26.250 189.729 Td /F1 9.8 Tf [(found in)] TJ ET 0.267 0.267 0.267 rg BT 60.941 191.237 Td /F4 8.7 Tf [(16)] TJ ET BT 70.578 191.237 Td /F4 8.7 Tf [(20)] TJ ET BT 80.215 191.237 Td /F4 8.7 Tf [(27)] TJ ET 0.271 0.267 0.267 rg BT 89.853 189.729 Td /F1 9.8 Tf [(. The individual-based model used in simulating the spread of disease in this paper was first described in )] TJ ET 0.267 0.267 0.267 rg BT 543.423 191.237 Td /F4 8.7 Tf [(16)] TJ ET 0.271 0.267 0.267 rg BT 553.060 189.729 Td /F1 9.8 Tf [(. )] TJ ET BT 26.250 177.825 Td /F1 9.8 Tf [(Since, these models are not a novel contribution of this paper and has been thoroughly described in several other publications, )] TJ ET BT 26.250 165.920 Td /F1 9.8 Tf [(we therefore summarize both the components briefly; see )] TJ ET 0.267 0.267 0.267 rg BT 277.147 167.427 Td /F4 8.7 Tf [(17)] TJ ET BT 286.784 167.427 Td /F4 8.7 Tf [(18)] TJ ET BT 296.421 167.427 Td /F4 8.7 Tf [(19)] TJ ET BT 306.059 167.427 Td /F4 8.7 Tf [(27)] TJ ET 0.271 0.267 0.267 rg BT 315.696 165.920 Td /F1 9.8 Tf [( for additional details.)] TJ ET BT 26.250 146.515 Td /F1 9.8 Tf [(Synthetic social contact networks for an urban region are constructed using a variety of open source and commercially available )] TJ ET BT 26.250 134.610 Td /F1 9.8 Tf [(data combined with social and behavioral theories. A synthetic social contact network of an urban region is a particular kind of )] TJ ET BT 26.250 122.706 Td /F1 9.8 Tf [(random network that preserves anonymity and privacy of individuals and yet is statistically similar to a realistic social contact )] TJ ET BT 26.250 110.801 Td /F1 9.8 Tf [(network. It is important to note that such networks cannot be obtained by simple measurements alone.)] TJ ET BT 26.250 91.396 Td /F1 9.8 Tf [(First, a large time-scale is associated with land use and demographic distribution as a characterization of travelers including )] TJ ET BT 26.250 79.491 Td /F1 9.8 Tf [(their spatial distribution. In this phase, a synthetic population is created. The synthetic population is a set of synthetic people, )] TJ ET BT 26.250 67.587 Td /F1 9.8 Tf [(each associated with demographic variables drawn from demographical information available in the US census. Joint )] TJ ET BT 26.250 55.682 Td /F1 9.8 Tf [(demographic distributions can be reconstructed from the marginal distributions available in typical census data using the )] TJ ET BT 26.250 43.777 Td /F6 9.8 Tf [(iterative proportional fitting)] TJ ET BT 140.588 43.777 Td /F1 9.8 Tf [( technique. Each synthetic individual is placed in a household with other synthetic people and each )] TJ ET Q q 15.000 29.492 577.500 747.508 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(simple humidity-forced susceptible-infectious-recovered-susceptible \(SIRS\) mathematical model. The humidity-driven model is )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(due to findings suggesting that changes in susceptibility and population-contact patterns are not the sole drivers of influenza )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(outbreaks, but also changes in environmental variables such as absolute humidity )] TJ ET 0.267 0.267 0.267 rg BT 381.745 745.174 Td /F4 8.7 Tf [(11)] TJ ET 0.271 0.267 0.267 rg BT 391.382 743.667 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(In contrast, we present a method, which combines an individual-based model and an optimization approach for influenza )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(forecasting. The individual-based model aims to capture the underlying process of disease transmission based on population )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(contact patterns, which characterizes the dynamics in the observed epidemic time series curve. Individual-based models and )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(other large-scale computational models have been widely used for evaluating control measures for public policy and pandemic )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(planning )] TJ ET 0.267 0.267 0.267 rg BT 65.816 678.150 Td /F4 8.7 Tf [(12)] TJ ET BT 75.453 678.150 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 85.090 676.643 Td /F1 9.8 Tf [(. The optimization approach is used to produce possible parameters, which capture the trend observed in the )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(data. Since the process is stochastic, several possible realizations of the epidemic are produced enabling the estimation of )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(confidence bounds for the predicted measures, which are essential for forecasting. For simplicity, we focus on forecasting the )] TJ ET BT 26.250 640.929 Td /F1 9.8 Tf [(peak time. However, preliminary validation of the methods functionality was applied to forecasting of the peak time, in addition )] TJ ET BT 26.250 629.024 Td /F1 9.8 Tf [(to peak height and magnitude using synthetic, model-generated epidemic time series curves )] TJ ET 0.267 0.267 0.267 rg BT 426.721 630.531 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 436.359 629.024 Td /F1 9.8 Tf [(. Here, we forecast and update )] TJ ET BT 26.250 617.119 Td /F1 9.8 Tf [(parameters on a weekly basis. Although applied to forecasting influenza-like illness \(ILI\), the method is not exclusive to )] TJ ET BT 26.250 605.214 Td /F1 9.8 Tf [(influenza but can be applied to other infectious diseases with similar modes of transmission.)] TJ ET BT 26.250 568.612 Td /F4 12.0 Tf [(Materials and Methods)] TJ ET BT 26.250 548.658 Td /F4 9.8 Tf [(Data )] TJ ET BT 55.510 548.658 Td /F5 9.8 Tf [(Google Flu Trends)] TJ ET BT 26.250 529.253 Td /F1 9.8 Tf [(ILI data or data from syndromic surveillance systems, which accurately capture influenza activity at a specific population level, )] TJ ET BT 26.250 517.348 Td /F1 9.8 Tf [(can be used in forecasting the epidemic peak. Typically, data from the U.S. Outpatient Influenza-like Illness Surveillance )] TJ ET BT 26.250 505.443 Td /F1 9.8 Tf [(Network \(ILINet\) provided by the Centers for Disease Control and Prevention \(CDC\) is considered the gold standard. However, )] TJ ET BT 26.250 493.539 Td /F1 9.8 Tf [(limitations exist in the availability of the data in near real-time. The data is usually subject to retrospective revisions as reports )] TJ ET BT 26.250 481.634 Td /F1 9.8 Tf [(on ILI cases are updated and also publicly released with a time delay. In addition, data is currently not available at the )] TJ ET BT 26.250 469.729 Td /F1 9.8 Tf [(necessary resolution \(city and surrounding metropolitan regions\) needed for the individual-based model. We therefore opt to )] TJ ET BT 26.250 457.824 Td /F1 9.8 Tf [(use GFT data, which is one of several alternative data sources shown to provide reasonable estimates of influenza activity. The )] TJ ET BT 26.250 445.920 Td /F1 9.8 Tf [(data is provided at a weekly resolution, is openly available in near real-time for several major cities in the US and is usually not )] TJ ET BT 26.250 434.015 Td /F1 9.8 Tf [(retrospectively updated. The process of constructing GFT is formally described in )] TJ ET 0.267 0.267 0.267 rg BT 379.005 435.522 Td /F4 8.7 Tf [(15)] TJ ET 0.271 0.267 0.267 rg BT 388.642 434.015 Td /F1 9.8 Tf [(. Similar to Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 500.270 435.522 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 509.907 434.015 Td /F1 9.8 Tf [(, we use GFT )] TJ ET BT 26.250 422.110 Td /F1 9.8 Tf [(data for the 2004-2005, and 2007-2008 influenza seasons. We also attempt to forecast the peak of the 2012-2013 influenza )] TJ ET BT 26.250 410.205 Td /F1 9.8 Tf [(epidemic. Peak times for these three epidemics are forecasted for Seattle, Washington.)] TJ ET BT 26.250 390.801 Td /F4 9.8 Tf [(Simulation Optimization Approach)] TJ ET BT 26.250 371.396 Td /F1 9.8 Tf [(The simulation optimization approach consists of two parts: a stochastic individual-based epidemiology model for simulating )] TJ ET BT 26.250 359.491 Td /F1 9.8 Tf [(influenza-like disease transmission and an optimization procedure for finding optimal parameters, which capture ongoing )] TJ ET BT 26.250 347.586 Td /F1 9.8 Tf [(disease activity. The optimization approach is used to recursively propose new parameter values, which are evaluated based on )] TJ ET BT 26.250 335.682 Td /F1 9.8 Tf [(simulated outcomes from the individual-based model. We separately describe the individual-based model and optimization )] TJ ET BT 26.250 323.777 Td /F1 9.8 Tf [(method.)] TJ ET BT 26.250 304.372 Td /F4 9.8 Tf [(Synthetic Networks and Individual-based Networked Model)] TJ ET BT 26.250 284.967 Td /F1 9.8 Tf [(The study of infectious disease dynamics has made significant strides due to factors such as improved computational )] TJ ET BT 26.250 273.063 Td /F1 9.8 Tf [(resources, novel surveillance methods, and improved technological devices for rapid tests and diagnostics. Individual-based )] TJ ET BT 26.250 261.158 Td /F1 9.8 Tf [(models requiring large computational resources have benefited from these advances. These methods have been applied to the )] TJ ET BT 26.250 249.253 Td /F1 9.8 Tf [(study of the socio-temporal transmission and the evaluation of measures for controlling the propagation of infectious disease )] TJ ET BT 26.250 237.348 Td /F1 9.8 Tf [(outbreaks in large populations )] TJ ET 0.267 0.267 0.267 rg BT 159.025 238.856 Td /F4 8.7 Tf [(12)] TJ ET 0.271 0.267 0.267 rg BT 168.663 237.348 Td /F1 9.8 Tf [(. The overall approach comprises of two parts: \(i\) synthesizing a social contact network that )] TJ ET BT 26.250 225.444 Td /F1 9.8 Tf [(captures detailed and time varying interactions between individuals comprising the urban region under consideration and \(ii\) a )] TJ ET BT 26.250 213.539 Td /F1 9.8 Tf [(high performance computing oriented dynamical model that simulates the spatial disease propagation and efficacy of )] TJ ET BT 26.250 201.634 Td /F1 9.8 Tf [(interventions. The process of synthesizing a social contact network for an urban region is based on our earlier work and can be )] TJ ET BT 26.250 189.729 Td /F1 9.8 Tf [(found in)] TJ ET 0.267 0.267 0.267 rg BT 60.941 191.237 Td /F4 8.7 Tf [(16)] TJ ET BT 70.578 191.237 Td /F4 8.7 Tf [(20)] TJ ET BT 80.215 191.237 Td /F4 8.7 Tf [(27)] TJ ET 0.271 0.267 0.267 rg BT 89.853 189.729 Td /F1 9.8 Tf [(. The individual-based model used in simulating the spread of disease in this paper was first described in )] TJ ET 0.267 0.267 0.267 rg BT 543.423 191.237 Td /F4 8.7 Tf [(16)] TJ ET 0.271 0.267 0.267 rg BT 553.060 189.729 Td /F1 9.8 Tf [(. )] TJ ET BT 26.250 177.825 Td /F1 9.8 Tf [(Since, these models are not a novel contribution of this paper and has been thoroughly described in several other publications, )] TJ ET BT 26.250 165.920 Td /F1 9.8 Tf [(we therefore summarize both the components briefly; see )] TJ ET 0.267 0.267 0.267 rg BT 277.147 167.427 Td /F4 8.7 Tf [(17)] TJ ET BT 286.784 167.427 Td /F4 8.7 Tf [(18)] TJ ET BT 296.421 167.427 Td /F4 8.7 Tf [(19)] TJ ET BT 306.059 167.427 Td /F4 8.7 Tf [(27)] TJ ET 0.271 0.267 0.267 rg BT 315.696 165.920 Td /F1 9.8 Tf [( for additional details.)] TJ ET BT 26.250 146.515 Td /F1 9.8 Tf [(Synthetic social contact networks for an urban region are constructed using a variety of open source and commercially available )] TJ ET BT 26.250 134.610 Td /F1 9.8 Tf [(data combined with social and behavioral theories. A synthetic social contact network of an urban region is a particular kind of )] TJ ET BT 26.250 122.706 Td /F1 9.8 Tf [(random network that preserves anonymity and privacy of individuals and yet is statistically similar to a realistic social contact )] TJ ET BT 26.250 110.801 Td /F1 9.8 Tf [(network. It is important to note that such networks cannot be obtained by simple measurements alone.)] TJ ET BT 26.250 91.396 Td /F1 9.8 Tf [(First, a large time-scale is associated with land use and demographic distribution as a characterization of travelers including )] TJ ET BT 26.250 79.491 Td /F1 9.8 Tf [(their spatial distribution. In this phase, a synthetic population is created. The synthetic population is a set of synthetic people, )] TJ ET BT 26.250 67.587 Td /F1 9.8 Tf [(each associated with demographic variables drawn from demographical information available in the US census. Joint )] TJ ET BT 26.250 55.682 Td /F1 9.8 Tf [(demographic distributions can be reconstructed from the marginal distributions available in typical census data using the )] TJ ET BT 26.250 43.777 Td /F6 9.8 Tf [(iterative proportional fitting)] TJ ET BT 140.588 43.777 Td /F1 9.8 Tf [( technique. Each synthetic individual is placed in a household with other synthetic people and each )] TJ ET Q q 15.000 29.492 577.500 747.508 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(simple humidity-forced susceptible-infectious-recovered-susceptible \(SIRS\) mathematical model. The humidity-driven model is )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(due to findings suggesting that changes in susceptibility and population-contact patterns are not the sole drivers of influenza )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(outbreaks, but also changes in environmental variables such as absolute humidity )] TJ ET 0.267 0.267 0.267 rg BT 381.745 745.174 Td /F4 8.7 Tf [(11)] TJ ET 0.271 0.267 0.267 rg BT 391.382 743.667 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(In contrast, we present a method, which combines an individual-based model and an optimization approach for influenza )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(forecasting. The individual-based model aims to capture the underlying process of disease transmission based on population )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(contact patterns, which characterizes the dynamics in the observed epidemic time series curve. Individual-based models and )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(other large-scale computational models have been widely used for evaluating control measures for public policy and pandemic )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(planning )] TJ ET 0.267 0.267 0.267 rg BT 65.816 678.150 Td /F4 8.7 Tf [(12)] TJ ET BT 75.453 678.150 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 85.090 676.643 Td /F1 9.8 Tf [(. The optimization approach is used to produce possible parameters, which capture the trend observed in the )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(data. Since the process is stochastic, several possible realizations of the epidemic are produced enabling the estimation of )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(confidence bounds for the predicted measures, which are essential for forecasting. For simplicity, we focus on forecasting the )] TJ ET BT 26.250 640.929 Td /F1 9.8 Tf [(peak time. However, preliminary validation of the methods functionality was applied to forecasting of the peak time, in addition )] TJ ET BT 26.250 629.024 Td /F1 9.8 Tf [(to peak height and magnitude using synthetic, model-generated epidemic time series curves )] TJ ET 0.267 0.267 0.267 rg BT 426.721 630.531 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 436.359 629.024 Td /F1 9.8 Tf [(. Here, we forecast and update )] TJ ET BT 26.250 617.119 Td /F1 9.8 Tf [(parameters on a weekly basis. Although applied to forecasting influenza-like illness \(ILI\), the method is not exclusive to )] TJ ET BT 26.250 605.214 Td /F1 9.8 Tf [(influenza but can be applied to other infectious diseases with similar modes of transmission.)] TJ ET BT 26.250 568.612 Td /F4 12.0 Tf [(Materials and Methods)] TJ ET BT 26.250 548.658 Td /F4 9.8 Tf [(Data )] TJ ET BT 55.510 548.658 Td /F5 9.8 Tf [(Google Flu Trends)] TJ ET BT 26.250 529.253 Td /F1 9.8 Tf [(ILI data or data from syndromic surveillance systems, which accurately capture influenza activity at a specific population level, )] TJ ET BT 26.250 517.348 Td /F1 9.8 Tf [(can be used in forecasting the epidemic peak. Typically, data from the U.S. Outpatient Influenza-like Illness Surveillance )] TJ ET BT 26.250 505.443 Td /F1 9.8 Tf [(Network \(ILINet\) provided by the Centers for Disease Control and Prevention \(CDC\) is considered the gold standard. However, )] TJ ET BT 26.250 493.539 Td /F1 9.8 Tf [(limitations exist in the availability of the data in near real-time. The data is usually subject to retrospective revisions as reports )] TJ ET BT 26.250 481.634 Td /F1 9.8 Tf [(on ILI cases are updated and also publicly released with a time delay. In addition, data is currently not available at the )] TJ ET BT 26.250 469.729 Td /F1 9.8 Tf [(necessary resolution \(city and surrounding metropolitan regions\) needed for the individual-based model. We therefore opt to )] TJ ET BT 26.250 457.824 Td /F1 9.8 Tf [(use GFT data, which is one of several alternative data sources shown to provide reasonable estimates of influenza activity. The )] TJ ET BT 26.250 445.920 Td /F1 9.8 Tf [(data is provided at a weekly resolution, is openly available in near real-time for several major cities in the US and is usually not )] TJ ET BT 26.250 434.015 Td /F1 9.8 Tf [(retrospectively updated. The process of constructing GFT is formally described in )] TJ ET 0.267 0.267 0.267 rg BT 379.005 435.522 Td /F4 8.7 Tf [(15)] TJ ET 0.271 0.267 0.267 rg BT 388.642 434.015 Td /F1 9.8 Tf [(. Similar to Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 500.270 435.522 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 509.907 434.015 Td /F1 9.8 Tf [(, we use GFT )] TJ ET BT 26.250 422.110 Td /F1 9.8 Tf [(data for the 2004-2005, and 2007-2008 influenza seasons. We also attempt to forecast the peak of the 2012-2013 influenza )] TJ ET BT 26.250 410.205 Td /F1 9.8 Tf [(epidemic. Peak times for these three epidemics are forecasted for Seattle, Washington.)] TJ ET BT 26.250 390.801 Td /F4 9.8 Tf [(Simulation Optimization Approach)] TJ ET BT 26.250 371.396 Td /F1 9.8 Tf [(The simulation optimization approach consists of two parts: a stochastic individual-based epidemiology model for simulating )] TJ ET BT 26.250 359.491 Td /F1 9.8 Tf [(influenza-like disease transmission and an optimization procedure for finding optimal parameters, which capture ongoing )] TJ ET BT 26.250 347.586 Td /F1 9.8 Tf [(disease activity. The optimization approach is used to recursively propose new parameter values, which are evaluated based on )] TJ ET BT 26.250 335.682 Td /F1 9.8 Tf [(simulated outcomes from the individual-based model. We separately describe the individual-based model and optimization )] TJ ET BT 26.250 323.777 Td /F1 9.8 Tf [(method.)] TJ ET BT 26.250 304.372 Td /F4 9.8 Tf [(Synthetic Networks and Individual-based Networked Model)] TJ ET BT 26.250 284.967 Td /F1 9.8 Tf [(The study of infectious disease dynamics has made significant strides due to factors such as improved computational )] TJ ET BT 26.250 273.063 Td /F1 9.8 Tf [(resources, novel surveillance methods, and improved technological devices for rapid tests and diagnostics. Individual-based )] TJ ET BT 26.250 261.158 Td /F1 9.8 Tf [(models requiring large computational resources have benefited from these advances. These methods have been applied to the )] TJ ET BT 26.250 249.253 Td /F1 9.8 Tf [(study of the socio-temporal transmission and the evaluation of measures for controlling the propagation of infectious disease )] TJ ET BT 26.250 237.348 Td /F1 9.8 Tf [(outbreaks in large populations )] TJ ET 0.267 0.267 0.267 rg BT 159.025 238.856 Td /F4 8.7 Tf [(12)] TJ ET 0.271 0.267 0.267 rg BT 168.663 237.348 Td /F1 9.8 Tf [(. The overall approach comprises of two parts: \(i\) synthesizing a social contact network that )] TJ ET BT 26.250 225.444 Td /F1 9.8 Tf [(captures detailed and time varying interactions between individuals comprising the urban region under consideration and \(ii\) a )] TJ ET BT 26.250 213.539 Td /F1 9.8 Tf [(high performance computing oriented dynamical model that simulates the spatial disease propagation and efficacy of )] TJ ET BT 26.250 201.634 Td /F1 9.8 Tf [(interventions. The process of synthesizing a social contact network for an urban region is based on our earlier work and can be )] TJ ET BT 26.250 189.729 Td /F1 9.8 Tf [(found in)] TJ ET 0.267 0.267 0.267 rg BT 60.941 191.237 Td /F4 8.7 Tf [(16)] TJ ET BT 70.578 191.237 Td /F4 8.7 Tf [(20)] TJ ET BT 80.215 191.237 Td /F4 8.7 Tf [(27)] TJ ET 0.271 0.267 0.267 rg BT 89.853 189.729 Td /F1 9.8 Tf [(. The individual-based model used in simulating the spread of disease in this paper was first described in )] TJ ET 0.267 0.267 0.267 rg BT 543.423 191.237 Td /F4 8.7 Tf [(16)] TJ ET 0.271 0.267 0.267 rg BT 553.060 189.729 Td /F1 9.8 Tf [(. )] TJ ET BT 26.250 177.825 Td /F1 9.8 Tf [(Since, these models are not a novel contribution of this paper and has been thoroughly described in several other publications, )] TJ ET BT 26.250 165.920 Td /F1 9.8 Tf [(we therefore summarize both the components briefly; see )] TJ ET 0.267 0.267 0.267 rg BT 277.147 167.427 Td /F4 8.7 Tf [(17)] TJ ET BT 286.784 167.427 Td /F4 8.7 Tf [(18)] TJ ET BT 296.421 167.427 Td /F4 8.7 Tf [(19)] TJ ET BT 306.059 167.427 Td /F4 8.7 Tf [(27)] TJ ET 0.271 0.267 0.267 rg BT 315.696 165.920 Td /F1 9.8 Tf [( for additional details.)] TJ ET BT 26.250 146.515 Td /F1 9.8 Tf [(Synthetic social contact networks for an urban region are constructed using a variety of open source and commercially available )] TJ ET BT 26.250 134.610 Td /F1 9.8 Tf [(data combined with social and behavioral theories. A synthetic social contact network of an urban region is a particular kind of )] TJ ET BT 26.250 122.706 Td /F1 9.8 Tf [(random network that preserves anonymity and privacy of individuals and yet is statistically similar to a realistic social contact )] TJ ET BT 26.250 110.801 Td /F1 9.8 Tf [(network. It is important to note that such networks cannot be obtained by simple measurements alone.)] TJ ET BT 26.250 91.396 Td /F1 9.8 Tf [(First, a large time-scale is associated with land use and demographic distribution as a characterization of travelers including )] TJ ET BT 26.250 79.491 Td /F1 9.8 Tf [(their spatial distribution. In this phase, a synthetic population is created. The synthetic population is a set of synthetic people, )] TJ ET BT 26.250 67.587 Td /F1 9.8 Tf [(each associated with demographic variables drawn from demographical information available in the US census. Joint )] TJ ET BT 26.250 55.682 Td /F1 9.8 Tf [(demographic distributions can be reconstructed from the marginal distributions available in typical census data using the )] TJ ET BT 26.250 43.777 Td /F6 9.8 Tf [(iterative proportional fitting)] TJ ET BT 140.588 43.777 Td /F1 9.8 Tf [( technique. 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for households are determined, based on several thousand responses to an activity or time-use )] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(survey. These activity templates include what sort of activities each household member performs and what time of day they are )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(performed. Each synthetic household is then matched with one of the survey households, using a decision tree based on )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(demographics such as the number of workers in the household, number of children of various ages, etc. The synthetic )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(household is assigned the activity template of its matching survey household. For each household and each activity performed )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(by this household, a preliminary assignment of a location is made based on observed land-use patterns, tax data, etc. This )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(guess must be calibrated against observed travel-time distributions. Combining these steps, one obtains a synthetic )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(representation of individuals in an urban region carrying out daily activity patterns at realistic spatial locations.)] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(This information can be abstractly represented by a \(vertex and edge\) labeled bipartite graph G)] TJ ET BT 436.481 631.364 Td /F1 8.7 Tf [(PL)] TJ ET BT 447.081 633.429 Td /F1 9.8 Tf [(, where )] TJ ET BT 481.761 633.429 Td /F6 9.8 Tf [(P)] TJ ET BT 488.265 633.429 Td /F1 9.8 Tf [( is the set of people )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(and )] TJ ET BT 45.224 621.524 Td /F6 9.8 Tf [(L )] TJ ET BT 53.355 621.524 Td /F1 9.8 Tf [(is the set of locations. If a person )] TJ ET q 23.250 0 0 10.500 198.601 620.548 cm /I4 Do Q BT 221.851 621.524 Td /F1 9.8 Tf [(visits a location )] TJ ET q 18.750 0 0 9.000 290.666 622.048 cm /I6 Do Q BT 309.416 621.524 Td /F1 9.8 Tf [(, there is an edge \()] TJ ET BT 390.712 621.524 Td /F6 9.8 Tf [(p, l, label)] TJ ET BT 429.731 621.524 Td /F1 9.8 Tf [(\) )] TJ ET q 6.000 0 0 7.500 435.688 623.548 cm /I8 Do Q BT 441.688 621.524 Td /F1 9.8 Tf [( E\(G)] TJ ET BT 461.734 619.460 Td /F1 8.7 Tf [(PL)] TJ ET BT 472.334 621.524 Td /F1 9.8 Tf [(\) between them, where )] TJ ET BT 26.250 609.619 Td /F6 9.8 Tf [(label)] TJ ET BT 46.842 609.619 Td /F1 9.8 Tf [( is a record of the type of activity of the visit and its start and end points. Each vertex \(person or location\) can also have )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(labels. A persons labels correspond to his/her demographic attributes such as age, income, etc. The labels attached to )] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(locations specify the locations attributes such as its )] TJ ET BT 251.680 585.810 Td /F6 9.8 Tf [(x )] TJ ET BT 259.265 585.810 Td /F1 9.8 Tf [(and )] TJ ET BT 278.239 585.810 Td /F6 9.8 Tf [(y)] TJ ET BT 283.114 585.810 Td /F1 9.8 Tf [( coordinates, the type of activity performed, maximum capacity, etc. )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(Note that there can be multiple edges between a person and a location recording different visits. We use the term )] TJ ET BT 517.240 573.905 Td /F6 9.8 Tf [(people-)] TJ ET BT 26.250 562.000 Td /F6 9.8 Tf [(location-visitation graph)] TJ ET BT 128.664 562.000 Td /F1 9.8 Tf [( to refer to the above bipartite graph, wherein multiple edges are discarded and time labels are omitted. )] TJ ET BT 26.250 550.095 Td /F1 9.8 Tf [(Several projections of the bipartite graphs are possible. The )] TJ ET BT 286.370 550.095 Td /F6 9.8 Tf [(people-people-spatial-proximity)] TJ ET BT 421.827 550.095 Td /F1 9.8 Tf [( graph has as its vertices individual )] TJ ET BT 26.250 538.191 Td /F1 9.8 Tf [(people in an urban region and an edge between two people denotes that the individuals came within certain spatial proximity )] TJ ET BT 26.250 526.286 Td /F1 9.8 Tf [(during the course of the day. The modeling approaches used in constructing this model can be found in several publications. )] TJ ET BT 26.250 514.381 Td /F1 9.8 Tf [(See)] TJ ET 0.267 0.267 0.267 rg BT 43.595 515.888 Td /F4 8.7 Tf [(20)] TJ ET 0.271 0.267 0.267 rg BT 53.233 514.381 Td /F1 9.8 Tf [( , and )] TJ ET 0.267 0.267 0.267 rg BT 80.338 515.888 Td /F4 8.7 Tf [(21)] TJ ET 0.271 0.267 0.267 rg BT 89.975 514.381 Td /F1 9.8 Tf [( , and )] TJ ET 0.267 0.267 0.267 rg BT 117.080 515.888 Td /F4 8.7 Tf [(22)] TJ ET 0.271 0.267 0.267 rg BT 126.717 514.381 Td /F1 9.8 Tf [( for information on urban population mobility models. See )] TJ ET 0.267 0.267 0.267 rg BT 375.996 515.888 Td /F4 8.7 Tf [(13)] TJ ET BT 385.633 515.888 Td /F4 8.7 Tf [(23)] TJ ET BT 395.270 515.888 Td /F4 8.7 Tf [(24)] TJ ET BT 404.908 515.888 Td /F4 8.7 Tf [(25)] TJ ET 0.271 0.267 0.267 rg BT 414.545 514.381 Td /F1 9.8 Tf [(, and )] TJ ET 0.267 0.267 0.267 rg BT 438.939 515.888 Td /F4 8.7 Tf [(26)] TJ ET 0.271 0.267 0.267 rg BT 448.577 514.381 Td /F1 9.8 Tf [(, for information on disease )] TJ ET BT 26.250 502.476 Td /F1 9.8 Tf [(transmission models and the natural history of the disease. For further information on contact networks, see )] TJ ET 0.267 0.267 0.267 rg BT 492.827 503.984 Td /F4 8.7 Tf [(13)] TJ ET BT 502.464 503.984 Td /F4 8.7 Tf [(27)] TJ ET 0.271 0.267 0.267 rg BT 512.101 502.476 Td /F1 9.8 Tf [(, and )] TJ ET 0.267 0.267 0.267 rg BT 536.496 503.984 Td /F4 8.7 Tf [(28)] TJ ET 0.271 0.267 0.267 rg BT 546.133 502.476 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 483.072 Td /F1 9.8 Tf [(As stated, the individual-based model consists of the dynamic social contact network and an individualized disease model. The )] TJ ET BT 26.250 471.167 Td /F1 9.8 Tf [(within host disease model is based on a )] TJ ET BT 201.292 471.167 Td /F4 9.8 Tf [(S)] TJ ET BT 207.795 471.167 Td /F1 9.8 Tf [(usceptible, )] TJ ET BT 257.111 471.167 Td /F4 9.8 Tf [(E)] TJ ET BT 263.614 471.167 Td /F1 9.8 Tf [(xposed, )] TJ ET BT 300.469 471.167 Td /F4 9.8 Tf [(I)] TJ ET BT 303.179 471.167 Td /F1 9.8 Tf [(nfectious, )] TJ ET BT 347.620 471.167 Td /F4 9.8 Tf [(R)] TJ ET BT 354.659 471.167 Td /F1 9.8 Tf [(ecovered \(SEIR\) representation. Each infected )] TJ ET BT 26.250 459.262 Td /F1 9.8 Tf [(agent progresses through the different transmission states based on defined incubating and infectiousness time periods. The )] TJ ET BT 26.250 447.357 Td /F1 9.8 Tf [(incubation and infectious periods are described using discrete probability distributions. Transition between states can be )] TJ ET BT 26.250 435.453 Td /F1 9.8 Tf [(affected by the attributes of the individuals \(such as age, and health status\) and the type of contact \(casual, or intimate\). The )] TJ ET BT 26.250 423.548 Td /F1 9.8 Tf [(probability of transmission between susceptible \(u\) and infectious \(v\) individuals is given by:)] TJ ET BT 26.250 404.143 Td /F1 9.8 Tf [(p\(w\(u,v\)\)=1 ?\(1 ?r\))] TJ ET BT 107.243 408.031 Td /F1 8.7 Tf [(w\(u,v\))] TJ ET BT 26.250 384.738 Td /F1 9.8 Tf [(Here w\(u, v\) represents the contact duration and r is the disease transmission rate, which is defined per sec/contact time. We )] TJ ET BT 26.250 372.834 Td /F1 9.8 Tf [(have one such model per individual. These individualized models are connected based on the people-people proximity graph )] TJ ET BT 26.250 360.929 Td /F1 9.8 Tf [(described above. The networked model is too complex to study analytically. Over the last several years, faster simulations have )] TJ ET BT 26.250 349.024 Td /F1 9.8 Tf [(been progressively developed to study the dynamics of disease spread. Here we use a modeling environment called Epifast. )] TJ ET BT 26.250 337.119 Td /F1 9.8 Tf [(Epifast can simulate disease dynamics over a large social contact network in a matter of minutes. It also has the ability to )] TJ ET BT 26.250 325.215 Td /F1 9.8 Tf [(realistically represent natural intervention strategies. To simulate epidemics, the population, disease characteristics and initial )] TJ ET BT 26.250 313.310 Td /F1 9.8 Tf [(conditions, such as the number of initially infected individuals are selected. Published studies have validated different )] TJ ET BT 26.250 301.405 Td /F1 9.8 Tf [(components of the model. Examples illustrating structural validity include )] TJ ET 0.267 0.267 0.267 rg BT 342.160 302.912 Td /F4 8.7 Tf [(17)] TJ ET BT 351.797 302.912 Td /F4 8.7 Tf [(27)] TJ ET 0.271 0.267 0.267 rg BT 361.434 301.405 Td /F1 9.8 Tf [( and )] TJ ET 0.267 0.267 0.267 rg BT 383.118 302.912 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 392.756 301.405 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 282.000 Td /F5 9.8 Tf [(Parameters)] TJ ET BT 26.250 262.596 Td /F1 9.8 Tf [(The SEIR model requires three disease parameters: incubation period, infectious period and transmissibility. All other )] TJ ET BT 26.250 250.691 Td /F1 9.8 Tf [(parameters are assumed fixed. Both the infectious and incubation periods are defined as discrete probability distributions. )] TJ ET BT 26.250 238.786 Td /F1 9.8 Tf [(Individuals in the synthetic population have a probability of 0.3, 0.5 and 0.2 of experiencing an incubation period of 1, 2, or 3 )] TJ ET BT 26.250 226.881 Td /F1 9.8 Tf [(day\(s\) respectively. Similarly, individuals can also have an infectious period of 3, 4, 5, or 6 days with probabilities 0.3, 0.4, 0.2 )] TJ ET BT 26.250 214.977 Td /F1 9.8 Tf [(and 0.1 respectively. The mean incubation and infectious durations are therefore individually 2 and 4 days. These and similar )] TJ ET BT 26.250 203.072 Td /F1 9.8 Tf [(parameters have been used in several studies on seasonal influenza dynamics )] TJ ET 0.267 0.267 0.267 rg BT 369.284 204.579 Td /F4 8.7 Tf [(13)] TJ ET BT 378.922 204.579 Td /F4 8.7 Tf [(29)] TJ ET 0.271 0.267 0.267 rg BT 388.559 203.072 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 183.667 Td /F1 9.8 Tf [(In the individual-based model, the transmissibility parameter is defined as the probability of transmission per unit of contact time )] TJ ET BT 26.250 171.762 Td /F1 9.8 Tf [(given contact between an infectious and susceptible individual. In this study, we limit parameter estimation to the disease )] TJ ET BT 26.250 159.858 Td /F1 9.8 Tf [(transmissibility, although the overall approach is designed to forecast the epidemic curve based on estimation of these three )] TJ ET BT 26.250 147.953 Td /F1 9.8 Tf [(parameters. Since we are solely forecasting seasonal epidemics, we assume that the incubation and infectious periods are )] TJ ET BT 26.250 136.048 Td /F1 9.8 Tf [(consistent. We also assume that in addition to changes in environmental conditions and contact patterns, variability in )] TJ ET BT 26.250 124.143 Td /F1 9.8 Tf [(transmission influences peak time. Studies have indicated that influenza epidemics with higher transmissibility would likely result )] TJ ET BT 26.250 112.239 Td /F1 9.8 Tf [(in higher morbidity, higher peak height and earlier peaks )] TJ ET 0.267 0.267 0.267 rg BT 271.736 113.746 Td /F4 8.7 Tf [(30)] TJ ET BT 281.373 113.746 Td /F4 8.7 Tf [(31)] TJ ET 0.271 0.267 0.267 rg BT 291.010 112.239 Td /F1 9.8 Tf [(.)] TJ ET Q q 15.000 35.334 577.500 741.666 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(household is located geographically in such a way that a census of the synthetic population yields results that are statistically )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(indistinguishable from the original census data if they are both aggregated to the block group level.)] TJ ET BT 26.250 736.167 Td /F1 9.8 Tf [(Next, a set of activity templates for households are determined, based on several thousand responses to an activity or time-use )] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(survey. These activity templates include what sort of activities each household member performs and what time of day they are )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(performed. Each synthetic household is then matched with one of the survey households, using a decision tree based on )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(demographics such as the number of workers in the household, number of children of various ages, etc. The synthetic )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(household is assigned the activity template of its matching survey household. For each household and each activity performed )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(by this household, a preliminary assignment of a location is made based on observed land-use patterns, tax data, etc. This )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(guess must be calibrated against observed travel-time distributions. Combining these steps, one obtains a synthetic )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(representation of individuals in an urban region carrying out daily activity patterns at realistic spatial locations.)] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(This information can be abstractly represented by a \(vertex and edge\) labeled bipartite graph G)] TJ ET BT 436.481 631.364 Td /F1 8.7 Tf [(PL)] TJ ET BT 447.081 633.429 Td /F1 9.8 Tf [(, where )] TJ ET BT 481.761 633.429 Td /F6 9.8 Tf [(P)] TJ ET BT 488.265 633.429 Td /F1 9.8 Tf [( is the set of people )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(and )] TJ ET BT 45.224 621.524 Td /F6 9.8 Tf [(L )] TJ ET BT 53.355 621.524 Td /F1 9.8 Tf [(is the set of locations. If a person )] TJ ET q 23.250 0 0 10.500 198.601 620.548 cm /I10 Do Q BT 221.851 621.524 Td /F1 9.8 Tf [(visits a location )] TJ ET q 18.750 0 0 9.000 290.666 622.048 cm /I12 Do Q BT 309.416 621.524 Td /F1 9.8 Tf [(, there is an edge \()] TJ ET BT 390.712 621.524 Td /F6 9.8 Tf [(p, l, label)] TJ ET BT 429.731 621.524 Td /F1 9.8 Tf [(\) )] TJ ET q 6.000 0 0 7.500 435.688 623.548 cm /I14 Do Q BT 441.688 621.524 Td /F1 9.8 Tf [( E\(G)] TJ ET BT 461.734 619.460 Td /F1 8.7 Tf [(PL)] TJ ET BT 472.334 621.524 Td /F1 9.8 Tf [(\) between them, where )] TJ ET BT 26.250 609.619 Td /F6 9.8 Tf [(label)] TJ ET BT 46.842 609.619 Td /F1 9.8 Tf [( is a record of the type of activity of the visit and its start and end points. Each vertex \(person or location\) can also have )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(labels. A persons labels correspond to his/her demographic attributes such as age, income, etc. The labels attached to )] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(locations specify the locations attributes such as its )] TJ ET BT 251.680 585.810 Td /F6 9.8 Tf [(x )] TJ ET BT 259.265 585.810 Td /F1 9.8 Tf [(and )] TJ ET BT 278.239 585.810 Td /F6 9.8 Tf [(y)] TJ ET BT 283.114 585.810 Td /F1 9.8 Tf [( coordinates, the type of activity performed, maximum capacity, etc. )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(Note that there can be multiple edges between a person and a location recording different visits. We use the term )] TJ ET BT 517.240 573.905 Td /F6 9.8 Tf [(people-)] TJ ET BT 26.250 562.000 Td /F6 9.8 Tf [(location-visitation graph)] TJ ET BT 128.664 562.000 Td /F1 9.8 Tf [( to refer to the above bipartite graph, wherein multiple edges are discarded and time labels are omitted. )] TJ ET BT 26.250 550.095 Td /F1 9.8 Tf [(Several projections of the bipartite graphs are possible. The )] TJ ET BT 286.370 550.095 Td /F6 9.8 Tf [(people-people-spatial-proximity)] TJ ET BT 421.827 550.095 Td /F1 9.8 Tf [( graph has as its vertices individual )] TJ ET BT 26.250 538.191 Td /F1 9.8 Tf [(people in an urban region and an edge between two people denotes that the individuals came within certain spatial proximity )] TJ ET BT 26.250 526.286 Td /F1 9.8 Tf [(during the course of the day. The modeling approaches used in constructing this model can be found in several publications. )] TJ ET BT 26.250 514.381 Td /F1 9.8 Tf [(See)] TJ ET 0.267 0.267 0.267 rg BT 43.595 515.888 Td /F4 8.7 Tf [(20)] TJ ET 0.271 0.267 0.267 rg BT 53.233 514.381 Td /F1 9.8 Tf [( , and )] TJ ET 0.267 0.267 0.267 rg BT 80.338 515.888 Td /F4 8.7 Tf [(21)] TJ ET 0.271 0.267 0.267 rg BT 89.975 514.381 Td /F1 9.8 Tf [( , and )] TJ ET 0.267 0.267 0.267 rg BT 117.080 515.888 Td /F4 8.7 Tf [(22)] TJ ET 0.271 0.267 0.267 rg BT 126.717 514.381 Td /F1 9.8 Tf [( for information on urban population mobility models. See )] TJ ET 0.267 0.267 0.267 rg BT 375.996 515.888 Td /F4 8.7 Tf [(13)] TJ ET BT 385.633 515.888 Td /F4 8.7 Tf [(23)] TJ ET BT 395.270 515.888 Td /F4 8.7 Tf [(24)] TJ ET BT 404.908 515.888 Td /F4 8.7 Tf [(25)] TJ ET 0.271 0.267 0.267 rg BT 414.545 514.381 Td /F1 9.8 Tf [(, and )] TJ ET 0.267 0.267 0.267 rg BT 438.939 515.888 Td /F4 8.7 Tf [(26)] TJ ET 0.271 0.267 0.267 rg BT 448.577 514.381 Td /F1 9.8 Tf [(, for information on disease )] TJ ET BT 26.250 502.476 Td /F1 9.8 Tf [(transmission models and the natural history of the disease. For further information on contact networks, see )] TJ ET 0.267 0.267 0.267 rg BT 492.827 503.984 Td /F4 8.7 Tf [(13)] TJ ET BT 502.464 503.984 Td /F4 8.7 Tf [(27)] TJ ET 0.271 0.267 0.267 rg BT 512.101 502.476 Td /F1 9.8 Tf [(, and )] TJ ET 0.267 0.267 0.267 rg BT 536.496 503.984 Td /F4 8.7 Tf [(28)] TJ ET 0.271 0.267 0.267 rg BT 546.133 502.476 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 483.072 Td /F1 9.8 Tf [(As stated, the individual-based model consists of the dynamic social contact network and an individualized disease model. The )] TJ ET BT 26.250 471.167 Td /F1 9.8 Tf [(within host disease model is based on a )] TJ ET BT 201.292 471.167 Td /F4 9.8 Tf [(S)] TJ ET BT 207.795 471.167 Td /F1 9.8 Tf [(usceptible, )] TJ ET BT 257.111 471.167 Td /F4 9.8 Tf [(E)] TJ ET BT 263.614 471.167 Td /F1 9.8 Tf [(xposed, )] TJ ET BT 300.469 471.167 Td /F4 9.8 Tf [(I)] TJ ET BT 303.179 471.167 Td /F1 9.8 Tf [(nfectious, )] TJ ET BT 347.620 471.167 Td /F4 9.8 Tf [(R)] TJ ET BT 354.659 471.167 Td /F1 9.8 Tf [(ecovered \(SEIR\) representation. Each infected )] TJ ET BT 26.250 459.262 Td /F1 9.8 Tf [(agent progresses through the different transmission states based on defined incubating and infectiousness time periods. The )] TJ ET BT 26.250 447.357 Td /F1 9.8 Tf [(incubation and infectious periods are described using discrete probability distributions. Transition between states can be )] TJ ET BT 26.250 435.453 Td /F1 9.8 Tf [(affected by the attributes of the individuals \(such as age, and health status\) and the type of contact \(casual, or intimate\). The )] TJ ET BT 26.250 423.548 Td /F1 9.8 Tf [(probability of transmission between susceptible \(u\) and infectious \(v\) individuals is given by:)] TJ ET BT 26.250 404.143 Td /F1 9.8 Tf [(p\(w\(u,v\)\)=1 ?\(1 ?r\))] TJ ET BT 107.243 408.031 Td /F1 8.7 Tf [(w\(u,v\))] TJ ET BT 26.250 384.738 Td /F1 9.8 Tf [(Here w\(u, v\) represents the contact duration and r is the disease transmission rate, which is defined per sec/contact time. We )] TJ ET BT 26.250 372.834 Td /F1 9.8 Tf [(have one such model per individual. These individualized models are connected based on the people-people proximity graph )] TJ ET BT 26.250 360.929 Td /F1 9.8 Tf [(described above. The networked model is too complex to study analytically. Over the last several years, faster simulations have )] TJ ET BT 26.250 349.024 Td /F1 9.8 Tf [(been progressively developed to study the dynamics of disease spread. Here we use a modeling environment called Epifast. )] TJ ET BT 26.250 337.119 Td /F1 9.8 Tf [(Epifast can simulate disease dynamics over a large social contact network in a matter of minutes. It also has the ability to )] TJ ET BT 26.250 325.215 Td /F1 9.8 Tf [(realistically represent natural intervention strategies. To simulate epidemics, the population, disease characteristics and initial )] TJ ET BT 26.250 313.310 Td /F1 9.8 Tf [(conditions, such as the number of initially infected individuals are selected. Published studies have validated different )] TJ ET BT 26.250 301.405 Td /F1 9.8 Tf [(components of the model. Examples illustrating structural validity include )] TJ ET 0.267 0.267 0.267 rg BT 342.160 302.912 Td /F4 8.7 Tf [(17)] TJ ET BT 351.797 302.912 Td /F4 8.7 Tf [(27)] TJ ET 0.271 0.267 0.267 rg BT 361.434 301.405 Td /F1 9.8 Tf [( and )] TJ ET 0.267 0.267 0.267 rg BT 383.118 302.912 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 392.756 301.405 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 282.000 Td /F5 9.8 Tf [(Parameters)] TJ ET BT 26.250 262.596 Td /F1 9.8 Tf [(The SEIR model requires three disease parameters: incubation period, infectious period and transmissibility. All other )] TJ ET BT 26.250 250.691 Td /F1 9.8 Tf [(parameters are assumed fixed. Both the infectious and incubation periods are defined as discrete probability distributions. )] TJ ET BT 26.250 238.786 Td /F1 9.8 Tf [(Individuals in the synthetic population have a probability of 0.3, 0.5 and 0.2 of experiencing an incubation period of 1, 2, or 3 )] TJ ET BT 26.250 226.881 Td /F1 9.8 Tf [(day\(s\) respectively. Similarly, individuals can also have an infectious period of 3, 4, 5, or 6 days with probabilities 0.3, 0.4, 0.2 )] TJ ET BT 26.250 214.977 Td /F1 9.8 Tf [(and 0.1 respectively. The mean incubation and infectious durations are therefore individually 2 and 4 days. These and similar )] TJ ET BT 26.250 203.072 Td /F1 9.8 Tf [(parameters have been used in several studies on seasonal influenza dynamics )] TJ ET 0.267 0.267 0.267 rg BT 369.284 204.579 Td /F4 8.7 Tf [(13)] TJ ET BT 378.922 204.579 Td /F4 8.7 Tf [(29)] TJ ET 0.271 0.267 0.267 rg BT 388.559 203.072 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 183.667 Td /F1 9.8 Tf [(In the individual-based model, the transmissibility parameter is defined as the probability of transmission per unit of contact time )] TJ ET BT 26.250 171.762 Td /F1 9.8 Tf [(given contact between an infectious and susceptible individual. In this study, we limit parameter estimation to the disease )] TJ ET BT 26.250 159.858 Td /F1 9.8 Tf [(transmissibility, although the overall approach is designed to forecast the epidemic curve based on estimation of these three )] TJ ET BT 26.250 147.953 Td /F1 9.8 Tf [(parameters. Since we are solely forecasting seasonal epidemics, we assume that the incubation and infectious periods are )] TJ ET BT 26.250 136.048 Td /F1 9.8 Tf [(consistent. We also assume that in addition to changes in environmental conditions and contact patterns, variability in )] TJ ET BT 26.250 124.143 Td /F1 9.8 Tf [(transmission influences peak time. Studies have indicated that influenza epidemics with higher transmissibility would likely result )] TJ ET BT 26.250 112.239 Td /F1 9.8 Tf [(in higher morbidity, higher peak height and earlier peaks )] TJ ET 0.267 0.267 0.267 rg BT 271.736 113.746 Td /F4 8.7 Tf [(30)] TJ ET BT 281.373 113.746 Td /F4 8.7 Tf [(31)] TJ ET 0.271 0.267 0.267 rg BT 291.010 112.239 Td /F1 9.8 Tf [(.)] TJ ET Q q 15.000 35.334 577.500 741.666 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(household is located geographically in such a way that a census of the synthetic population yields results that are statistically )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(indistinguishable from the original census data if they are both aggregated to the block group level.)] TJ ET BT 26.250 736.167 Td /F1 9.8 Tf [(Next, a set of activity templates for households are determined, based on several thousand responses to an activity or time-use )] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(survey. These activity templates include what sort of activities each household member performs and what time of day they are )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(performed. Each synthetic household is then matched with one of the survey households, using a decision tree based on )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(demographics such as the number of workers in the household, number of children of various ages, etc. The synthetic )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(household is assigned the activity template of its matching survey household. For each household and each activity performed )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(by this household, a preliminary assignment of a location is made based on observed land-use patterns, tax data, etc. This )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(guess must be calibrated against observed travel-time distributions. Combining these steps, one obtains a synthetic )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(representation of individuals in an urban region carrying out daily activity patterns at realistic spatial locations.)] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(This information can be abstractly represented by a \(vertex and edge\) labeled bipartite graph G)] TJ ET BT 436.481 631.364 Td /F1 8.7 Tf [(PL)] TJ ET BT 447.081 633.429 Td /F1 9.8 Tf [(, where )] TJ ET BT 481.761 633.429 Td /F6 9.8 Tf [(P)] TJ ET BT 488.265 633.429 Td /F1 9.8 Tf [( is the set of people )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(and )] TJ ET BT 45.224 621.524 Td /F6 9.8 Tf [(L )] TJ ET BT 53.355 621.524 Td /F1 9.8 Tf [(is the set of locations. If a person )] TJ ET q 23.250 0 0 10.500 198.601 620.548 cm /I16 Do Q BT 221.851 621.524 Td /F1 9.8 Tf [(visits a location )] TJ ET q 18.750 0 0 9.000 290.666 622.048 cm /I18 Do Q BT 309.416 621.524 Td /F1 9.8 Tf [(, there is an edge \()] TJ ET BT 390.712 621.524 Td /F6 9.8 Tf [(p, l, label)] TJ ET BT 429.731 621.524 Td /F1 9.8 Tf [(\) )] TJ ET q 6.000 0 0 7.500 435.688 623.548 cm /I20 Do Q BT 441.688 621.524 Td /F1 9.8 Tf [( E\(G)] TJ ET BT 461.734 619.460 Td /F1 8.7 Tf [(PL)] TJ ET BT 472.334 621.524 Td /F1 9.8 Tf [(\) between them, where )] TJ ET BT 26.250 609.619 Td /F6 9.8 Tf [(label)] TJ ET BT 46.842 609.619 Td /F1 9.8 Tf [( is a record of the type of activity of the visit and its start and end points. Each vertex \(person or location\) can also have )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(labels. A persons labels correspond to his/her demographic attributes such as age, income, etc. The labels attached to )] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(locations specify the locations attributes such as its )] TJ ET BT 251.680 585.810 Td /F6 9.8 Tf [(x )] TJ ET BT 259.265 585.810 Td /F1 9.8 Tf [(and )] TJ ET BT 278.239 585.810 Td /F6 9.8 Tf [(y)] TJ ET BT 283.114 585.810 Td /F1 9.8 Tf [( coordinates, the type of activity performed, maximum capacity, etc. )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(Note that there can be multiple edges between a person and a location recording different visits. We use the term )] TJ ET BT 517.240 573.905 Td /F6 9.8 Tf [(people-)] TJ ET BT 26.250 562.000 Td /F6 9.8 Tf [(location-visitation graph)] TJ ET BT 128.664 562.000 Td /F1 9.8 Tf [( to refer to the above bipartite graph, wherein multiple edges are discarded and time labels are omitted. )] TJ ET BT 26.250 550.095 Td /F1 9.8 Tf [(Several projections of the bipartite graphs are possible. The )] TJ ET BT 286.370 550.095 Td /F6 9.8 Tf [(people-people-spatial-proximity)] TJ ET BT 421.827 550.095 Td /F1 9.8 Tf [( graph has as its vertices individual )] TJ ET BT 26.250 538.191 Td /F1 9.8 Tf [(people in an urban region and an edge between two people denotes that the individuals came within certain spatial proximity )] TJ ET BT 26.250 526.286 Td /F1 9.8 Tf [(during the course of the day. The modeling approaches used in constructing this model can be found in several publications. )] TJ ET BT 26.250 514.381 Td /F1 9.8 Tf [(See)] TJ ET 0.267 0.267 0.267 rg BT 43.595 515.888 Td /F4 8.7 Tf [(20)] TJ ET 0.271 0.267 0.267 rg BT 53.233 514.381 Td /F1 9.8 Tf [( , and )] TJ ET 0.267 0.267 0.267 rg BT 80.338 515.888 Td /F4 8.7 Tf [(21)] TJ ET 0.271 0.267 0.267 rg BT 89.975 514.381 Td /F1 9.8 Tf [( , and )] TJ ET 0.267 0.267 0.267 rg BT 117.080 515.888 Td /F4 8.7 Tf [(22)] TJ ET 0.271 0.267 0.267 rg BT 126.717 514.381 Td /F1 9.8 Tf [( for information on urban population mobility models. See )] TJ ET 0.267 0.267 0.267 rg BT 375.996 515.888 Td /F4 8.7 Tf [(13)] TJ ET BT 385.633 515.888 Td /F4 8.7 Tf [(23)] TJ ET BT 395.270 515.888 Td /F4 8.7 Tf [(24)] TJ ET BT 404.908 515.888 Td /F4 8.7 Tf [(25)] TJ ET 0.271 0.267 0.267 rg BT 414.545 514.381 Td /F1 9.8 Tf [(, and )] TJ ET 0.267 0.267 0.267 rg BT 438.939 515.888 Td /F4 8.7 Tf [(26)] TJ ET 0.271 0.267 0.267 rg BT 448.577 514.381 Td /F1 9.8 Tf [(, for information on disease )] TJ ET BT 26.250 502.476 Td /F1 9.8 Tf [(transmission models and the natural history of the disease. For further information on contact networks, see )] TJ ET 0.267 0.267 0.267 rg BT 492.827 503.984 Td /F4 8.7 Tf [(13)] TJ ET BT 502.464 503.984 Td /F4 8.7 Tf [(27)] TJ ET 0.271 0.267 0.267 rg BT 512.101 502.476 Td /F1 9.8 Tf [(, and )] TJ ET 0.267 0.267 0.267 rg BT 536.496 503.984 Td /F4 8.7 Tf [(28)] TJ ET 0.271 0.267 0.267 rg BT 546.133 502.476 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 483.072 Td /F1 9.8 Tf [(As stated, the individual-based model consists of the dynamic social contact network and an individualized disease model. The )] TJ ET BT 26.250 471.167 Td /F1 9.8 Tf [(within host disease model is based on a )] TJ ET BT 201.292 471.167 Td /F4 9.8 Tf [(S)] TJ ET BT 207.795 471.167 Td /F1 9.8 Tf [(usceptible, )] TJ ET BT 257.111 471.167 Td /F4 9.8 Tf [(E)] TJ ET BT 263.614 471.167 Td /F1 9.8 Tf [(xposed, )] TJ ET BT 300.469 471.167 Td /F4 9.8 Tf [(I)] TJ ET BT 303.179 471.167 Td /F1 9.8 Tf [(nfectious, )] TJ ET BT 347.620 471.167 Td /F4 9.8 Tf [(R)] TJ ET BT 354.659 471.167 Td /F1 9.8 Tf [(ecovered \(SEIR\) representation. Each infected )] TJ ET BT 26.250 459.262 Td /F1 9.8 Tf [(agent progresses through the different transmission states based on defined incubating and infectiousness time periods. The )] TJ ET BT 26.250 447.357 Td /F1 9.8 Tf [(incubation and infectious periods are described using discrete probability distributions. Transition between states can be )] TJ ET BT 26.250 435.453 Td /F1 9.8 Tf [(affected by the attributes of the individuals \(such as age, and health status\) and the type of contact \(casual, or intimate\). The )] TJ ET BT 26.250 423.548 Td /F1 9.8 Tf [(probability of transmission between susceptible \(u\) and infectious \(v\) individuals is given by:)] TJ ET BT 26.250 404.143 Td /F1 9.8 Tf [(p\(w\(u,v\)\)=1 ?\(1 ?r\))] TJ ET BT 107.243 408.031 Td /F1 8.7 Tf [(w\(u,v\))] TJ ET BT 26.250 384.738 Td /F1 9.8 Tf [(Here w\(u, v\) represents the contact duration and r is the disease transmission rate, which is defined per sec/contact time. We )] TJ ET BT 26.250 372.834 Td /F1 9.8 Tf [(have one such model per individual. These individualized models are connected based on the people-people proximity graph )] TJ ET BT 26.250 360.929 Td /F1 9.8 Tf [(described above. The networked model is too complex to study analytically. Over the last several years, faster simulations have )] TJ ET BT 26.250 349.024 Td /F1 9.8 Tf [(been progressively developed to study the dynamics of disease spread. Here we use a modeling environment called Epifast. )] TJ ET BT 26.250 337.119 Td /F1 9.8 Tf [(Epifast can simulate disease dynamics over a large social contact network in a matter of minutes. It also has the ability to )] TJ ET BT 26.250 325.215 Td /F1 9.8 Tf [(realistically represent natural intervention strategies. To simulate epidemics, the population, disease characteristics and initial )] TJ ET BT 26.250 313.310 Td /F1 9.8 Tf [(conditions, such as the number of initially infected individuals are selected. Published studies have validated different )] TJ ET BT 26.250 301.405 Td /F1 9.8 Tf [(components of the model. Examples illustrating structural validity include )] TJ ET 0.267 0.267 0.267 rg BT 342.160 302.912 Td /F4 8.7 Tf [(17)] TJ ET BT 351.797 302.912 Td /F4 8.7 Tf [(27)] TJ ET 0.271 0.267 0.267 rg BT 361.434 301.405 Td /F1 9.8 Tf [( and )] TJ ET 0.267 0.267 0.267 rg BT 383.118 302.912 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 392.756 301.405 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 282.000 Td /F5 9.8 Tf [(Parameters)] TJ ET BT 26.250 262.596 Td /F1 9.8 Tf [(The SEIR model requires three disease parameters: incubation period, infectious period and transmissibility. All other )] TJ ET BT 26.250 250.691 Td /F1 9.8 Tf [(parameters are assumed fixed. Both the infectious and incubation periods are defined as discrete probability distributions. )] TJ ET BT 26.250 238.786 Td /F1 9.8 Tf [(Individuals in the synthetic population have a probability of 0.3, 0.5 and 0.2 of experiencing an incubation period of 1, 2, or 3 )] TJ ET BT 26.250 226.881 Td /F1 9.8 Tf [(day\(s\) respectively. Similarly, individuals can also have an infectious period of 3, 4, 5, or 6 days with probabilities 0.3, 0.4, 0.2 )] TJ ET BT 26.250 214.977 Td /F1 9.8 Tf [(and 0.1 respectively. The mean incubation and infectious durations are therefore individually 2 and 4 days. These and similar )] TJ ET BT 26.250 203.072 Td /F1 9.8 Tf [(parameters have been used in several studies on seasonal influenza dynamics )] TJ ET 0.267 0.267 0.267 rg BT 369.284 204.579 Td /F4 8.7 Tf [(13)] TJ ET BT 378.922 204.579 Td /F4 8.7 Tf [(29)] TJ ET 0.271 0.267 0.267 rg BT 388.559 203.072 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 183.667 Td /F1 9.8 Tf [(In the individual-based model, the transmissibility parameter is defined as the probability of transmission per unit of contact time )] TJ ET BT 26.250 171.762 Td /F1 9.8 Tf [(given contact between an infectious and susceptible individual. In this study, we limit parameter estimation to the disease )] TJ ET BT 26.250 159.858 Td /F1 9.8 Tf [(transmissibility, although the overall approach is designed to forecast the epidemic curve based on estimation of these three )] TJ ET BT 26.250 147.953 Td /F1 9.8 Tf [(parameters. Since we are solely forecasting seasonal epidemics, we assume that the incubation and infectious periods are )] TJ ET BT 26.250 136.048 Td /F1 9.8 Tf [(consistent. We also assume that in addition to changes in environmental conditions and contact patterns, variability in )] TJ ET BT 26.250 124.143 Td /F1 9.8 Tf [(transmission influences peak time. Studies have indicated that influenza epidemics with higher transmissibility would likely result )] TJ ET BT 26.250 112.239 Td /F1 9.8 Tf [(in higher morbidity, higher peak height and earlier peaks )] TJ ET 0.267 0.267 0.267 rg BT 271.736 113.746 Td /F4 8.7 Tf [(30)] TJ ET BT 281.373 113.746 Td /F4 8.7 Tf [(31)] TJ ET 0.271 0.267 0.267 rg BT 291.010 112.239 Td /F1 9.8 Tf [(.)] TJ ET Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(3)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Outbreaks)] TJ ET Q endstream endobj 242 0 obj << /Type /XObject /Subtype /Image /Width 31 /Height 14 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 31 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 205>> stream c`x@$Xǡ &1 @_GPdm[ ;t ti +J26)myr6p1r7!ڶ$"kš2yB@\BJY18`@;#8Հj~6U9& f"lO'+++ asm 0,: endstream endobj 243 0 obj << /Type /XObject /Subtype /Image /Width 31 /Height 14 /SMask 242 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 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of the transmissibility of an infectious disease is an important bio-surveillance issue especially for outbreaks such as )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(influenza, which have a mean serial interval shorter than that of most infectious diseases )] TJ ET 0.267 0.267 0.267 rg BT 411.005 757.079 Td /F4 8.7 Tf [(32)] TJ ET 0.271 0.267 0.267 rg BT 420.642 755.571 Td /F1 9.8 Tf [(. In addition to the serial interval, )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(other measures such as the basic and effective reproduction numbers are typically used in estimating disease transmissibility. )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(We estimate the model transmissibility parameter using a simulation optimization approach. The proposed transmissibility is )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(used in epidemic simulation and forecast of peak time.)] TJ ET BT 26.250 700.452 Td /F5 9.8 Tf [(Simulation Initialization)] TJ ET BT 26.250 681.048 Td /F1 9.8 Tf [(The individual-based model simulates disease spread on a daily time scale, while GFT data is presented at a weekly resolution. )] TJ ET BT 26.250 669.143 Td /F1 9.8 Tf [(Assuming that infections at time )] TJ ET BT 166.601 669.143 Td /F6 9.8 Tf [(t)] TJ ET BT 169.312 669.143 Td /F1 9.8 Tf [( are a result of infections at previous time steps )] TJ ET BT 375.778 669.143 Td /F6 9.8 Tf [(1t-1)] TJ ET BT 402.327 669.143 Td /F1 9.8 Tf [(, we need to simulate approximately the )] TJ ET BT 26.250 657.238 Td /F1 9.8 Tf [(same number of ILIs during the first week as observed in week one of the GFT time series curve. However, we seed the )] TJ ET BT 26.250 645.333 Td /F1 9.8 Tf [(individual-based model with infected persons on day one. Taking into consideration that synthetic individuals in the network can )] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(have different infectious and incubation periods and infectiousness can last up to 6 days, we search for a possible initial seeding )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(scenario. We randomly infect different number of individuals on day one and compare the resulting weekly ILI to that observed )] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(in the GFT data. This process is evaluated using data from the 2004-2005 influenza season. We decide to seed the simulations )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(with an initially infected count of approximately one-fifth of the GFT counts observed in week one. This results in simulated ILI )] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(count on week one that is within 5% of that observed in the first week of the GFT data. In addition, to introduce prior immunity )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(into the network, we randomly vaccinate 20% of the synthetic population.)] TJ ET BT 26.250 554.500 Td /F4 9.8 Tf [(Parameter Search)] TJ ET BT 26.250 535.095 Td /F5 9.8 Tf [(Optimization Approach)] TJ ET BT 26.250 515.691 Td /F1 9.8 Tf [(Several algorithms can be used in the parameter search problem. Here we apply a classical stochastic root finding optimization )] TJ ET BT 26.250 503.786 Td /F1 9.8 Tf [(approach proposed by Robbins and Monro )] TJ ET 0.267 0.267 0.267 rg BT 213.762 505.293 Td /F4 8.7 Tf [(33)] TJ ET 0.271 0.267 0.267 rg BT 223.399 503.786 Td /F1 9.8 Tf [( with additional constraints. We illustrate that under certain assumptions the )] TJ ET BT 26.250 491.881 Td /F1 9.8 Tf [(proposed simulation optimization technique can be used in conjunction with the individual-based model to forecast the peak of )] TJ ET BT 26.250 479.976 Td /F1 9.8 Tf [(an ongoing epidemic by minimizing the difference between cumulative infections for the ongoing epidemic and simulated )] TJ ET BT 26.250 468.072 Td /F1 9.8 Tf [(instances for the same time period.)] TJ ET BT 26.250 448.667 Td /F1 9.8 Tf [(The algorithm can be explained as follows. Let ? represent the transmissibility where)] TJ ET BT 26.250 429.262 Td /F1 9.8 Tf [(M\(?\) = ?)] TJ ET BT 62.822 427.198 Td /F1 8.7 Tf [(t)] TJ ET BT 26.250 409.857 Td /F1 9.8 Tf [(Here, M\(?\) represents the current cumulative ILI counts as a function of the disease transmissibility ? and ?)] TJ ET BT 487.942 407.793 Td /F1 8.7 Tf [(t)] TJ ET BT 490.351 409.857 Td /F1 9.8 Tf [( is the total ILI )] TJ ET BT 26.250 397.953 Td /F1 9.8 Tf [(observed from week )] TJ ET BT 116.740 397.953 Td /F6 9.8 Tf [(1 . . . t)] TJ ET BT 143.845 397.953 Td /F1 9.8 Tf [(. Estimated values of ? are expected to vary initially, but converge towards a specific value as the )] TJ ET BT 26.250 386.048 Td /F1 9.8 Tf [(epidemic nears its peak. The definition of week )] TJ ET BT 231.634 386.048 Td /F6 9.8 Tf [(1 . . . t)] TJ ET BT 258.739 386.048 Td /F1 9.8 Tf [( is not fixed. Here, we define week one as the first week in October since )] TJ ET BT 26.250 374.143 Td /F1 9.8 Tf [(we construct the epidemic curve using data starting from that week. The algorithm also assumes that M is a monotonic function )] TJ ET BT 26.250 362.238 Td /F1 9.8 Tf [(of ?, which is reasonable since increasing the disease transmissibility also increases the total ILI for a given contact network )] TJ ET 0.267 0.267 0.267 rg BT 562.724 363.746 Td /F4 8.7 Tf [(30)] TJ ET 0.271 0.267 0.267 rg BT 572.362 362.238 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 342.834 Td /F1 9.8 Tf [(The iterative step of the Robbins-Monro algorithm is given by)] TJ ET q 117.000 0 0 15.000 26.250 317.953 cm /I22 Do Q BT 26.250 298.453 Td /F1 9.8 Tf [(where, )] TJ ET q 33.750 0 0 15.000 58.220 295.453 cm /I24 Do Q BT 91.970 298.453 Td /F1 9.8 Tf [( is the estimate of total ILI for the transmissibility rate x)] TJ ET BT 326.604 297.936 Td /F1 8.7 Tf [(n)] TJ ET BT 331.423 298.453 Td /F1 9.8 Tf [( and is obtained by simulation. {a)] TJ ET BT 473.958 297.936 Td /F1 8.7 Tf [(n)] TJ ET BT 478.777 298.453 Td /F1 9.8 Tf [(} is an appropriately )] TJ ET BT 26.250 285.929 Td /F1 9.8 Tf [(chosen sequence of positive real numbers that satisfy the following conditions.)] TJ ET q 57.000 0 0 13.500 26.250 262.548 cm /I26 Do Q BT 83.250 265.248 Td /F1 9.8 Tf [( and )] TJ ET q 53.250 0 0 13.500 104.934 262.548 cm /I28 Do Q BT 26.250 245.524 Td /F1 9.8 Tf [(The algorithm terminates when the iterations \(set at 5000\) are depleted or the percent error is less than the tolerance, which is )] TJ ET BT 26.250 233.619 Td /F1 9.8 Tf [(set at 0.05%. The percent error at time t is defined as:)] TJ ET q 114.750 0 0 15.000 26.250 208.738 cm /I30 Do Q BT 26.250 191.715 Td /F1 9.8 Tf [(Here, M\(?\) represents cumulative ILI counts for the ongoing epidemic and \(x)] TJ ET BT 355.176 189.650 Td /F1 8.7 Tf [(n)] TJ ET BT 359.995 191.715 Td /F1 9.8 Tf [(\) are the cumulative simulated ILI counts. We also )] TJ ET BT 26.250 179.810 Td /F1 9.8 Tf [(considered using the doubling time, Pearson and Spearman correlation coefficients, but these as well had limitations, and )] TJ ET BT 26.250 167.905 Td /F1 9.8 Tf [(appeared to be affected by slight deviations in the trend of the data.)] TJ ET BT 26.250 148.500 Td /F1 9.8 Tf [(As stated, the algorithm stops when the number of maximum iterations is reached or the percent error is less than the tolerance. )] TJ ET BT 26.250 136.596 Td /F1 9.8 Tf [(If the number of iterations is depleted before convergence, we randomly select a new initial value in the current path and restart )] TJ ET BT 26.250 124.691 Td /F1 9.8 Tf [(the optimization process. The transmissibility at convergence is used to initialize the forecasting process for the next week. )] TJ ET BT 26.250 112.786 Td /F1 9.8 Tf [(Since the analysis is retrospective, each forecast is assumed to be made at the end of each week. We start the forecasting )] TJ ET BT 26.250 100.881 Td /F1 9.8 Tf [(process on week 8 representing the last week of November. Starting the forecasting process in November seems reasonable )] TJ ET BT 26.250 88.977 Td /F1 9.8 Tf [(since the typical influenza season runs from November to April in the Northern Hemisphere )] TJ ET 0.267 0.267 0.267 rg BT 421.271 90.484 Td /F4 8.7 Tf [(34)] TJ ET 0.271 0.267 0.267 rg BT 430.909 88.977 Td /F1 9.8 Tf [(. Note that both the objective )] TJ ET BT 26.250 77.072 Td /F1 9.8 Tf [(function and optimization algorithm can be substituted.)] TJ ET Q q 15.000 30.039 577.500 746.961 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(Estimation of the transmissibility of an infectious disease is an important bio-surveillance issue especially for outbreaks such as )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(influenza, which have a mean serial interval shorter than that of most infectious diseases )] TJ ET 0.267 0.267 0.267 rg BT 411.005 757.079 Td /F4 8.7 Tf [(32)] TJ ET 0.271 0.267 0.267 rg BT 420.642 755.571 Td /F1 9.8 Tf [(. In addition to the serial interval, )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(other measures such as the basic and effective reproduction numbers are typically used in estimating disease transmissibility. )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(We estimate the model transmissibility parameter using a simulation optimization approach. The proposed transmissibility is )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(used in epidemic simulation and forecast of peak time.)] TJ ET BT 26.250 700.452 Td /F5 9.8 Tf [(Simulation Initialization)] TJ ET BT 26.250 681.048 Td /F1 9.8 Tf [(The individual-based model simulates disease spread on a daily time scale, while GFT data is presented at a weekly resolution. )] TJ ET BT 26.250 669.143 Td /F1 9.8 Tf [(Assuming that infections at time )] TJ ET BT 166.601 669.143 Td /F6 9.8 Tf [(t)] TJ ET BT 169.312 669.143 Td /F1 9.8 Tf [( are a result of infections at previous time steps )] TJ ET BT 375.778 669.143 Td /F6 9.8 Tf [(1t-1)] TJ ET BT 402.327 669.143 Td /F1 9.8 Tf [(, we need to simulate approximately the )] TJ ET BT 26.250 657.238 Td /F1 9.8 Tf [(same number of ILIs during the first week as observed in week one of the GFT time series curve. However, we seed the )] TJ ET BT 26.250 645.333 Td /F1 9.8 Tf [(individual-based model with infected persons on day one. Taking into consideration that synthetic individuals in the network can )] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(have different infectious and incubation periods and infectiousness can last up to 6 days, we search for a possible initial seeding )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(scenario. We randomly infect different number of individuals on day one and compare the resulting weekly ILI to that observed )] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(in the GFT data. This process is evaluated using data from the 2004-2005 influenza season. We decide to seed the simulations )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(with an initially infected count of approximately one-fifth of the GFT counts observed in week one. This results in simulated ILI )] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(count on week one that is within 5% of that observed in the first week of the GFT data. In addition, to introduce prior immunity )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(into the network, we randomly vaccinate 20% of the synthetic population.)] TJ ET BT 26.250 554.500 Td /F4 9.8 Tf [(Parameter Search)] TJ ET BT 26.250 535.095 Td /F5 9.8 Tf [(Optimization Approach)] TJ ET BT 26.250 515.691 Td /F1 9.8 Tf [(Several algorithms can be used in the parameter search problem. Here we apply a classical stochastic root finding optimization )] TJ ET BT 26.250 503.786 Td /F1 9.8 Tf [(approach proposed by Robbins and Monro )] TJ ET 0.267 0.267 0.267 rg BT 213.762 505.293 Td /F4 8.7 Tf [(33)] TJ ET 0.271 0.267 0.267 rg BT 223.399 503.786 Td /F1 9.8 Tf [( with additional constraints. We illustrate that under certain assumptions the )] TJ ET BT 26.250 491.881 Td /F1 9.8 Tf [(proposed simulation optimization technique can be used in conjunction with the individual-based model to forecast the peak of )] TJ ET BT 26.250 479.976 Td /F1 9.8 Tf [(an ongoing epidemic by minimizing the difference between cumulative infections for the ongoing epidemic and simulated )] TJ ET BT 26.250 468.072 Td /F1 9.8 Tf [(instances for the same time period.)] TJ ET BT 26.250 448.667 Td /F1 9.8 Tf [(The algorithm can be explained as follows. Let ? represent the transmissibility where)] TJ ET BT 26.250 429.262 Td /F1 9.8 Tf [(M\(?\) = ?)] TJ ET BT 62.822 427.198 Td /F1 8.7 Tf [(t)] TJ ET BT 26.250 409.857 Td /F1 9.8 Tf [(Here, M\(?\) represents the current cumulative ILI counts as a function of the disease transmissibility ? and ?)] TJ ET BT 487.942 407.793 Td /F1 8.7 Tf [(t)] TJ ET BT 490.351 409.857 Td /F1 9.8 Tf [( is the total ILI )] TJ ET BT 26.250 397.953 Td /F1 9.8 Tf [(observed from week )] TJ ET BT 116.740 397.953 Td /F6 9.8 Tf [(1 . . . t)] TJ ET BT 143.845 397.953 Td /F1 9.8 Tf [(. Estimated values of ? are expected to vary initially, but converge towards a specific value as the )] TJ ET BT 26.250 386.048 Td /F1 9.8 Tf [(epidemic nears its peak. The definition of week )] TJ ET BT 231.634 386.048 Td /F6 9.8 Tf [(1 . . . t)] TJ ET BT 258.739 386.048 Td /F1 9.8 Tf [( is not fixed. Here, we define week one as the first week in October since )] TJ ET BT 26.250 374.143 Td /F1 9.8 Tf [(we construct the epidemic curve using data starting from that week. The algorithm also assumes that M is a monotonic function )] TJ ET BT 26.250 362.238 Td /F1 9.8 Tf [(of ?, which is reasonable since increasing the disease transmissibility also increases the total ILI for a given contact network )] TJ ET 0.267 0.267 0.267 rg BT 562.724 363.746 Td /F4 8.7 Tf [(30)] TJ ET 0.271 0.267 0.267 rg BT 572.362 362.238 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 342.834 Td /F1 9.8 Tf [(The iterative step of the Robbins-Monro algorithm is given by)] TJ ET q 117.000 0 0 15.000 26.250 317.953 cm /I32 Do Q BT 26.250 298.453 Td /F1 9.8 Tf [(where, )] TJ ET q 33.750 0 0 15.000 58.220 295.453 cm /I34 Do Q BT 91.970 298.453 Td /F1 9.8 Tf [( is the estimate of total ILI for the transmissibility rate x)] TJ ET BT 326.604 297.936 Td /F1 8.7 Tf [(n)] TJ ET BT 331.423 298.453 Td /F1 9.8 Tf [( and is obtained by simulation. {a)] TJ ET BT 473.958 297.936 Td /F1 8.7 Tf [(n)] TJ ET BT 478.777 298.453 Td /F1 9.8 Tf [(} is an appropriately )] TJ ET BT 26.250 285.929 Td /F1 9.8 Tf [(chosen sequence of positive real numbers that satisfy the following conditions.)] TJ ET q 57.000 0 0 13.500 26.250 262.548 cm /I36 Do Q BT 83.250 265.248 Td /F1 9.8 Tf [( and )] TJ ET q 53.250 0 0 13.500 104.934 262.548 cm /I38 Do Q BT 26.250 245.524 Td /F1 9.8 Tf [(The algorithm terminates when the iterations \(set at 5000\) are depleted or the percent error is less than the tolerance, which is )] TJ ET BT 26.250 233.619 Td /F1 9.8 Tf [(set at 0.05%. The percent error at time t is defined as:)] TJ ET q 114.750 0 0 15.000 26.250 208.738 cm /I40 Do Q BT 26.250 191.715 Td /F1 9.8 Tf [(Here, M\(?\) represents cumulative ILI counts for the ongoing epidemic and \(x)] TJ ET BT 355.176 189.650 Td /F1 8.7 Tf [(n)] TJ ET BT 359.995 191.715 Td /F1 9.8 Tf [(\) are the cumulative simulated ILI counts. We also )] TJ ET BT 26.250 179.810 Td /F1 9.8 Tf [(considered using the doubling time, Pearson and Spearman correlation coefficients, but these as well had limitations, and )] TJ ET BT 26.250 167.905 Td /F1 9.8 Tf [(appeared to be affected by slight deviations in the trend of the data.)] TJ ET BT 26.250 148.500 Td /F1 9.8 Tf [(As stated, the algorithm stops when the number of maximum iterations is reached or the percent error is less than the tolerance. )] TJ ET BT 26.250 136.596 Td /F1 9.8 Tf [(If the number of iterations is depleted before convergence, we randomly select a new initial value in the current path and restart )] TJ ET BT 26.250 124.691 Td /F1 9.8 Tf [(the optimization process. The transmissibility at convergence is used to initialize the forecasting process for the next week. )] TJ ET BT 26.250 112.786 Td /F1 9.8 Tf [(Since the analysis is retrospective, each forecast is assumed to be made at the end of each week. We start the forecasting )] TJ ET BT 26.250 100.881 Td /F1 9.8 Tf [(process on week 8 representing the last week of November. Starting the forecasting process in November seems reasonable )] TJ ET BT 26.250 88.977 Td /F1 9.8 Tf [(since the typical influenza season runs from November to April in the Northern Hemisphere )] TJ ET 0.267 0.267 0.267 rg BT 421.271 90.484 Td /F4 8.7 Tf [(34)] TJ ET 0.271 0.267 0.267 rg BT 430.909 88.977 Td /F1 9.8 Tf [(. Note that both the objective )] TJ ET BT 26.250 77.072 Td /F1 9.8 Tf [(function and optimization algorithm can be substituted.)] TJ ET Q q 15.000 30.039 577.500 746.961 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(Estimation of the transmissibility of an infectious disease is an important bio-surveillance issue especially for outbreaks such as )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(influenza, which have a mean serial interval shorter than that of most infectious diseases )] TJ ET 0.267 0.267 0.267 rg BT 411.005 757.079 Td /F4 8.7 Tf [(32)] TJ ET 0.271 0.267 0.267 rg BT 420.642 755.571 Td /F1 9.8 Tf [(. In addition to the serial interval, )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(other measures such as the basic and effective reproduction numbers are typically used in estimating disease transmissibility. )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(We estimate the model transmissibility parameter using a simulation optimization approach. The proposed transmissibility is )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(used in epidemic simulation and forecast of peak time.)] TJ ET BT 26.250 700.452 Td /F5 9.8 Tf [(Simulation Initialization)] TJ ET BT 26.250 681.048 Td /F1 9.8 Tf [(The individual-based model simulates disease spread on a daily time scale, while GFT data is presented at a weekly resolution. )] TJ ET BT 26.250 669.143 Td /F1 9.8 Tf [(Assuming that infections at time )] TJ ET BT 166.601 669.143 Td /F6 9.8 Tf [(t)] TJ ET BT 169.312 669.143 Td /F1 9.8 Tf [( are a result of infections at previous time steps )] TJ ET BT 375.778 669.143 Td /F6 9.8 Tf [(1t-1)] TJ ET BT 402.327 669.143 Td /F1 9.8 Tf [(, we need to simulate approximately the )] TJ ET BT 26.250 657.238 Td /F1 9.8 Tf [(same number of ILIs during the first week as observed in week one of the GFT time series curve. However, we seed the )] TJ ET BT 26.250 645.333 Td /F1 9.8 Tf [(individual-based model with infected persons on day one. Taking into consideration that synthetic individuals in the network can )] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(have different infectious and incubation periods and infectiousness can last up to 6 days, we search for a possible initial seeding )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(scenario. We randomly infect different number of individuals on day one and compare the resulting weekly ILI to that observed )] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(in the GFT data. This process is evaluated using data from the 2004-2005 influenza season. We decide to seed the simulations )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(with an initially infected count of approximately one-fifth of the GFT counts observed in week one. This results in simulated ILI )] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(count on week one that is within 5% of that observed in the first week of the GFT data. In addition, to introduce prior immunity )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(into the network, we randomly vaccinate 20% of the synthetic population.)] TJ ET BT 26.250 554.500 Td /F4 9.8 Tf [(Parameter Search)] TJ ET BT 26.250 535.095 Td /F5 9.8 Tf [(Optimization Approach)] TJ ET BT 26.250 515.691 Td /F1 9.8 Tf [(Several algorithms can be used in the parameter search problem. Here we apply a classical stochastic root finding optimization )] TJ ET BT 26.250 503.786 Td /F1 9.8 Tf [(approach proposed by Robbins and Monro )] TJ ET 0.267 0.267 0.267 rg BT 213.762 505.293 Td /F4 8.7 Tf [(33)] TJ ET 0.271 0.267 0.267 rg BT 223.399 503.786 Td /F1 9.8 Tf [( with additional constraints. We illustrate that under certain assumptions the )] TJ ET BT 26.250 491.881 Td /F1 9.8 Tf [(proposed simulation optimization technique can be used in conjunction with the individual-based model to forecast the peak of )] TJ ET BT 26.250 479.976 Td /F1 9.8 Tf [(an ongoing epidemic by minimizing the difference between cumulative infections for the ongoing epidemic and simulated )] TJ ET BT 26.250 468.072 Td /F1 9.8 Tf [(instances for the same time period.)] TJ ET BT 26.250 448.667 Td /F1 9.8 Tf [(The algorithm can be explained as follows. Let ? represent the transmissibility where)] TJ ET BT 26.250 429.262 Td /F1 9.8 Tf [(M\(?\) = ?)] TJ ET BT 62.822 427.198 Td /F1 8.7 Tf [(t)] TJ ET BT 26.250 409.857 Td /F1 9.8 Tf [(Here, M\(?\) represents the current cumulative ILI counts as a function of the disease transmissibility ? and ?)] TJ ET BT 487.942 407.793 Td /F1 8.7 Tf [(t)] TJ ET BT 490.351 409.857 Td /F1 9.8 Tf [( is the total ILI )] TJ ET BT 26.250 397.953 Td /F1 9.8 Tf [(observed from week )] TJ ET BT 116.740 397.953 Td /F6 9.8 Tf [(1 . . . t)] TJ ET BT 143.845 397.953 Td /F1 9.8 Tf [(. Estimated values of ? are expected to vary initially, but converge towards a specific value as the )] TJ ET BT 26.250 386.048 Td /F1 9.8 Tf [(epidemic nears its peak. The definition of week )] TJ ET BT 231.634 386.048 Td /F6 9.8 Tf [(1 . . . t)] TJ ET BT 258.739 386.048 Td /F1 9.8 Tf [( is not fixed. Here, we define week one as the first week in October since )] TJ ET BT 26.250 374.143 Td /F1 9.8 Tf [(we construct the epidemic curve using data starting from that week. The algorithm also assumes that M is a monotonic function )] TJ ET BT 26.250 362.238 Td /F1 9.8 Tf [(of ?, which is reasonable since increasing the disease transmissibility also increases the total ILI for a given contact network )] TJ ET 0.267 0.267 0.267 rg BT 562.724 363.746 Td /F4 8.7 Tf [(30)] TJ ET 0.271 0.267 0.267 rg BT 572.362 362.238 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 342.834 Td /F1 9.8 Tf [(The iterative step of the Robbins-Monro algorithm is given by)] TJ ET q 117.000 0 0 15.000 26.250 317.953 cm /I42 Do Q BT 26.250 298.453 Td /F1 9.8 Tf [(where, )] TJ ET q 33.750 0 0 15.000 58.220 295.453 cm /I44 Do Q BT 91.970 298.453 Td /F1 9.8 Tf [( is the estimate of total ILI for the transmissibility rate x)] TJ ET BT 326.604 297.936 Td /F1 8.7 Tf [(n)] TJ ET BT 331.423 298.453 Td /F1 9.8 Tf [( and is obtained by simulation. {a)] TJ ET BT 473.958 297.936 Td /F1 8.7 Tf [(n)] TJ ET BT 478.777 298.453 Td /F1 9.8 Tf [(} is an appropriately )] TJ ET BT 26.250 285.929 Td /F1 9.8 Tf [(chosen sequence of positive real numbers that satisfy the following conditions.)] TJ ET q 57.000 0 0 13.500 26.250 262.548 cm /I46 Do Q BT 83.250 265.248 Td /F1 9.8 Tf [( and )] TJ ET q 53.250 0 0 13.500 104.934 262.548 cm /I48 Do Q BT 26.250 245.524 Td /F1 9.8 Tf [(The algorithm terminates when the iterations \(set at 5000\) are depleted or the percent error is less than the tolerance, which is )] TJ ET BT 26.250 233.619 Td /F1 9.8 Tf [(set at 0.05%. The percent error at time t is defined as:)] TJ ET q 114.750 0 0 15.000 26.250 208.738 cm /I50 Do Q BT 26.250 191.715 Td /F1 9.8 Tf [(Here, M\(?\) represents cumulative ILI counts for the ongoing epidemic and \(x)] TJ ET BT 355.176 189.650 Td /F1 8.7 Tf [(n)] TJ ET BT 359.995 191.715 Td /F1 9.8 Tf [(\) are the cumulative simulated ILI counts. We also )] TJ ET BT 26.250 179.810 Td /F1 9.8 Tf [(considered using the doubling time, Pearson and Spearman correlation coefficients, but these as well had limitations, and )] TJ ET BT 26.250 167.905 Td /F1 9.8 Tf [(appeared to be affected by slight deviations in the trend of the data.)] TJ ET BT 26.250 148.500 Td /F1 9.8 Tf [(As stated, the algorithm stops when the number of maximum iterations is reached or the percent error is less than the tolerance. )] TJ ET BT 26.250 136.596 Td /F1 9.8 Tf [(If the number of iterations is depleted before convergence, we randomly select a new initial value in the current path and restart )] TJ ET BT 26.250 124.691 Td /F1 9.8 Tf [(the optimization process. The transmissibility at convergence is used to initialize the forecasting process for the next week. )] TJ ET BT 26.250 112.786 Td /F1 9.8 Tf [(Since the analysis is retrospective, each forecast is assumed to be made at the end of each week. We start the forecasting )] TJ ET BT 26.250 100.881 Td /F1 9.8 Tf [(process on week 8 representing the last week of November. Starting the forecasting process in November seems reasonable )] TJ ET BT 26.250 88.977 Td /F1 9.8 Tf [(since the typical influenza season runs from November to April in the Northern Hemisphere )] TJ ET 0.267 0.267 0.267 rg BT 421.271 90.484 Td /F4 8.7 Tf [(34)] TJ ET 0.271 0.267 0.267 rg BT 430.909 88.977 Td /F1 9.8 Tf [(. Note that both the objective )] TJ ET BT 26.250 77.072 Td /F1 9.8 Tf [(function and optimization algorithm can be substituted.)] TJ ET Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(4)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Outbreaks)] TJ ET Q endstream endobj 370 0 obj << /Type /Annot /Subtype /Link /A 371 0 R /Border [0 0 0] /H /I /Rect [ 411.0045 756.2769 420.6418 765.0952 ] >> endobj 371 0 obj << /Type /Action >> endobj 372 0 obj << /Type /Annot /Subtype /Link /A 373 0 R /Border [0 0 0] /H /I /Rect [ 213.7620 504.4914 223.3993 513.3097 ] >> endobj 373 0 obj << /Type /Action >> endobj 374 0 obj << /Type /Annot /Subtype /Link /A 375 0 R /Border [0 0 0] /H /I /Rect [ 562.7242 362.9439 572.3616 371.7622 ] >> endobj 375 0 obj << /Type /Action >> endobj 376 0 obj << /Type /XObject /Subtype /Image /Width 156 /Height 20 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 156 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 905>> stream HVgPSSU115U3g*NM9S5gffjΙ95SS35U3̙f&ly>% ~E"sZofus>=ʾ3;o8v3ʻY蝶x19e!S*4#A3Ry(=k0~^8Ԍm<@jo#aU:tꕎyŽTv_ovV`#O,Jb]chFXМjXުs"k *uEkR]m 1U'RY2@l(.g8;c;YQ`R#s,xb!m>F+E'q-`FFЃ]/oP]\wyTZ!=\ ITrtErc)N;n f:|Q!ϫ@>Ng;55L6,$d^j_;o@NJgE1yEnt '˰QDn[|n@վIAUV &cG `by6sS:uD)$;(Rtxx"~p˃9n Ar j(1 /9,*>n=rf%ϖ# ֫aT 5S M__ZJr$PnC+G}Xr=%M+`j*\1TnB;4o`K!NVP0^qTUμ3fX.lө=r\']:M6^y tRA\t37mߺ \,i'yyl⎮/\6l endstream endobj 377 0 obj << /Type /XObject /Subtype /Image /Width 156 /Height 20 /SMask 376 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 156 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 32>> stream h1 Om ?~$ endstream endobj 378 0 obj << /Type /XObject /Subtype /Image /Width 45 /Height 20 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 45 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 408>> stream (kP!,""J "!R%B(sN"HM%8HDO˗AHbmKTc@'$Gڇ}Ʃ0x3bq{Z3BV"]$*;D!lCZv`c/\kL9?E dAYR]d]zdY.Zz]Mzv=0ePEUNUՔ> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 26>> stream H1 Om   endstream endobj 380 0 obj << /Type /XObject /Subtype /Image /Width 76 /Height 18 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 76 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 486>> stream 8gpǿgjbCTꊪ="5jsTUEPS/ImC99;'׭'mVuu[f4OM R?)b牃Pq fQ 2 Y5%ԄlU'Z: ߏE*-/pZ|vF'_o8waU1EX )@NH'F(v MEdUybwX~ѨL8}df4O3AƏ_sMkDs#]-wd6/})~o; 0EOsa#Zm:H\*e( ?W=\Wu晠Ҿ endstream endobj 381 0 obj << /Type /XObject /Subtype /Image /Width 76 /Height 18 /SMask 380 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 76 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 26>> stream X nH@ endstream endobj 382 0 obj << /Type /XObject /Subtype /Image /Width 71 /Height 18 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 71 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 557>> stream 8T"a~d$#JIru?$k8+I$++#g$ke%#9+'g:'#+c9ku}M3y{ [_Y;Q/;wlJ:2ԏW/aF'}% 9؈|#YQfEXl~wF2>X*C3LC {ZFt&mi ]1/W v^&>itvy{ eS}bNLnߦDF^uᜓ 6RUܟ< M:j|#"`/ +tS_,o#YBh_ch_0{+B_\FY!@ Dm:9/fՉ<ͻB޶@o58PDA? 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8ccS(GPmSL\}!^2җ5NnpV-|%,d)tpB[8gao9U endstream endobj 419 0 obj << /Type /XObject /Subtype /Image /Width 71 /Height 18 /SMask 418 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 71 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 26>> stream H nH@  endstream endobj 420 0 obj << /Type /XObject /Subtype /Image /Width 153 /Height 20 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 153 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 1057>> stream HVQ#Y>qJZDD=5-V-D1JREDXkkֈyhZ<C'9ޤR陇{DSuwwsuW>?uUo<ͼV~hָu㇇r<;r򽞵ťwVnEF,%grm$FEK'j)ۖAsTDN䈘m >]tw .kvZ˦f.YC^ۏHn)64Kz2b/oc^}pwP +#+I`mLT[Bws Rx- $5 W%T 1NIo}< }҅Vy!Xo9X+yVHAGsHhKbCpvu 뵲5V@Wn>PP" }1QT=ժ%[6Hhs8u&$,< Bx( cozrz>6mPID}ڢ ]=%4`Qj 16hVwe kGsjK[:?VPm&14L'̦q9 BhtɚVSI@} Dρ 6ð 6m~! lbq˔ 1:dAָkAfkkFC6Ϧ*$gi>9u#3Tg7?FTZxeZaƌZΑ9z{ȵ9-Sk#A*U^ o"C^.=Jf|n!fɷ5 3FnYGK"&de/>PĂ㭫1.ӽ'11C? >U[ōWl}hA&Xwby^[z|`w`ۘ@}؋}b7D~ endstream endobj 421 0 obj << /Type /XObject /Subtype /Image /Width 153 /Height 20 /SMask 420 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 153 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 32>> stream h  Om7# endstream endobj 422 0 obj << /Type /Annot /Subtype /Link /A 423 0 R /Border [0 0 0] /H /I /Rect [ 421.2713 89.6822 430.9086 98.5005 ] >> endobj 423 0 obj << /Type /Action >> endobj 424 0 obj << /Type /Page /Parent 3 0 R /Annots [ 426 0 R 429 0 R 432 0 R 434 0 R 436 0 R 438 0 R ] /Contents 425 0 R >> endobj 425 0 obj << /Length 13264 >> stream 0.271 0.267 0.267 rg q 15.000 24.985 577.500 752.015 re W n 0.271 0.267 0.267 rg BT 26.250 750.278 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 730.324 Td /F1 9.8 Tf [(We present results for the 2007-2008 and 2012-2013 influenza seasons. Forecasts are made from the last week of November )] TJ ET BT 26.250 718.419 Td /F1 9.8 Tf [(starting on 11/25/07 and 11/25/12 respectively. As stated, the first week of October is designated as week one. We also )] TJ ET BT 26.250 706.515 Td /F1 9.8 Tf [(considered starting the forecasting process as early as October based on data observed from August to October. However, the )] TJ ET BT 26.250 694.610 Td /F1 9.8 Tf [(forecast accuracy did not improve and in some cases degraded, which is probably due to the noise introduced by off-season )] TJ ET BT 26.250 682.705 Td /F1 9.8 Tf [(influenza cases.)] TJ ET BT 26.250 663.300 Td /F5 9.8 Tf [(2007-2008 influenza season)] TJ ET BT 26.250 643.896 Td /F1 9.8 Tf [(We present weekly forecasts several weeks before and after the peak starting from the end of November for the 2007-2008 )] TJ ET BT 26.250 631.991 Td /F1 9.8 Tf [(influenza season in Figure 1. The epidemic peak is observed during the week starting on 02/17/2008, which is week 20 of the )] TJ ET BT 26.250 620.086 Td /F1 9.8 Tf [(time series GFT curve. Initially, the forecasting process produces a higher transmissibility since weekly ILI counts are much )] TJ ET BT 26.250 608.181 Td /F1 9.8 Tf [(higher than that produced by the individual-based model. Nevertheless, as the epidemic nears the peak, forecasts of the peak )] TJ ET BT 26.250 596.277 Td /F1 9.8 Tf [(improves. Peak forecasts become stable between weeks 14 and 15, which is five to six weeks before the actual peak. 95% )] TJ ET BT 26.250 584.372 Td /F1 9.8 Tf [(sample confidence intervals \(CI\) and standard deviations around the mean are presented in Figure 2. The 95% confidence )] TJ ET BT 26.250 572.467 Td /F1 9.8 Tf [(bounds are close to the mean suggesting low variance in the forecasting procedure. On week fifteen \(mid January\), the mean )] TJ ET BT 26.250 560.562 Td /F1 9.8 Tf [(and median peak forecasts both fall on the actual peak week. The 95% CI forecasts the epidemic peak between early to mid )] TJ ET BT 26.250 548.658 Td /F1 9.8 Tf [(February, which agrees with the true peak week of 02/17/2008. The true peak is also captured within peak ranges observed on )] TJ ET BT 26.250 536.753 Td /F1 9.8 Tf [(weeks 13 and 14 \(per Figure 1\).)] TJ ET 0.965 0.965 0.965 rg 26.250 273.745 555.000 253.127 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 526.872 m 581.250 526.872 l 581.250 526.122 l 26.250 526.122 l f 26.250 273.745 m 581.250 273.745 l 581.250 274.495 l 26.250 274.495 l f q 225.000 0 0 173.250 35.250 343.872 cm /I51 Do Q q 35.250 284.995 537.000 52.877 re W n 0.271 0.267 0.267 rg BT 35.250 328.348 Td /F4 9.8 Tf [(Fig. 1: Peak forecast for the 2007-2008 influenza season using GFT for Seattle, WA.)] TJ ET BT 35.250 308.978 Td /F1 9.8 Tf [(Actual peak is observed on week 20. The black curve is the GFT data, the red line is the mean predicted curve and the grey )] TJ ET BT 35.250 295.242 Td /F1 9.8 Tf [(curves show fifty replicates of the stochastic process.)] TJ ET Q 0.965 0.965 0.965 rg 26.250 87.604 555.000 178.641 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 266.245 m 581.250 266.245 l 581.250 265.495 l 26.250 265.495 l f 26.250 87.604 m 581.250 87.604 l 581.250 88.354 l 26.250 88.354 l f q 112.500 0 0 112.500 35.250 143.995 cm /I52 Do Q q 35.250 98.854 537.000 39.141 re W n 0.271 0.267 0.267 rg BT 35.250 128.471 Td /F4 9.8 Tf [(Fig. 2: Predicted peak by week of forecast for Seattle, WA.)] TJ ET BT 35.250 109.101 Td /F1 9.8 Tf [(\(A\) 95% CI around the mean and \(B\) standard deviations around the mean. The true peak is observed on week 20.)] TJ ET Q BT 26.250 70.580 Td /F5 9.8 Tf [(2012-2013 influenza season)] TJ ET BT 26.250 51.175 Td /F1 9.8 Tf [(The 2012-2013 influenza season was more severe than the last five previous seasonal influenza epidemics. The GFT peak was )] TJ ET BT 26.250 39.270 Td /F1 9.8 Tf [(observed during the week starting on 01/13/2013, which is the 15)] TJ ET BT 307.528 43.159 Td /F1 8.7 Tf [(th)] TJ ET BT 314.756 39.270 Td /F1 9.8 Tf [(week for the GFT time series curve used in forecasting. )] TJ ET Q q 15.000 24.985 577.500 752.015 re W n 0.271 0.267 0.267 rg BT 26.250 750.278 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 730.324 Td /F1 9.8 Tf [(We present results for the 2007-2008 and 2012-2013 influenza seasons. Forecasts are made from the last week of November )] TJ ET BT 26.250 718.419 Td /F1 9.8 Tf [(starting on 11/25/07 and 11/25/12 respectively. As stated, the first week of October is designated as week one. We also )] TJ ET BT 26.250 706.515 Td /F1 9.8 Tf [(considered starting the forecasting process as early as October based on data observed from August to October. However, the )] TJ ET BT 26.250 694.610 Td /F1 9.8 Tf [(forecast accuracy did not improve and in some cases degraded, which is probably due to the noise introduced by off-season )] TJ ET BT 26.250 682.705 Td /F1 9.8 Tf [(influenza cases.)] TJ ET BT 26.250 663.300 Td /F5 9.8 Tf [(2007-2008 influenza season)] TJ ET BT 26.250 643.896 Td /F1 9.8 Tf [(We present weekly forecasts several weeks before and after the peak starting from the end of November for the 2007-2008 )] TJ ET BT 26.250 631.991 Td /F1 9.8 Tf [(influenza season in Figure 1. The epidemic peak is observed during the week starting on 02/17/2008, which is week 20 of the )] TJ ET BT 26.250 620.086 Td /F1 9.8 Tf [(time series GFT curve. Initially, the forecasting process produces a higher transmissibility since weekly ILI counts are much )] TJ ET BT 26.250 608.181 Td /F1 9.8 Tf [(higher than that produced by the individual-based model. Nevertheless, as the epidemic nears the peak, forecasts of the peak )] TJ ET BT 26.250 596.277 Td /F1 9.8 Tf [(improves. Peak forecasts become stable between weeks 14 and 15, which is five to six weeks before the actual peak. 95% )] TJ ET BT 26.250 584.372 Td /F1 9.8 Tf [(sample confidence intervals \(CI\) and standard deviations around the mean are presented in Figure 2. The 95% confidence )] TJ ET BT 26.250 572.467 Td /F1 9.8 Tf [(bounds are close to the mean suggesting low variance in the forecasting procedure. On week fifteen \(mid January\), the mean )] TJ ET BT 26.250 560.562 Td /F1 9.8 Tf [(and median peak forecasts both fall on the actual peak week. The 95% CI forecasts the epidemic peak between early to mid )] TJ ET BT 26.250 548.658 Td /F1 9.8 Tf [(February, which agrees with the true peak week of 02/17/2008. The true peak is also captured within peak ranges observed on )] TJ ET BT 26.250 536.753 Td /F1 9.8 Tf [(weeks 13 and 14 \(per Figure 1\).)] TJ ET 0.965 0.965 0.965 rg 26.250 273.745 555.000 253.127 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 526.872 m 581.250 526.872 l 581.250 526.122 l 26.250 526.122 l f 26.250 273.745 m 581.250 273.745 l 581.250 274.495 l 26.250 274.495 l f q 225.000 0 0 173.250 35.250 343.872 cm /I51 Do Q q 35.250 284.995 537.000 52.877 re W n 0.271 0.267 0.267 rg BT 35.250 328.348 Td /F4 9.8 Tf [(Fig. 1: Peak forecast for the 2007-2008 influenza season using GFT for Seattle, WA.)] TJ ET BT 35.250 308.978 Td /F1 9.8 Tf [(Actual peak is observed on week 20. The black curve is the GFT data, the red line is the mean predicted curve and the grey )] TJ ET BT 35.250 295.242 Td /F1 9.8 Tf [(curves show fifty replicates of the stochastic process.)] TJ ET Q 0.965 0.965 0.965 rg 26.250 87.604 555.000 178.641 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 266.245 m 581.250 266.245 l 581.250 265.495 l 26.250 265.495 l f 26.250 87.604 m 581.250 87.604 l 581.250 88.354 l 26.250 88.354 l f q 112.500 0 0 112.500 35.250 143.995 cm /I52 Do Q q 35.250 98.854 537.000 39.141 re W n 0.271 0.267 0.267 rg BT 35.250 128.471 Td /F4 9.8 Tf [(Fig. 2: Predicted peak by week of forecast for Seattle, WA.)] TJ ET BT 35.250 109.101 Td /F1 9.8 Tf [(\(A\) 95% CI around the mean and \(B\) standard deviations around the mean. The true peak is observed on week 20.)] TJ ET Q BT 26.250 70.580 Td /F5 9.8 Tf [(2012-2013 influenza season)] TJ ET BT 26.250 51.175 Td /F1 9.8 Tf [(The 2012-2013 influenza season was more severe than the last five previous seasonal influenza epidemics. The GFT peak was )] TJ ET BT 26.250 39.270 Td /F1 9.8 Tf [(observed during the week starting on 01/13/2013, which is the 15)] TJ ET BT 307.528 43.159 Td /F1 8.7 Tf [(th)] TJ ET BT 314.756 39.270 Td /F1 9.8 Tf [(week for the GFT time series curve used in forecasting. )] TJ ET Q q 15.000 24.985 577.500 752.015 re W n 0.271 0.267 0.267 rg BT 26.250 750.278 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 730.324 Td /F1 9.8 Tf [(We present results for the 2007-2008 and 2012-2013 influenza seasons. Forecasts are made from the last week of November )] TJ ET BT 26.250 718.419 Td /F1 9.8 Tf [(starting on 11/25/07 and 11/25/12 respectively. As stated, the first week of October is designated as week one. We also )] TJ ET BT 26.250 706.515 Td /F1 9.8 Tf [(considered starting the forecasting process as early as October based on data observed from August to October. However, the )] TJ ET BT 26.250 694.610 Td /F1 9.8 Tf [(forecast accuracy did not improve and in some cases degraded, which is probably due to the noise introduced by off-season )] TJ ET BT 26.250 682.705 Td /F1 9.8 Tf [(influenza cases.)] TJ ET BT 26.250 663.300 Td /F5 9.8 Tf [(2007-2008 influenza season)] TJ ET BT 26.250 643.896 Td /F1 9.8 Tf [(We present weekly forecasts several weeks before and after the peak starting from the end of November for the 2007-2008 )] TJ ET BT 26.250 631.991 Td /F1 9.8 Tf [(influenza season in Figure 1. The epidemic peak is observed during the week starting on 02/17/2008, which is week 20 of the )] TJ ET BT 26.250 620.086 Td /F1 9.8 Tf [(time series GFT curve. Initially, the forecasting process produces a higher transmissibility since weekly ILI counts are much )] TJ ET BT 26.250 608.181 Td /F1 9.8 Tf [(higher than that produced by the individual-based model. Nevertheless, as the epidemic nears the peak, forecasts of the peak )] TJ ET BT 26.250 596.277 Td /F1 9.8 Tf [(improves. Peak forecasts become stable between weeks 14 and 15, which is five to six weeks before the actual peak. 95% )] TJ ET BT 26.250 584.372 Td /F1 9.8 Tf [(sample confidence intervals \(CI\) and standard deviations around the mean are presented in Figure 2. The 95% confidence )] TJ ET BT 26.250 572.467 Td /F1 9.8 Tf [(bounds are close to the mean suggesting low variance in the forecasting procedure. On week fifteen \(mid January\), the mean )] TJ ET BT 26.250 560.562 Td /F1 9.8 Tf [(and median peak forecasts both fall on the actual peak week. The 95% CI forecasts the epidemic peak between early to mid )] TJ ET BT 26.250 548.658 Td /F1 9.8 Tf [(February, which agrees with the true peak week of 02/17/2008. The true peak is also captured within peak ranges observed on )] TJ ET BT 26.250 536.753 Td /F1 9.8 Tf [(weeks 13 and 14 \(per Figure 1\).)] TJ ET 0.965 0.965 0.965 rg 26.250 273.745 555.000 253.127 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 526.872 m 581.250 526.872 l 581.250 526.122 l 26.250 526.122 l f 26.250 273.745 m 581.250 273.745 l 581.250 274.495 l 26.250 274.495 l f q 225.000 0 0 173.250 35.250 343.872 cm /I51 Do Q q 35.250 284.995 537.000 52.877 re W n 0.271 0.267 0.267 rg BT 35.250 328.348 Td /F4 9.8 Tf [(Fig. 1: Peak forecast for the 2007-2008 influenza season using GFT for Seattle, WA.)] TJ ET BT 35.250 308.978 Td /F1 9.8 Tf [(Actual peak is observed on week 20. The black curve is the GFT data, the red line is the mean predicted curve and the grey )] TJ ET BT 35.250 295.242 Td /F1 9.8 Tf [(curves show fifty replicates of the stochastic process.)] TJ ET Q 0.965 0.965 0.965 rg 26.250 87.604 555.000 178.641 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 266.245 m 581.250 266.245 l 581.250 265.495 l 26.250 265.495 l f 26.250 87.604 m 581.250 87.604 l 581.250 88.354 l 26.250 88.354 l f q 112.500 0 0 112.500 35.250 143.995 cm /I52 Do Q q 35.250 98.854 537.000 39.141 re W n 0.271 0.267 0.267 rg BT 35.250 128.471 Td /F4 9.8 Tf [(Fig. 2: Predicted peak by week of forecast for Seattle, WA.)] TJ ET BT 35.250 109.101 Td /F1 9.8 Tf [(\(A\) 95% CI around the mean and \(B\) standard deviations around the mean. The true peak is observed on week 20.)] TJ ET Q BT 26.250 70.580 Td /F5 9.8 Tf [(2012-2013 influenza season)] TJ ET BT 26.250 51.175 Td /F1 9.8 Tf [(The 2012-2013 influenza season was more severe than the last five previous seasonal influenza epidemics. The GFT peak was )] TJ ET BT 26.250 39.270 Td /F1 9.8 Tf [(observed during the week starting on 01/13/2013, which is the 15)] TJ ET BT 307.528 43.159 Td /F1 8.7 Tf [(th)] TJ ET BT 314.756 39.270 Td /F1 9.8 Tf [(week for the GFT time series curve used in forecasting. )] TJ ET Q q 225.000 0 0 173.250 35.250 343.872 cm /I51 Do Q q 112.500 0 0 112.500 35.250 143.995 cm /I52 Do Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(5)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Outbreaks)] TJ ET Q endstream endobj 426 0 obj << /Type /Annot /Subtype /Link /A 427 0 R /Border [0 0 0] /H /I /Rect [ 35.2500 343.8720 260.2500 517.1220 ] >> endobj 427 0 obj << /Type /Action /S /URI /URI (http://currents.plos.org/outbreaks/files/2013/06/Peakprogress0708third-copy.jpg) >> endobj 428 0 obj << /Type /XObject /Subtype /Image /Width 300 /Height 231 /ColorSpace /DeviceRGB /Filter /DCTDecode /BitsPerComponent 8 /Length 27314>> stream JFIF;CREATOR: gd-jpeg v1.0 (using IJG JPEG v62), quality = 90 C     C   ," }!1AQa"q2#BR$3br %&'()*456789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz w!1AQaq"2B #3Rbr $4%&'()*56789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz ?Q#ގ=Mz2=ZҖ5xĉyUyC>䁒e#޼ÿeD{O xe,hŜnj ˑ^ǭd{ǩS@Gqk:OE~ռLo.yFY0Q}@XPsFGx?j}ZXXK#44nHnf,#e7^Ӽty,t-mdPGqhFGzO|'OWO^7"/-`rho#ތz4b/ HgUSop#5gmTkX̟S"`6CsFGz84d{ёGƀ z2=#x٭XD 0mu\)Ijz2=g?:nyy;hb;nXy=Md{ǩS@GCi6% iorX"6/K x ]vKQ;d t2wpW#8#ތzoxES@=T|_͂p9 ݾk-[ĥf$dRENZk]>x* B ּP>كS A.o]&!!v]VV&ʅ`!o9e@zx4m2[h&ڭD|<;ָ/~~ntmkM,/nmt-m= 5[{yFOFG9-9;'oow]xqo")AJN5ԹcH5gkB׿6{9V)"1rwְ4M>axꌍQ?:xVO ͩ$M D l9$(8̯lNUҭK+۫[{{RxbY$d5V>0񆣠jZgdB~y.c<odY`tX[whc,9bE>c+ce0~ZDwa&trO|-[ZJ.Tkmz>.YG:MST&x#UYӃq###\˩iwZ`/h#wdV<6əFwXY7%=5=TIzOă'>!7;#b}k?h/juIM=:#_*F7+sPq$`I,-A 4W=AV^◵'mCS xd{fQVFT~T$&1Ӛ$<_Dw(7r[S.qݽr|B~1q,r/fyq*[ǃ^WIULnHV}mrO#T$Wÿn 6X;MCI1"ꑖ,}jcv5Zo"E17$rU0 Fpy#ޮ>ȇ᾿ KZڔm]K2#@Țic8K3(I=d>(Уխ-ϒ7LKs Wx;ź?g^zZo Yُ$,Icuݟ Gg@dmZ7ςA,~S[<)<؝B_-GNXhoH7BLHc8+QSW_]"5Ed-IXKr}srK#e>{EB.7/Ŀڭ6y]Z %لIER9uvW3`?2 UXK #-ʦTSвkj}ԐiOi浏ݷgnq97q(2sj?O#e\*vc9ݴTn  pD2'ޫ=I$bq%lvB4*zqW9㞙k@Y𾉫6\=Me%@ ) 8r8 gs&V ARY^RH$:d־pX\ Guy04V`]6ץSiiy=*4HHYcsp tخg_ _t*Yi1G%彔r8U3 Oa\'_j^ Jzi8(#i HW!ݍl(%׃nxJL^򸄱p҆c|`]Q=UvU;Bg?ehT"ɒDLRM<?[!RA;Ks,=iDU6,Cd\{~!Ri841kcjqR]Y$z еx8][~XZGFHzZ=a[j~ mIUfMa؉ 7tz>xG.mm!wErvI z"F`}@ 1ږqpf5(PAܫ;xO!KI1d$0 yT=aSs% E54)]}<_z^|'5.^6V1@y>׊NfHmtMoCP+-.O|k7s~Zŭbӿm~j׶mbYtd` Y^&^axrfi)Ңqoy4h9[q׍r]~%kX#kk ;tI8wU 㓍6+CSv2 DQ,Te8M'_kgœMQt/ݔgA%b9#-:qIL]LlSow5Qi4eZ2IF{o5&1=sm2`l7 Gך|[kvQ[Kqo}tSiWyawSF&Ǎ%uikWKgnp^40 fE 57ĥiz{(:]8ֹ ?߁-*]PK΂Hʂ31FwX|Bͫ@Nc%ג ltlڀJg⋘? >xWՍֱgCy|cV~G8HV5oVvèq6;(_Zz%?#?ÍK(ob_<}\Z4x<Ź#zoO_v3en͌$uU?c^i[s{oaITk^ˮw~GXIyNkk,w:oDdְn[ET+Ɏ?cc/N!~;mWO؞V ~BI=8+xmoW7}ûmUKI,DE3Un ݵ#b6Lei_u XIXg$m|x0rw~ \>2vD3IKL9|J :NOT|cQW<xa[.EG@dcc=;כͺlko3˩#E>!Xq ' Î|w={o&.ߛk~O> N/|~5C/nkcW Gj][/ !3M2qIwzc 3ٽ议5 +x'T _im, څAZEvi@w0YkeI4 $ۅq>Wž="xGÏ.y"/h}i:OojG[/:ċRo"Ō2Vnp+*sz^JKrok7nyVݝw\H&E7H?Ogz[qs} ..' 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Per Figure 3, peak forecasts improves over time, becoming )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(stable between weeks ten to eleven, which is 4 to 5 weeks from the peak. By week 11, we are 95% confident that the peak )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(would be observed between weeks 14 and 15 \(see Figure 4\). Similar to observations for 2007-2008 influenza season, the )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(variance around the forecasted mean peak is small. Results observed for 2012-2013 suggests that if GFT data captures the )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(epidemic trend but overestimates the peak, the data could still be used in forecasting the peak.)] TJ ET 0.965 0.965 0.965 rg 26.250 517.599 555.000 192.377 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 709.976 m 581.250 709.976 l 581.250 709.226 l 26.250 709.226 l f 26.250 517.599 m 581.250 517.599 l 581.250 518.349 l 26.250 518.349 l f q 112.500 0 0 112.500 35.250 587.726 cm /I53 Do Q q 35.250 528.849 537.000 52.877 re W n 0.271 0.267 0.267 rg BT 35.250 572.202 Td /F4 9.8 Tf [(Fig. 3: Peak forecast for the 2012-2013 influenza season using GFT for Seattle, WA.)] TJ ET BT 35.250 552.832 Td /F1 9.8 Tf [(Actual peak is observed on week 15. The black curve is the GFT data, the red line is the mean predicted curve and the grey )] TJ ET BT 35.250 539.096 Td /F1 9.8 Tf [(curves show fifty replicates of the stochastic process.)] TJ ET Q 0.965 0.965 0.965 rg 26.250 191.208 555.000 318.891 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 510.099 m 581.250 510.099 l 581.250 509.349 l 26.250 509.349 l f 26.250 191.208 m 581.250 191.208 l 581.250 191.958 l 26.250 191.958 l f q 225.000 0 0 252.750 35.250 247.599 cm /I54 Do Q q 35.250 202.458 537.000 39.141 re W n 0.271 0.267 0.267 rg BT 35.250 232.075 Td /F4 9.8 Tf [(Fig. 4: Predicted peak by week of forecast for Seattle, WA.)] TJ ET BT 35.250 212.705 Td /F1 9.8 Tf [(\(A\) 95% CI around the mean and \(B\) standard deviations around the mean. The true peak is observed on week 15.)] TJ ET Q BT 26.250 156.986 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 137.032 Td /F1 9.8 Tf [(Reliable forecasts of influenza events could influence the allocation of public health resources and control measures. In this )] TJ ET BT 26.250 125.127 Td /F1 9.8 Tf [(initial study, we present a simulation optimization approach for forecasting the peak of seasonal influenza epidemics. The )] TJ ET BT 26.250 113.223 Td /F1 9.8 Tf [(method presented in this study is based on the idea that by using parameters based on the natural history of influenza, )] TJ ET BT 26.250 101.318 Td /F1 9.8 Tf [(epidemics similar to seasonal outbreaks can be produced using the individual-based model. The model disease transmissibility )] TJ ET BT 26.250 89.413 Td /F1 9.8 Tf [(is estimated by recursively proposing new values, simulating epidemics and evaluating the difference between the cumulative )] TJ ET BT 26.250 77.508 Td /F1 9.8 Tf [(illness of the seasonal epidemic and the simulated cases. The transmissibility at convergence is used in forecasting. Different )] TJ ET BT 26.250 65.604 Td /F1 9.8 Tf [(aspects of the model can be replaced; including the optimization algorithm, and the function minimized.)] TJ ET BT 26.250 46.199 Td /F1 9.8 Tf [(Data from GFT, which estimates weekly ILI counts per 100,000 persons, is used in forecasting. The results are presented for )] TJ ET Q q 15.000 31.913 577.500 745.087 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(Similar to the 2007-2008 epidemic, we start forecasting on week 8. Per Figure 3, peak forecasts improves over time, becoming )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(stable between weeks ten to eleven, which is 4 to 5 weeks from the peak. By week 11, we are 95% confident that the peak )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(would be observed between weeks 14 and 15 \(see Figure 4\). Similar to observations for 2007-2008 influenza season, the )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(variance around the forecasted mean peak is small. Results observed for 2012-2013 suggests that if GFT data captures the )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(epidemic trend but overestimates the peak, the data could still be used in forecasting the peak.)] TJ ET 0.965 0.965 0.965 rg 26.250 517.599 555.000 192.377 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 709.976 m 581.250 709.976 l 581.250 709.226 l 26.250 709.226 l f 26.250 517.599 m 581.250 517.599 l 581.250 518.349 l 26.250 518.349 l f q 112.500 0 0 112.500 35.250 587.726 cm /I53 Do Q q 35.250 528.849 537.000 52.877 re W n 0.271 0.267 0.267 rg BT 35.250 572.202 Td /F4 9.8 Tf [(Fig. 3: Peak forecast for the 2012-2013 influenza season using GFT for Seattle, WA.)] TJ ET BT 35.250 552.832 Td /F1 9.8 Tf [(Actual peak is observed on week 15. The black curve is the GFT data, the red line is the mean predicted curve and the grey )] TJ ET BT 35.250 539.096 Td /F1 9.8 Tf [(curves show fifty replicates of the stochastic process.)] TJ ET Q 0.965 0.965 0.965 rg 26.250 191.208 555.000 318.891 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 510.099 m 581.250 510.099 l 581.250 509.349 l 26.250 509.349 l f 26.250 191.208 m 581.250 191.208 l 581.250 191.958 l 26.250 191.958 l f q 225.000 0 0 252.750 35.250 247.599 cm /I54 Do Q q 35.250 202.458 537.000 39.141 re W n 0.271 0.267 0.267 rg BT 35.250 232.075 Td /F4 9.8 Tf [(Fig. 4: Predicted peak by week of forecast for Seattle, WA.)] TJ ET BT 35.250 212.705 Td /F1 9.8 Tf [(\(A\) 95% CI around the mean and \(B\) standard deviations around the mean. The true peak is observed on week 15.)] TJ ET Q BT 26.250 156.986 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 137.032 Td /F1 9.8 Tf [(Reliable forecasts of influenza events could influence the allocation of public health resources and control measures. In this )] TJ ET BT 26.250 125.127 Td /F1 9.8 Tf [(initial study, we present a simulation optimization approach for forecasting the peak of seasonal influenza epidemics. The )] TJ ET BT 26.250 113.223 Td /F1 9.8 Tf [(method presented in this study is based on the idea that by using parameters based on the natural history of influenza, )] TJ ET BT 26.250 101.318 Td /F1 9.8 Tf [(epidemics similar to seasonal outbreaks can be produced using the individual-based model. The model disease transmissibility )] TJ ET BT 26.250 89.413 Td /F1 9.8 Tf [(is estimated by recursively proposing new values, simulating epidemics and evaluating the difference between the cumulative )] TJ ET BT 26.250 77.508 Td /F1 9.8 Tf [(illness of the seasonal epidemic and the simulated cases. The transmissibility at convergence is used in forecasting. Different )] TJ ET BT 26.250 65.604 Td /F1 9.8 Tf [(aspects of the model can be replaced; including the optimization algorithm, and the function minimized.)] TJ ET BT 26.250 46.199 Td /F1 9.8 Tf [(Data from GFT, which estimates weekly ILI counts per 100,000 persons, is used in forecasting. The results are presented for )] TJ ET Q q 15.000 31.913 577.500 745.087 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(Similar to the 2007-2008 epidemic, we start forecasting on week 8. Per Figure 3, peak forecasts improves over time, becoming )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(stable between weeks ten to eleven, which is 4 to 5 weeks from the peak. By week 11, we are 95% confident that the peak )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(would be observed between weeks 14 and 15 \(see Figure 4\). Similar to observations for 2007-2008 influenza season, the )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(variance around the forecasted mean peak is small. Results observed for 2012-2013 suggests that if GFT data captures the )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(epidemic trend but overestimates the peak, the data could still be used in forecasting the peak.)] TJ ET 0.965 0.965 0.965 rg 26.250 517.599 555.000 192.377 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 709.976 m 581.250 709.976 l 581.250 709.226 l 26.250 709.226 l f 26.250 517.599 m 581.250 517.599 l 581.250 518.349 l 26.250 518.349 l f q 112.500 0 0 112.500 35.250 587.726 cm /I53 Do Q q 35.250 528.849 537.000 52.877 re W n 0.271 0.267 0.267 rg BT 35.250 572.202 Td /F4 9.8 Tf [(Fig. 3: Peak forecast for the 2012-2013 influenza season using GFT for Seattle, WA.)] TJ ET BT 35.250 552.832 Td /F1 9.8 Tf [(Actual peak is observed on week 15. The black curve is the GFT data, the red line is the mean predicted curve and the grey )] TJ ET BT 35.250 539.096 Td /F1 9.8 Tf [(curves show fifty replicates of the stochastic process.)] TJ ET Q 0.965 0.965 0.965 rg 26.250 191.208 555.000 318.891 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 510.099 m 581.250 510.099 l 581.250 509.349 l 26.250 509.349 l f 26.250 191.208 m 581.250 191.208 l 581.250 191.958 l 26.250 191.958 l f q 225.000 0 0 252.750 35.250 247.599 cm /I54 Do Q q 35.250 202.458 537.000 39.141 re W n 0.271 0.267 0.267 rg BT 35.250 232.075 Td /F4 9.8 Tf [(Fig. 4: Predicted peak by week of forecast for Seattle, WA.)] TJ ET BT 35.250 212.705 Td /F1 9.8 Tf [(\(A\) 95% CI around the mean and \(B\) standard deviations around the mean. The true peak is observed on week 15.)] TJ ET Q BT 26.250 156.986 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 137.032 Td /F1 9.8 Tf [(Reliable forecasts of influenza events could influence the allocation of public health resources and control measures. In this )] TJ ET BT 26.250 125.127 Td /F1 9.8 Tf [(initial study, we present a simulation optimization approach for forecasting the peak of seasonal influenza epidemics. The )] TJ ET BT 26.250 113.223 Td /F1 9.8 Tf [(method presented in this study is based on the idea that by using parameters based on the natural history of influenza, )] TJ ET BT 26.250 101.318 Td /F1 9.8 Tf [(epidemics similar to seasonal outbreaks can be produced using the individual-based model. The model disease transmissibility )] TJ ET BT 26.250 89.413 Td /F1 9.8 Tf [(is estimated by recursively proposing new values, simulating epidemics and evaluating the difference between the cumulative )] TJ ET BT 26.250 77.508 Td /F1 9.8 Tf [(illness of the seasonal epidemic and the simulated cases. The transmissibility at convergence is used in forecasting. Different )] TJ ET BT 26.250 65.604 Td /F1 9.8 Tf [(aspects of the model can be replaced; including the optimization algorithm, and the function minimized.)] TJ ET BT 26.250 46.199 Td /F1 9.8 Tf [(Data from GFT, which estimates weekly ILI counts per 100,000 persons, is used in forecasting. 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(kw_jKr>oiX_ؙUE.l%sYhhaZY}{.s1IIT~4~4QGG@y_xxsMkE5Ufh.̨%@2t ^#A׼3᳧ؤR-ńVÁGo9 Rz??(5|]'oZn"[f{]3[&æ vFx|cOCz?Bw^[ȗ*¸|Ü.>o^Zk8A5ex-e4.xaqs# 9$[>TЍhMk^RϹ< Zxj^.EZ6Oovd?RJ9 {Wf{O X-tYeK|jgK)/#8u?o[MP7)%!*yxF0*:>"VZYh|O3x}*h]jz?'PvL`[&4'pU>`r8)iOougUEżȝ Y  m-򚐔#RI94ٯs5'2NqFFGE|w~𯅤t)Kz^x6# -FU1 Xwŝg26M𮕫I#=O`) l3`JnZV8|k_fǹx?@Ū_Y'uajno\=EFG/HW O7k 9t ͮ>+es^wu ŪIp:As$++;S sd?>ҭ] KthL 1YxJh)bOLUMl]m4f8?j7{4Qu /"6[ͨ]E7MBR`mWVbWZXX̳@|_UU7U270|;\LZw^#ӴmGPuU4[WK(rH끴>A$b[uy\Ci@Y ˁ Xo}&<[i^$կ!Xt3FA *fEL$9K^rU^n]|56L6*ۧ9\c9Rɢi쭞B^Wgޕw񭬏/3 W1GZGnS1P/GLM~4~4~4~4????????????????????Z( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (? endstream endobj 448 0 obj << /Type /Annot /Subtype /Link /A 449 0 R /Border [0 0 0] /H /I /Rect [ 35.2500 587.7262 147.7500 700.2262 ] >> endobj 449 0 obj << /Type /Action /S /URI /URI (http://currents.plos.org/outbreaks/files/2013/06/Peakprogress1213third-copy-copy.jpg) >> endobj 450 0 obj << /Type /Annot /Subtype /Link /A 451 0 R /Border [0 0 0] /H /I /Rect [ 35.2500 247.5990 260.2500 500.3490 ] >> endobj 451 0 obj << /Type /Action /S /URI /URI (http://currents.plos.org/outbreaks/files/2013/06/TTP1213Review1-copy-copy.jpg) >> endobj 452 0 obj << /Type /Annot /Subtype /Link /A 453 0 R /Border [0 0 0] /H /I /Rect [ 35.2500 587.7262 147.7500 700.2262 ] >> endobj 453 0 obj << /Type /Action /S /URI /URI (http://currents.plos.org/outbreaks/files/2013/06/Peakprogress1213third-copy-copy.jpg) >> endobj 454 0 obj << /Type /Annot /Subtype /Link /A 455 0 R /Border [0 0 0] /H /I /Rect [ 35.2500 247.5990 260.2500 500.3490 ] >> endobj 455 0 obj << /Type /Action /S /URI /URI (http://currents.plos.org/outbreaks/files/2013/06/TTP1213Review1-copy-copy.jpg) >> endobj 456 0 obj << /Type /Page /Parent 3 0 R /Annots [ 458 0 R 460 0 R 462 0 R 464 0 R 466 0 R 468 0 R 470 0 R 472 0 R 474 0 R 476 0 R 478 0 R 480 0 R 482 0 R 484 0 R 486 0 R ] /Contents 457 0 R >> endobj 457 0 obj << /Length 25651 >> stream 0.271 0.267 0.267 rg q 15.000 33.768 577.500 743.232 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(Seattle, Washington for the 2007-2008 and 2012-2013 influenza seasons. Although the overall concept of minimizing the )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(difference between cumulative ILI counts and simulated instances is relatively simple, the observed results are promising. The )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(peak is predicted in one case as early as 5-6 weeks before the actual peak and in another, as early as a month.)] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(As noted in the results, there are deviations in how early the peak can be forecasted by influenza season. These differences )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(could also be observed by region. In this study we used a social contact network developed based on census data for Seattle, )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(while the study by Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 169.321 701.960 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 178.959 700.452 Td /F1 9.8 Tf [( focused on New York. Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 342.622 701.960 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 352.260 700.452 Td /F1 9.8 Tf [( suggest that the peak could be forecasted as early )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(as 7 weeks before it is observed. Results in this study agree with that observation though contrary to the study by Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 26.250 678.150 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 35.887 676.643 Td /F1 9.8 Tf [(, no climate variables are included in the simulation optimization approach.)] TJ ET BT 26.250 657.238 Td /F1 9.8 Tf [(In addition to common challenges to influenza forecasting, there are some limitations introduced by the different components of )] TJ ET BT 26.250 645.333 Td /F1 9.8 Tf [(the simulation optimization approach. First, ILI is typically underreported and can result from a variety of etiologies. Different )] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(studies have used different approaches for estimating influenza-attributable symptomatic disease from syndromic data and )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(correcting for bias due to underreporting. However, to our knowledge, there are no standard approaches for dealing with either )] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(challenge. In converse, underreporting can be assumed constant over time and introduced into the forecasting approach by )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(scaling the model-generated data. Though, deciding on the appropriate scaling factor can also be difficult.)] TJ ET BT 26.250 578.310 Td /F1 9.8 Tf [(Second, since the simulation optimization approach does not involve a curve fitting step, the shape of the curve is not )] TJ ET BT 26.250 566.405 Td /F1 9.8 Tf [(accounted for, which could sometimes lead to incorrect forecasts of the peak. Third, the individual-based model does not always )] TJ ET BT 26.250 554.500 Td /F1 9.8 Tf [(capture reality. The lack of information on pharmaceutical and non-pharmaceutical intervention coverage and efficacy, which )] TJ ET BT 26.250 542.595 Td /F1 9.8 Tf [(might influence the shape of the epidemic curve are not readily available during an epidemic. In addition, the generation time for )] TJ ET BT 26.250 530.691 Td /F1 9.8 Tf [(influenza has been estimated to be closer to 3 days )] TJ ET 0.267 0.267 0.267 rg BT 251.163 532.198 Td /F4 8.7 Tf [(36)] TJ ET 0.271 0.267 0.267 rg BT 260.800 530.691 Td /F1 9.8 Tf [(, while that used in the model is approximately five days. Shortening the )] TJ ET BT 26.250 518.786 Td /F1 9.8 Tf [(length of the incubation period used in the model would shorten the generation time. Lastly, GFT is not always guaranteed to be )] TJ ET BT 26.250 506.881 Td /F1 9.8 Tf [(a reliable estimate of influenza activity. Worry and curiosity induced searches could affect the estimated ILI counts if the model )] TJ ET BT 26.250 494.976 Td /F1 9.8 Tf [(is not consistently retuned. Reports from the 2012-2013 influenza season suggest GFT might have overestimated influenza )] TJ ET BT 26.250 483.072 Td /F1 9.8 Tf [(activity )] TJ ET 0.267 0.267 0.267 rg BT 58.757 484.579 Td /F4 8.7 Tf [(35)] TJ ET 0.271 0.267 0.267 rg BT 68.394 483.072 Td /F1 9.8 Tf [(. GFT data has also been shown to deviate from patterns of true influenza data.)] TJ ET BT 26.250 463.667 Td /F1 9.8 Tf [(In this study, GFT is used to illustrate the proposed approach. The results indicate that if the overall trend of the epidemic is )] TJ ET BT 26.250 451.762 Td /F1 9.8 Tf [(accurately captured, GFT could be used for peak forecasts as illustrated, but probably not for forecasting other epidemic )] TJ ET BT 26.250 439.857 Td /F1 9.8 Tf [(measures such as peak height and attack rate. Data from the CDC would be preferred for forecasting influenza, however there )] TJ ET BT 26.250 427.953 Td /F1 9.8 Tf [(are limitations that impede the use of such data presently. One major limitation is the lack of data at the city level. Contact )] TJ ET BT 26.250 416.048 Td /F1 9.8 Tf [(networks for the individual-based model are currently available only at the city level. In order to use CDC data at the regional )] TJ ET BT 26.250 404.143 Td /F1 9.8 Tf [(level, we would need to create regional contact networks. This is an endeavor we are interested in pursuing in future studies.)] TJ ET BT 26.250 384.738 Td /F1 9.8 Tf [(The approach presented in this study can be made more rigorous by incorporating more information about the influenza strain, )] TJ ET BT 26.250 372.834 Td /F1 9.8 Tf [(and environmental variables such as humidity. However, observations in this study agree with other proposed approaches that )] TJ ET BT 26.250 360.929 Td /F1 9.8 Tf [(influenza forecasting is possible and reliable forecasts can be achieved much earlier than expected.)] TJ ET BT 26.250 324.326 Td /F4 12.0 Tf [(Acknowledgements)] TJ ET BT 26.250 304.372 Td /F1 9.8 Tf [(We thank Kalyani Nagaraj, the reviewers and editors for comments and suggestions.)] TJ ET BT 26.250 275.270 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 247.815 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 247.815 Td /F1 9.8 Tf [(Longini IM, Fine PEM, Thacker SB \(1986\) Predicting the global spread of new infectious agents. American Journal of )] TJ ET BT 26.250 235.911 Td /F1 9.8 Tf [(Epidemiology 123: 383-391.)] TJ ET BT 26.250 216.506 Td /F1 9.8 Tf [(2.)] TJ ET BT 38.132 216.506 Td /F1 9.8 Tf [(Ong J, Mark I, Chen C, Cook A, Lee H, et al. \(2010\) Real-time epidemic monitoring and fore- casting of H1N1-2009 using )] TJ ET BT 26.250 204.601 Td /F1 9.8 Tf [(influenza-like illness from general practice and family doctor clinics in Singapore. PloS one 5: e10036.)] TJ ET BT 26.250 185.196 Td /F1 9.8 Tf [(3.)] TJ ET BT 38.132 185.196 Td /F1 9.8 Tf [(Towers S, Feng Z \(2009\) Pandemic h1n1 influenza: predicting the course of a pandemic and assessing the efficacy of the )] TJ ET BT 26.250 173.292 Td /F1 9.8 Tf [(planned vaccination programme in the united states. Euro surveillance : bulletin europeen sur les maladies transmissibles = )] TJ ET BT 26.250 161.387 Td /F1 9.8 Tf [(European communicable disease bulletin 14: 19358.)] TJ ET BT 26.250 141.982 Td /F1 9.8 Tf [(4.)] TJ ET BT 38.132 141.982 Td /F1 9.8 Tf [(Chao DL, Matrajt L, Basta NE, Sugimoto JD, Dean B, et al. \(2011\) Planning for the control of pandemic influenza A \(H1N1\) in )] TJ ET BT 26.250 130.077 Td /F1 9.8 Tf [(Los Angeles county and the United States. American Journal of Epidemiology 173: 11211130.)] TJ ET BT 26.250 110.673 Td /F1 9.8 Tf [(5.)] TJ ET BT 38.132 110.673 Td /F1 9.8 Tf [(Tizzoni M, Bajardi P, Poletto C, Ramasco J, Balcan D, et al. \(2012\) Real-time numerical forecast of global epidemic )] TJ ET BT 26.250 98.768 Td /F1 9.8 Tf [(spreading: case study of 2009 A/H1N1pdm. BMC Medicine 10: 165.)] TJ ET BT 26.250 79.363 Td /F1 9.8 Tf [(6.)] TJ ET BT 38.132 79.363 Td /F1 9.8 Tf [(Dukic V, Lopes HF, Polson NG \(2012\) Tracking epidemics with Google flu trends data and a state-space SEIR model. )] TJ ET BT 26.250 67.458 Td /F1 9.8 Tf [(Journal of the American Statistical Association 107: 1410-1426.)] TJ ET BT 26.250 48.054 Td /F1 9.8 Tf [(7.)] TJ ET BT 38.132 48.054 Td /F1 9.8 Tf [(Sumi A, ichi Kamo K, Ohtomo N, Mise K, Kobayashi N \(2011\) Time series analysis of incidence data of influenza in japan. )] TJ ET Q q 15.000 33.768 577.500 743.232 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(Seattle, Washington for the 2007-2008 and 2012-2013 influenza seasons. Although the overall concept of minimizing the )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(difference between cumulative ILI counts and simulated instances is relatively simple, the observed results are promising. The )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(peak is predicted in one case as early as 5-6 weeks before the actual peak and in another, as early as a month.)] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(As noted in the results, there are deviations in how early the peak can be forecasted by influenza season. These differences )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(could also be observed by region. In this study we used a social contact network developed based on census data for Seattle, )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(while the study by Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 169.321 701.960 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 178.959 700.452 Td /F1 9.8 Tf [( focused on New York. Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 342.622 701.960 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 352.260 700.452 Td /F1 9.8 Tf [( suggest that the peak could be forecasted as early )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(as 7 weeks before it is observed. Results in this study agree with that observation though contrary to the study by Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 26.250 678.150 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 35.887 676.643 Td /F1 9.8 Tf [(, no climate variables are included in the simulation optimization approach.)] TJ ET BT 26.250 657.238 Td /F1 9.8 Tf [(In addition to common challenges to influenza forecasting, there are some limitations introduced by the different components of )] TJ ET BT 26.250 645.333 Td /F1 9.8 Tf [(the simulation optimization approach. First, ILI is typically underreported and can result from a variety of etiologies. Different )] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(studies have used different approaches for estimating influenza-attributable symptomatic disease from syndromic data and )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(correcting for bias due to underreporting. However, to our knowledge, there are no standard approaches for dealing with either )] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(challenge. In converse, underreporting can be assumed constant over time and introduced into the forecasting approach by )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(scaling the model-generated data. Though, deciding on the appropriate scaling factor can also be difficult.)] TJ ET BT 26.250 578.310 Td /F1 9.8 Tf [(Second, since the simulation optimization approach does not involve a curve fitting step, the shape of the curve is not )] TJ ET BT 26.250 566.405 Td /F1 9.8 Tf [(accounted for, which could sometimes lead to incorrect forecasts of the peak. Third, the individual-based model does not always )] TJ ET BT 26.250 554.500 Td /F1 9.8 Tf [(capture reality. The lack of information on pharmaceutical and non-pharmaceutical intervention coverage and efficacy, which )] TJ ET BT 26.250 542.595 Td /F1 9.8 Tf [(might influence the shape of the epidemic curve are not readily available during an epidemic. In addition, the generation time for )] TJ ET BT 26.250 530.691 Td /F1 9.8 Tf [(influenza has been estimated to be closer to 3 days )] TJ ET 0.267 0.267 0.267 rg BT 251.163 532.198 Td /F4 8.7 Tf [(36)] TJ ET 0.271 0.267 0.267 rg BT 260.800 530.691 Td /F1 9.8 Tf [(, while that used in the model is approximately five days. Shortening the )] TJ ET BT 26.250 518.786 Td /F1 9.8 Tf [(length of the incubation period used in the model would shorten the generation time. Lastly, GFT is not always guaranteed to be )] TJ ET BT 26.250 506.881 Td /F1 9.8 Tf [(a reliable estimate of influenza activity. Worry and curiosity induced searches could affect the estimated ILI counts if the model )] TJ ET BT 26.250 494.976 Td /F1 9.8 Tf [(is not consistently retuned. Reports from the 2012-2013 influenza season suggest GFT might have overestimated influenza )] TJ ET BT 26.250 483.072 Td /F1 9.8 Tf [(activity )] TJ ET 0.267 0.267 0.267 rg BT 58.757 484.579 Td /F4 8.7 Tf [(35)] TJ ET 0.271 0.267 0.267 rg BT 68.394 483.072 Td /F1 9.8 Tf [(. GFT data has also been shown to deviate from patterns of true influenza data.)] TJ ET BT 26.250 463.667 Td /F1 9.8 Tf [(In this study, GFT is used to illustrate the proposed approach. The results indicate that if the overall trend of the epidemic is )] TJ ET BT 26.250 451.762 Td /F1 9.8 Tf [(accurately captured, GFT could be used for peak forecasts as illustrated, but probably not for forecasting other epidemic )] TJ ET BT 26.250 439.857 Td /F1 9.8 Tf [(measures such as peak height and attack rate. Data from the CDC would be preferred for forecasting influenza, however there )] TJ ET BT 26.250 427.953 Td /F1 9.8 Tf [(are limitations that impede the use of such data presently. One major limitation is the lack of data at the city level. Contact )] TJ ET BT 26.250 416.048 Td /F1 9.8 Tf [(networks for the individual-based model are currently available only at the city level. In order to use CDC data at the regional )] TJ ET BT 26.250 404.143 Td /F1 9.8 Tf [(level, we would need to create regional contact networks. This is an endeavor we are interested in pursuing in future studies.)] TJ ET BT 26.250 384.738 Td /F1 9.8 Tf [(The approach presented in this study can be made more rigorous by incorporating more information about the influenza strain, )] TJ ET BT 26.250 372.834 Td /F1 9.8 Tf [(and environmental variables such as humidity. However, observations in this study agree with other proposed approaches that )] TJ ET BT 26.250 360.929 Td /F1 9.8 Tf [(influenza forecasting is possible and reliable forecasts can be achieved much earlier than expected.)] TJ ET BT 26.250 324.326 Td /F4 12.0 Tf [(Acknowledgements)] TJ ET BT 26.250 304.372 Td /F1 9.8 Tf [(We thank Kalyani Nagaraj, the reviewers and editors for comments and suggestions.)] TJ ET BT 26.250 275.270 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 247.815 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 247.815 Td /F1 9.8 Tf [(Longini IM, Fine PEM, Thacker SB \(1986\) Predicting the global spread of new infectious agents. American Journal of )] TJ ET BT 26.250 235.911 Td /F1 9.8 Tf [(Epidemiology 123: 383-391.)] TJ ET BT 26.250 216.506 Td /F1 9.8 Tf [(2.)] TJ ET BT 38.132 216.506 Td /F1 9.8 Tf [(Ong J, Mark I, Chen C, Cook A, Lee H, et al. \(2010\) Real-time epidemic monitoring and fore- casting of H1N1-2009 using )] TJ ET BT 26.250 204.601 Td /F1 9.8 Tf [(influenza-like illness from general practice and family doctor clinics in Singapore. PloS one 5: e10036.)] TJ ET BT 26.250 185.196 Td /F1 9.8 Tf [(3.)] TJ ET BT 38.132 185.196 Td /F1 9.8 Tf [(Towers S, Feng Z \(2009\) Pandemic h1n1 influenza: predicting the course of a pandemic and assessing the efficacy of the )] TJ ET BT 26.250 173.292 Td /F1 9.8 Tf [(planned vaccination programme in the united states. Euro surveillance : bulletin europeen sur les maladies transmissibles = )] TJ ET BT 26.250 161.387 Td /F1 9.8 Tf [(European communicable disease bulletin 14: 19358.)] TJ ET BT 26.250 141.982 Td /F1 9.8 Tf [(4.)] TJ ET BT 38.132 141.982 Td /F1 9.8 Tf [(Chao DL, Matrajt L, Basta NE, Sugimoto JD, Dean B, et al. \(2011\) Planning for the control of pandemic influenza A \(H1N1\) in )] TJ ET BT 26.250 130.077 Td /F1 9.8 Tf [(Los Angeles county and the United States. American Journal of Epidemiology 173: 11211130.)] TJ ET BT 26.250 110.673 Td /F1 9.8 Tf [(5.)] TJ ET BT 38.132 110.673 Td /F1 9.8 Tf [(Tizzoni M, Bajardi P, Poletto C, Ramasco J, Balcan D, et al. \(2012\) Real-time numerical forecast of global epidemic )] TJ ET BT 26.250 98.768 Td /F1 9.8 Tf [(spreading: case study of 2009 A/H1N1pdm. BMC Medicine 10: 165.)] TJ ET BT 26.250 79.363 Td /F1 9.8 Tf [(6.)] TJ ET BT 38.132 79.363 Td /F1 9.8 Tf [(Dukic V, Lopes HF, Polson NG \(2012\) Tracking epidemics with Google flu trends data and a state-space SEIR model. )] TJ ET BT 26.250 67.458 Td /F1 9.8 Tf [(Journal of the American Statistical Association 107: 1410-1426.)] TJ ET BT 26.250 48.054 Td /F1 9.8 Tf [(7.)] TJ ET BT 38.132 48.054 Td /F1 9.8 Tf [(Sumi A, ichi Kamo K, Ohtomo N, Mise K, Kobayashi N \(2011\) Time series analysis of incidence data of influenza in japan. )] TJ ET Q q 15.000 33.768 577.500 743.232 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(Seattle, Washington for the 2007-2008 and 2012-2013 influenza seasons. Although the overall concept of minimizing the )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(difference between cumulative ILI counts and simulated instances is relatively simple, the observed results are promising. The )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(peak is predicted in one case as early as 5-6 weeks before the actual peak and in another, as early as a month.)] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(As noted in the results, there are deviations in how early the peak can be forecasted by influenza season. These differences )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(could also be observed by region. In this study we used a social contact network developed based on census data for Seattle, )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(while the study by Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 169.321 701.960 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 178.959 700.452 Td /F1 9.8 Tf [( focused on New York. Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 342.622 701.960 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 352.260 700.452 Td /F1 9.8 Tf [( suggest that the peak could be forecasted as early )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(as 7 weeks before it is observed. Results in this study agree with that observation though contrary to the study by Shaman et al. )] TJ ET 0.267 0.267 0.267 rg BT 26.250 678.150 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 35.887 676.643 Td /F1 9.8 Tf [(, no climate variables are included in the simulation optimization approach.)] TJ ET BT 26.250 657.238 Td /F1 9.8 Tf [(In addition to common challenges to influenza forecasting, there are some limitations introduced by the different components of )] TJ ET BT 26.250 645.333 Td /F1 9.8 Tf [(the simulation optimization approach. First, ILI is typically underreported and can result from a variety of etiologies. Different )] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(studies have used different approaches for estimating influenza-attributable symptomatic disease from syndromic data and )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(correcting for bias due to underreporting. However, to our knowledge, there are no standard approaches for dealing with either )] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(challenge. In converse, underreporting can be assumed constant over time and introduced into the forecasting approach by )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(scaling the model-generated data. Though, deciding on the appropriate scaling factor can also be difficult.)] TJ ET BT 26.250 578.310 Td /F1 9.8 Tf [(Second, since the simulation optimization approach does not involve a curve fitting step, the shape of the curve is not )] TJ ET BT 26.250 566.405 Td /F1 9.8 Tf [(accounted for, which could sometimes lead to incorrect forecasts of the peak. Third, the individual-based model does not always )] TJ ET BT 26.250 554.500 Td /F1 9.8 Tf [(capture reality. The lack of information on pharmaceutical and non-pharmaceutical intervention coverage and efficacy, which )] TJ ET BT 26.250 542.595 Td /F1 9.8 Tf [(might influence the shape of the epidemic curve are not readily available during an epidemic. In addition, the generation time for )] TJ ET BT 26.250 530.691 Td /F1 9.8 Tf [(influenza has been estimated to be closer to 3 days )] TJ ET 0.267 0.267 0.267 rg BT 251.163 532.198 Td /F4 8.7 Tf [(36)] TJ ET 0.271 0.267 0.267 rg BT 260.800 530.691 Td /F1 9.8 Tf [(, while that used in the model is approximately five days. Shortening the )] TJ ET BT 26.250 518.786 Td /F1 9.8 Tf [(length of the incubation period used in the model would shorten the generation time. Lastly, GFT is not always guaranteed to be )] TJ ET BT 26.250 506.881 Td /F1 9.8 Tf [(a reliable estimate of influenza activity. Worry and curiosity induced searches could affect the estimated ILI counts if the model )] TJ ET BT 26.250 494.976 Td /F1 9.8 Tf [(is not consistently retuned. Reports from the 2012-2013 influenza season suggest GFT might have overestimated influenza )] TJ ET BT 26.250 483.072 Td /F1 9.8 Tf [(activity )] TJ ET 0.267 0.267 0.267 rg BT 58.757 484.579 Td /F4 8.7 Tf [(35)] TJ ET 0.271 0.267 0.267 rg BT 68.394 483.072 Td /F1 9.8 Tf [(. GFT data has also been shown to deviate from patterns of true influenza data.)] TJ ET BT 26.250 463.667 Td /F1 9.8 Tf [(In this study, GFT is used to illustrate the proposed approach. The results indicate that if the overall trend of the epidemic is )] TJ ET BT 26.250 451.762 Td /F1 9.8 Tf [(accurately captured, GFT could be used for peak forecasts as illustrated, but probably not for forecasting other epidemic )] TJ ET BT 26.250 439.857 Td /F1 9.8 Tf [(measures such as peak height and attack rate. Data from the CDC would be preferred for forecasting influenza, however there )] TJ ET BT 26.250 427.953 Td /F1 9.8 Tf [(are limitations that impede the use of such data presently. One major limitation is the lack of data at the city level. Contact )] TJ ET BT 26.250 416.048 Td /F1 9.8 Tf [(networks for the individual-based model are currently available only at the city level. In order to use CDC data at the regional )] TJ ET BT 26.250 404.143 Td /F1 9.8 Tf [(level, we would need to create regional contact networks. This is an endeavor we are interested in pursuing in future studies.)] TJ ET BT 26.250 384.738 Td /F1 9.8 Tf [(The approach presented in this study can be made more rigorous by incorporating more information about the influenza strain, )] TJ ET BT 26.250 372.834 Td /F1 9.8 Tf [(and environmental variables such as humidity. However, observations in this study agree with other proposed approaches that )] TJ ET BT 26.250 360.929 Td /F1 9.8 Tf [(influenza forecasting is possible and reliable forecasts can be achieved much earlier than expected.)] TJ ET BT 26.250 324.326 Td /F4 12.0 Tf [(Acknowledgements)] TJ ET BT 26.250 304.372 Td /F1 9.8 Tf [(We thank Kalyani Nagaraj, the reviewers and editors for comments and suggestions.)] TJ ET BT 26.250 275.270 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 247.815 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 247.815 Td /F1 9.8 Tf [(Longini IM, Fine PEM, Thacker SB \(1986\) Predicting the global spread of new infectious agents. 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Statistics in Medicine 30: 31253136.)] TJ ET BT 26.250 716.762 Td /F1 9.8 Tf [(9.)] TJ ET BT 38.132 716.762 Td /F1 9.8 Tf [(Dugas AF, Jalalpour M, Gel Y, Levin S, Torcaso F, et al. \(2013\) Influenza forecasting with Google flu trends. PLoS ONE 8: )] TJ ET BT 26.250 704.857 Td /F1 9.8 Tf [(e56176.)] TJ ET BT 26.250 685.452 Td /F1 9.8 Tf [(10.)] TJ ET BT 43.553 685.452 Td /F1 9.8 Tf [(Shaman J, Karspeck A \(2012\) Forecasting seasonal outbreaks of influenza. Proceedings of the National Academy of )] TJ ET BT 26.250 673.548 Td /F1 9.8 Tf [(Sciences 109: 20425-20430.)] TJ ET BT 26.250 654.143 Td /F1 9.8 Tf [(11.)] TJ ET BT 43.553 654.143 Td /F1 9.8 Tf [(Shaman J, Pitzer VE, Viboud C, Grenfell BT, Lipsitch M \(2010\) Absolute humidity and the seasonal onset of influenza in the )] TJ ET BT 26.250 642.238 Td /F1 9.8 Tf [(continental united states. PLoS Biol 8: e1000316.)] TJ ET BT 26.250 622.833 Td /F1 9.8 Tf [(12.)] TJ ET BT 43.553 622.833 Td /F1 9.8 Tf [(Barrett C, Bisset K, Leidig J, Marathe A, Marathe M \(2011\) Economic and social impact of influenza mitigation strategies by )] TJ ET BT 26.250 610.929 Td /F1 9.8 Tf [(demographic class. Epidemics 3: 1931.)] TJ ET BT 26.250 591.524 Td /F1 9.8 Tf [(13.)] TJ ET BT 43.553 591.524 Td /F1 9.8 Tf [(Halloran ME, Ferguson N, Eubank S, Longini I, Cummings D, et al. \(2008\) Modeling targeted layered containment of an )] TJ ET BT 26.250 579.619 Td /F1 9.8 Tf [(influenza pandemic in the United States. Proceedings of the National Academy of Sciences 105: 4639-4644.)] TJ ET BT 26.250 560.214 Td /F1 9.8 Tf [(14.)] TJ ET BT 43.553 560.214 Td /F1 9.8 Tf [(Nsoesie EO, Beckman RJ, Shashaani S, Nagaraj KS, Marathe MV \(2013\) A simulation optimization approach to epidemic )] TJ ET BT 26.250 548.310 Td /F1 9.8 Tf [(forecasting. PLoS ONE \(In Press\).)] TJ ET BT 26.250 528.905 Td /F1 9.8 Tf [(15.)] TJ ET BT 43.553 528.905 Td /F1 9.8 Tf [(Ginsberg J, Mohebbi M, Patel R, Brammer L, Smolinski M, et al. \(2008\) Detecting influenza epidemics using search engine )] TJ ET BT 26.250 517.000 Td /F1 9.8 Tf [(query data. Nature 457: 10121014.)] TJ ET BT 26.250 497.595 Td /F1 9.8 Tf [(16.)] TJ ET BT 43.553 497.595 Td /F1 9.8 Tf [(Bisset K, Chen J, Feng X, Kumar VSA, Marathe M \(2009\) Epifast: a fast algorithm for large scale realistic epidemic )] TJ ET BT 26.250 485.691 Td /F1 9.8 Tf [(simulations on distributed memory systems. In: Proceedings of the 23rd international conference on Supercomputing. ICS 09, )] TJ ET BT 26.250 473.786 Td /F1 9.8 Tf [(pp. 430439.)] TJ ET BT 26.250 454.381 Td /F1 9.8 Tf [(17.)] TJ ET BT 43.553 454.381 Td /F1 9.8 Tf [(Beckman R, Baggerly K, Mckay M \(1996\) Creating synthetic baseline populations. Transportation Research Part A: Policy )] TJ ET BT 26.250 442.476 Td /F1 9.8 Tf [(and Practice 30: 415-429.)] TJ ET BT 26.250 423.072 Td /F1 9.8 Tf [(18.)] TJ ET BT 43.553 423.072 Td /F1 9.8 Tf [(Speckman P, Vaughn K, Pas E \(1997a\) Generating household activity-travel patterns \(HATPs\) for synthetic populations. )] TJ ET BT 26.250 411.167 Td /F1 9.8 Tf [(Transportation Research Board 1997 Annual Meeting.)] TJ ET BT 26.250 391.762 Td /F1 9.8 Tf [(19.)] TJ ET BT 43.553 391.762 Td /F1 9.8 Tf [(Speckman P, Vaughn K, Pas E \(1997b\) A continuous spatial interaction model: Application to home-work travel in Portland, )] TJ ET BT 26.250 379.857 Td /F1 9.8 Tf [(Oregon. Transportation Research Board 1997 Annual Meeting.)] TJ ET BT 26.250 360.453 Td /F1 9.8 Tf [(20.)] TJ ET BT 43.553 360.453 Td /F1 9.8 Tf [(Barrett C, Beckman R, Khan M, Kumar VSA, Marathe M, et al. \(2009\) Generation and analysis of large synthetic social )] TJ ET BT 26.250 348.548 Td /F1 9.8 Tf [(contact networks. In: Winter Simulation Conference. WSC 09, pp. 1003 1014.)] TJ ET BT 26.250 329.143 Td /F1 9.8 Tf [(21.)] TJ ET BT 43.553 329.143 Td /F1 9.8 Tf [(TRBC \(1995-2003\) 5th-9th Biennial National Academies Transportation Research Board Conferences on Application Of )] TJ ET BT 26.250 317.238 Td /F1 9.8 Tf [(Transportation Planning Methods.)] TJ ET BT 26.250 297.834 Td /F1 9.8 Tf [(22.)] TJ ET BT 43.553 297.834 Td /F1 9.8 Tf [(Bowman J, Bradley M, Shiftan Y, Lawton TK, Ben-Akiva M \(1998\) Demonstration of an activity based model system for )] TJ ET BT 26.250 285.929 Td /F1 9.8 Tf [(Portland. In: Proceedings of the 8th World Conference on Transport Research.)] TJ ET BT 26.250 266.524 Td /F1 9.8 Tf [(23.)] TJ ET BT 43.553 266.524 Td /F1 9.8 Tf [(Bailey N \(1975\) The Mathematical Theory of Infectious Diseases and its Applications. London: Griffin.)] TJ ET BT 26.250 247.119 Td /F1 9.8 Tf [(24.)] TJ ET BT 43.553 247.119 Td /F1 9.8 Tf [(Elveback L, Fox J, Ackerman E, Langworthy A, Boyd M, et al. \(1976\) American Journal of Epidemiology 103: 152-165.)] TJ ET BT 26.250 227.715 Td /F1 9.8 Tf [(25.)] TJ ET BT 43.553 227.715 Td /F1 9.8 Tf [(Longini I, Nizam A, Xu S, Ungchusak K, Hanshaworakul W, et al. \(2005\) Containing pandemic influenza at the source. )] TJ ET BT 26.250 215.810 Td /F1 9.8 Tf [(Science 309: 1083-1087.)] TJ ET BT 26.250 196.405 Td /F1 9.8 Tf [(26.)] TJ ET BT 43.553 196.405 Td /F1 9.8 Tf [(Hethcote HW \(2000\) The mathematics of infectious diseases. SIAM Review 42: 599653.)] TJ ET BT 26.250 177.000 Td /F1 9.8 Tf [(27.)] TJ ET BT 43.553 177.000 Td /F1 9.8 Tf [(Eubank S, Guclu H, Kumar VSA, Marathe M, Srinivasan A, et al. \(2004\) Modelling disease outbreaks in realistic urban )] TJ ET BT 26.250 165.096 Td /F1 9.8 Tf [(social networks. Nature 429: 180-184.)] TJ ET BT 26.250 145.691 Td /F1 9.8 Tf [(28.)] TJ ET BT 43.553 145.691 Td /F1 9.8 Tf [(Newman M \(2003\) The structure and function of complex networks. SIAM Review 45: 167-256.)] TJ ET BT 26.250 126.286 Td /F1 9.8 Tf [(29.)] TJ ET BT 43.553 126.286 Td /F1 9.8 Tf [(Eubank S, Barrett C, Beckman R, Bisset K, Durbeck L, et al. \(2010\) Detail in network models of epidemiology: are we there )] TJ ET BT 26.250 114.381 Td /F1 9.8 Tf [(yet? Journal of Biological Dynamics 4: 446-455.)] TJ ET BT 26.250 94.977 Td /F1 9.8 Tf [(30.)] TJ ET BT 43.553 94.977 Td /F1 9.8 Tf [(Nsoesie EO, Beckman RJ, Marathe MV \(2012\) Sensitivity analysis of an individual-based model for simulation of influenza )] TJ ET BT 26.250 83.072 Td /F1 9.8 Tf [(epidemics. PLoS ONE 7: e45414.)] TJ ET BT 26.250 63.667 Td /F1 9.8 Tf [(31.)] TJ ET BT 43.553 63.667 Td /F1 9.8 Tf [(Ajelli M, Goncalves B, Balcan D, Colizza V, Hu H, et al. \(2010\) Comparing large-scale computational approaches to )] TJ ET BT 26.250 51.762 Td /F1 9.8 Tf [(epidemic modeling: Agent-based versus structured metapopulation models. BMC Infectious Diseases 10: 190.)] TJ ET Q q 15.000 41.882 577.500 735.118 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(Journal of Epidemiology 21: 21-29.)] TJ ET BT 26.250 748.071 Td /F1 9.8 Tf [(8.)] TJ ET BT 38.132 748.071 Td /F1 9.8 Tf [(Morin ?a D, Puig P, R ??os J, Vilella A, Trilla A \(2011\) A statistical model for hospital admissions caused by seasonal )] TJ ET BT 26.250 736.167 Td /F1 9.8 Tf [(diseases. Statistics in Medicine 30: 31253136.)] TJ ET BT 26.250 716.762 Td /F1 9.8 Tf [(9.)] TJ ET BT 38.132 716.762 Td /F1 9.8 Tf [(Dugas AF, Jalalpour M, Gel Y, Levin S, Torcaso F, et al. \(2013\) Influenza forecasting with Google flu trends. PLoS ONE 8: )] TJ ET BT 26.250 704.857 Td /F1 9.8 Tf [(e56176.)] TJ ET BT 26.250 685.452 Td /F1 9.8 Tf [(10.)] TJ ET BT 43.553 685.452 Td /F1 9.8 Tf [(Shaman J, Karspeck A \(2012\) Forecasting seasonal outbreaks of influenza. Proceedings of the National Academy of )] TJ ET BT 26.250 673.548 Td /F1 9.8 Tf [(Sciences 109: 20425-20430.)] TJ ET BT 26.250 654.143 Td /F1 9.8 Tf [(11.)] TJ ET BT 43.553 654.143 Td /F1 9.8 Tf [(Shaman J, Pitzer VE, Viboud C, Grenfell BT, Lipsitch M \(2010\) Absolute humidity and the seasonal onset of influenza in the )] TJ ET BT 26.250 642.238 Td /F1 9.8 Tf [(continental united states. PLoS Biol 8: e1000316.)] TJ ET BT 26.250 622.833 Td /F1 9.8 Tf [(12.)] TJ ET BT 43.553 622.833 Td /F1 9.8 Tf [(Barrett C, Bisset K, Leidig J, Marathe A, Marathe M \(2011\) Economic and social impact of influenza mitigation strategies by )] TJ ET BT 26.250 610.929 Td /F1 9.8 Tf [(demographic class. Epidemics 3: 1931.)] TJ ET BT 26.250 591.524 Td /F1 9.8 Tf [(13.)] TJ ET BT 43.553 591.524 Td /F1 9.8 Tf [(Halloran ME, Ferguson N, Eubank S, Longini I, Cummings D, et al. \(2008\) Modeling targeted layered containment of an )] TJ ET BT 26.250 579.619 Td /F1 9.8 Tf [(influenza pandemic in the United States. Proceedings of the National Academy of Sciences 105: 4639-4644.)] TJ ET BT 26.250 560.214 Td /F1 9.8 Tf [(14.)] TJ ET BT 43.553 560.214 Td /F1 9.8 Tf [(Nsoesie EO, Beckman RJ, Shashaani S, Nagaraj KS, Marathe MV \(2013\) A simulation optimization approach to epidemic )] TJ ET BT 26.250 548.310 Td /F1 9.8 Tf [(forecasting. PLoS ONE \(In Press\).)] TJ ET BT 26.250 528.905 Td /F1 9.8 Tf [(15.)] TJ ET BT 43.553 528.905 Td /F1 9.8 Tf [(Ginsberg J, Mohebbi M, Patel R, Brammer L, Smolinski M, et al. \(2008\) Detecting influenza epidemics using search engine )] TJ ET BT 26.250 517.000 Td /F1 9.8 Tf [(query data. Nature 457: 10121014.)] TJ ET BT 26.250 497.595 Td /F1 9.8 Tf [(16.)] TJ ET BT 43.553 497.595 Td /F1 9.8 Tf [(Bisset K, Chen J, Feng X, Kumar VSA, Marathe M \(2009\) Epifast: a fast algorithm for large scale realistic epidemic )] TJ ET BT 26.250 485.691 Td /F1 9.8 Tf [(simulations on distributed memory systems. In: Proceedings of the 23rd international conference on Supercomputing. ICS 09, )] TJ ET BT 26.250 473.786 Td /F1 9.8 Tf [(pp. 430439.)] TJ ET BT 26.250 454.381 Td /F1 9.8 Tf [(17.)] TJ ET BT 43.553 454.381 Td /F1 9.8 Tf [(Beckman R, Baggerly K, Mckay M \(1996\) Creating synthetic baseline populations. Transportation Research Part A: Policy )] TJ ET BT 26.250 442.476 Td /F1 9.8 Tf [(and Practice 30: 415-429.)] TJ ET BT 26.250 423.072 Td /F1 9.8 Tf [(18.)] TJ ET BT 43.553 423.072 Td /F1 9.8 Tf [(Speckman P, Vaughn K, Pas E \(1997a\) Generating household activity-travel patterns \(HATPs\) for synthetic populations. )] TJ ET BT 26.250 411.167 Td /F1 9.8 Tf [(Transportation Research Board 1997 Annual Meeting.)] TJ ET BT 26.250 391.762 Td /F1 9.8 Tf [(19.)] TJ ET BT 43.553 391.762 Td /F1 9.8 Tf [(Speckman P, Vaughn K, Pas E \(1997b\) A continuous spatial interaction model: Application to home-work travel in Portland, )] TJ ET BT 26.250 379.857 Td /F1 9.8 Tf [(Oregon. Transportation Research Board 1997 Annual Meeting.)] TJ ET BT 26.250 360.453 Td /F1 9.8 Tf [(20.)] TJ ET BT 43.553 360.453 Td /F1 9.8 Tf [(Barrett C, Beckman R, Khan M, Kumar VSA, Marathe M, et al. \(2009\) Generation and analysis of large synthetic social )] TJ ET BT 26.250 348.548 Td /F1 9.8 Tf [(contact networks. In: Winter Simulation Conference. WSC 09, pp. 1003 1014.)] TJ ET BT 26.250 329.143 Td /F1 9.8 Tf [(21.)] TJ ET BT 43.553 329.143 Td /F1 9.8 Tf [(TRBC \(1995-2003\) 5th-9th Biennial National Academies Transportation Research Board Conferences on Application Of )] TJ ET BT 26.250 317.238 Td /F1 9.8 Tf [(Transportation Planning Methods.)] TJ ET BT 26.250 297.834 Td /F1 9.8 Tf [(22.)] TJ ET BT 43.553 297.834 Td /F1 9.8 Tf [(Bowman J, Bradley M, Shiftan Y, Lawton TK, Ben-Akiva M \(1998\) Demonstration of an activity based model system for )] TJ ET BT 26.250 285.929 Td /F1 9.8 Tf [(Portland. In: Proceedings of the 8th World Conference on Transport Research.)] TJ ET BT 26.250 266.524 Td /F1 9.8 Tf [(23.)] TJ ET BT 43.553 266.524 Td /F1 9.8 Tf [(Bailey N \(1975\) The Mathematical Theory of Infectious Diseases and its Applications. London: Griffin.)] TJ ET BT 26.250 247.119 Td /F1 9.8 Tf [(24.)] TJ ET BT 43.553 247.119 Td /F1 9.8 Tf [(Elveback L, Fox J, Ackerman E, Langworthy A, Boyd M, et al. \(1976\) American Journal of Epidemiology 103: 152-165.)] TJ ET BT 26.250 227.715 Td /F1 9.8 Tf [(25.)] TJ ET BT 43.553 227.715 Td /F1 9.8 Tf [(Longini I, Nizam A, Xu S, Ungchusak K, Hanshaworakul W, et al. \(2005\) Containing pandemic influenza at the source. )] TJ ET BT 26.250 215.810 Td /F1 9.8 Tf [(Science 309: 1083-1087.)] TJ ET BT 26.250 196.405 Td /F1 9.8 Tf [(26.)] TJ ET BT 43.553 196.405 Td /F1 9.8 Tf [(Hethcote HW \(2000\) The mathematics of infectious diseases. SIAM Review 42: 599653.)] TJ ET BT 26.250 177.000 Td /F1 9.8 Tf [(27.)] TJ ET BT 43.553 177.000 Td /F1 9.8 Tf [(Eubank S, Guclu H, Kumar VSA, Marathe M, Srinivasan A, et al. \(2004\) Modelling disease outbreaks in realistic urban )] TJ ET BT 26.250 165.096 Td /F1 9.8 Tf [(social networks. Nature 429: 180-184.)] TJ ET BT 26.250 145.691 Td /F1 9.8 Tf [(28.)] TJ ET BT 43.553 145.691 Td /F1 9.8 Tf [(Newman M \(2003\) The structure and function of complex networks. SIAM Review 45: 167-256.)] TJ ET BT 26.250 126.286 Td /F1 9.8 Tf [(29.)] TJ ET BT 43.553 126.286 Td /F1 9.8 Tf [(Eubank S, Barrett C, Beckman R, Bisset K, Durbeck L, et al. \(2010\) Detail in network models of epidemiology: are we there )] TJ ET BT 26.250 114.381 Td /F1 9.8 Tf [(yet? Journal of Biological Dynamics 4: 446-455.)] TJ ET BT 26.250 94.977 Td /F1 9.8 Tf [(30.)] TJ ET BT 43.553 94.977 Td /F1 9.8 Tf [(Nsoesie EO, Beckman RJ, Marathe MV \(2012\) Sensitivity analysis of an individual-based model for simulation of influenza )] TJ ET BT 26.250 83.072 Td /F1 9.8 Tf [(epidemics. 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London: Griffin.)] TJ ET BT 26.250 247.119 Td /F1 9.8 Tf [(24.)] TJ ET BT 43.553 247.119 Td /F1 9.8 Tf [(Elveback L, Fox J, Ackerman E, Langworthy A, Boyd M, et al. \(1976\) American Journal of Epidemiology 103: 152-165.)] TJ ET BT 26.250 227.715 Td /F1 9.8 Tf [(25.)] TJ ET BT 43.553 227.715 Td /F1 9.8 Tf [(Longini I, Nizam A, Xu S, Ungchusak K, Hanshaworakul W, et al. \(2005\) Containing pandemic influenza at the source. )] TJ ET BT 26.250 215.810 Td /F1 9.8 Tf [(Science 309: 1083-1087.)] TJ ET BT 26.250 196.405 Td /F1 9.8 Tf [(26.)] TJ ET BT 43.553 196.405 Td /F1 9.8 Tf [(Hethcote HW \(2000\) The mathematics of infectious diseases. SIAM Review 42: 599653.)] TJ ET BT 26.250 177.000 Td /F1 9.8 Tf [(27.)] TJ ET BT 43.553 177.000 Td /F1 9.8 Tf [(Eubank S, Guclu H, Kumar VSA, Marathe M, Srinivasan A, et al. \(2004\) Modelling disease outbreaks in realistic urban )] TJ ET BT 26.250 165.096 Td /F1 9.8 Tf [(social networks. Nature 429: 180-184.)] TJ ET BT 26.250 145.691 Td /F1 9.8 Tf [(28.)] TJ ET BT 43.553 145.691 Td /F1 9.8 Tf [(Newman M \(2003\) The structure and function of complex networks. SIAM Review 45: 167-256.)] TJ ET BT 26.250 126.286 Td /F1 9.8 Tf [(29.)] TJ ET BT 43.553 126.286 Td /F1 9.8 Tf [(Eubank S, Barrett C, Beckman R, Bisset K, Durbeck L, et al. \(2010\) Detail in network models of epidemiology: are we there )] TJ ET BT 26.250 114.381 Td /F1 9.8 Tf [(yet? Journal of Biological Dynamics 4: 446-455.)] TJ ET BT 26.250 94.977 Td /F1 9.8 Tf [(30.)] TJ ET BT 43.553 94.977 Td /F1 9.8 Tf [(Nsoesie EO, Beckman RJ, Marathe MV \(2012\) Sensitivity analysis of an individual-based model for simulation of influenza )] TJ ET BT 26.250 83.072 Td /F1 9.8 Tf [(epidemics. PLoS ONE 7: e45414.)] TJ ET BT 26.250 63.667 Td /F1 9.8 Tf [(31.)] TJ ET BT 43.553 63.667 Td /F1 9.8 Tf [(Ajelli M, Goncalves B, Balcan D, Colizza V, Hu H, et al. \(2010\) Comparing large-scale computational approaches to )] TJ ET BT 26.250 51.762 Td /F1 9.8 Tf [(epidemic modeling: Agent-based versus structured metapopulation models. BMC Infectious Diseases 10: 190.)] TJ ET Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(8)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Outbreaks)] TJ ET Q endstream endobj 490 0 obj << /Type /Page /Parent 3 0 R /Contents 491 0 R >> endobj 491 0 obj << /Length 4513 >> stream 0.271 0.267 0.267 rg q 15.000 629.262 577.500 147.738 re W n 0.271 0.267 0.267 rg BT 26.250 759.976 Td /F1 9.8 Tf [(32.)] TJ ET BT 43.553 759.976 Td /F1 9.8 Tf [(Wallinga J, Teunis P \(2004\) Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of )] TJ ET BT 26.250 748.071 Td /F1 9.8 Tf [(control measures. 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Nature 494: 155156.)] TJ ET BT 26.250 658.548 Td /F1 9.8 Tf [(36.)] TJ ET BT 43.553 658.548 Td /F1 9.8 Tf [(Carrat F, Vergu E, Ferguson NM, Lemaitre M, Cauchemez S, et al. \(2008\) Time Lines of Infection and Disease in Human )] TJ ET BT 26.250 646.643 Td /F1 9.8 Tf [(Influenza: A Review of Volunteer Challenge Studies. American Journal of Epidemiology 167 \(7\): 775-785.)] TJ ET Q q 15.000 629.262 577.500 147.738 re W n 0.271 0.267 0.267 rg BT 26.250 759.976 Td /F1 9.8 Tf [(32.)] TJ ET BT 43.553 759.976 Td /F1 9.8 Tf [(Wallinga J, Teunis P \(2004\) Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of )] TJ ET BT 26.250 748.071 Td /F1 9.8 Tf [(control measures. American Journal of Epidemiology 160: 509-516.)] TJ ET BT 26.250 728.667 Td /F1 9.8 Tf [(33.)] TJ ET BT 43.553 728.667 Td /F1 9.8 Tf [(Robbins H, Monro S \(1951\) A stochastic approximation method. Annals of Mathematical Statistics 22: 400-407.)] TJ ET BT 26.250 709.262 Td /F1 9.8 Tf [(34.)] TJ ET BT 43.553 709.262 Td /F1 9.8 Tf [(Truscott J, Fraser C, Cauchemez S, Meeyai A, Hinsley W, et al. \(2012\) Essential epidemiological mechanisms underpinning )] TJ ET BT 26.250 697.357 Td /F1 9.8 Tf [(the transmission dynamics of seasonal influenza. Journal of The Royal Society Interface 9: 304-312.)] TJ ET BT 26.250 677.952 Td /F1 9.8 Tf [(35.)] TJ ET BT 43.553 677.952 Td /F1 9.8 Tf [(Butler D \(2013\) When Google got flu wrong. Nature 494: 155156.)] TJ ET BT 26.250 658.548 Td /F1 9.8 Tf [(36.)] TJ ET BT 43.553 658.548 Td /F1 9.8 Tf [(Carrat F, Vergu E, Ferguson NM, Lemaitre M, Cauchemez S, et al. \(2008\) Time Lines of Infection and Disease in Human )] TJ ET BT 26.250 646.643 Td /F1 9.8 Tf [(Influenza: A Review of Volunteer Challenge Studies. American Journal of Epidemiology 167 \(7\): 775-785.)] TJ ET Q q 15.000 629.262 577.500 147.738 re W n 0.271 0.267 0.267 rg BT 26.250 759.976 Td /F1 9.8 Tf [(32.)] TJ ET BT 43.553 759.976 Td /F1 9.8 Tf [(Wallinga J, Teunis P \(2004\) Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of )] TJ ET BT 26.250 748.071 Td /F1 9.8 Tf [(control measures. American Journal of Epidemiology 160: 509-516.)] TJ ET BT 26.250 728.667 Td /F1 9.8 Tf [(33.)] TJ ET BT 43.553 728.667 Td /F1 9.8 Tf [(Robbins H, Monro S \(1951\) A stochastic approximation method. Annals of Mathematical Statistics 22: 400-407.)] TJ ET BT 26.250 709.262 Td /F1 9.8 Tf [(34.)] TJ ET BT 43.553 709.262 Td /F1 9.8 Tf [(Truscott J, Fraser C, Cauchemez S, Meeyai A, Hinsley W, et al. \(2012\) Essential epidemiological mechanisms underpinning )] TJ ET BT 26.250 697.357 Td /F1 9.8 Tf [(the transmission dynamics of seasonal influenza. Journal of The Royal Society Interface 9: 304-312.)] TJ ET BT 26.250 677.952 Td /F1 9.8 Tf [(35.)] TJ ET BT 43.553 677.952 Td /F1 9.8 Tf [(Butler D \(2013\) When Google got flu wrong. Nature 494: 155156.)] TJ ET BT 26.250 658.548 Td /F1 9.8 Tf [(36.)] TJ ET BT 43.553 658.548 Td /F1 9.8 Tf [(Carrat F, Vergu E, Ferguson NM, Lemaitre M, Cauchemez S, et al. \(2008\) Time Lines of Infection and Disease in Human )] TJ ET BT 26.250 646.643 Td /F1 9.8 Tf [(Influenza: A Review of Volunteer Challenge Studies. 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