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/Title (Estimate of Novel Influenza A/H1N1 cases in Mexico at the early stage of the pandemic with a spatially structured epidemic model � PLOS Currents Influenza)
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BT 15.000 718.042 Td /F2 21.0 Tf  [(Estimate of Novel Influenza A/H1N1 cases in Mexico at the )] TJ ET
BT 15.000 693.094 Td /F2 21.0 Tf  [(early stage of the pandemic with a spatially structured epidemic )] TJ ET
BT 15.000 668.146 Td /F2 21.0 Tf  [(model)] TJ ET
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BT 15.000 650.140 Td /F3 9.8 Tf  [(November 17, 2009)] TJ ET
BT 96.510 650.140 Td /F3 9.8 Tf  [(�)] TJ ET
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BT 101.385 650.140 Td /F3 9.8 Tf  [(Influenza)] TJ ET
BT 26.250 638.299 Td /F1 9.8 Tf  [(Vittoria Colizza)] TJ ET
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BT 91.263 638.299 Td /F1 9.8 Tf  [(, )] TJ ET
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BT 96.684 638.299 Td /F1 9.8 Tf  [(Alessandro Vespignani)] TJ ET
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BT 201.818 638.299 Td /F1 9.8 Tf  [(Nicola Perra)] TJ ET
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BT 512.863 638.299 Td /F1 9.8 Tf  [(Daniela Paolotti)] TJ ET
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BT 31.671 626.394 Td /F1 9.8 Tf  [(Wouter Van den Broeck)] TJ ET
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BT 276.601 626.394 Td /F1 9.8 Tf  [(Jose J. Ramasco)] TJ ET
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BT 26.250 614.490 Td /F1 9.8 Tf  [(Colizza V, Vespignani A, Perra N, Poletto C, Gon�alves B, Hu H, Balcan D, Paolotti D, Van den Broeck W, Tizzoni M, Bajardi )] TJ ET
BT 568.126 614.490 Td /F1 9.8 Tf  [(P, )] TJ ET
BT 26.250 602.585 Td /F1 9.8 Tf  [(Ramasco JJ. Estimate of Novel Influenza A/H1N1 cases in Mexico at the early stage of the pandemic with a spatially structured )] TJ ET
BT 26.250 590.680 Td /F1 9.8 Tf  [(epidemic model. PLOS Currents Influenza. 2009 Nov 17 . Edition 1. doi: 10.1371/currents.RRN1129.)] TJ ET
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BT 26.250 561.578 Td /F4 12.0 Tf  [(Abstract)] TJ ET
BT 26.250 541.623 Td /F1 9.8 Tf  [(Determining the number of cases in an epidemic is fundamental to properly evaluate several disease features of high relevance )] TJ ET
BT 26.250 529.719 Td /F1 9.8 Tf  [(for public health policies such as mortality, morbidity or hospitalization rates. Surveillance efforts are however incomplete )] TJ ET
BT 26.250 517.814 Td /F1 9.8 Tf  [(especially at the early stage of an outbreak due to the ongoing learning process about the disease characteristics. An example )] TJ ET
BT 26.250 505.909 Td /F1 9.8 Tf  [(of this is represented by the number of H1N1 influenza cases in Mexico during the first months of the current pandemic. Several )] TJ ET
BT 26.250 494.004 Td /F1 9.8 Tf  [(estimates using backtrack calculation based on imported cases from Mexico in other countries point out that the actual number )] TJ ET
BT 26.250 482.100 Td /F1 9.8 Tf  [(of cases was likely orders of magnitude larger than the number of confirmed cases.)] TJ ET
BT 26.250 462.695 Td /F1 9.8 Tf  [(Realistic computational models fed with the best available estimates of the basic disease parameters can provide an ab-initio )] TJ ET
BT 26.250 450.790 Td /F1 9.8 Tf  [(calculation of the number of cases in Mexico as other countries. Here we use the Global Epidemic and Mobility \(GLEaM\) model )] TJ ET
BT 26.250 438.885 Td /F1 9.8 Tf  [(to obtain estimates of the size of the epidemic in Mexico as well as of imported cases at the end of April and beginning of May. )] TJ ET
BT 26.250 426.981 Td /F1 9.8 Tf  [(We find that the reference range for the number of cases in Mexico on April 30th is 121,000 to 1,394,000 in good agreement )] TJ ET
BT 26.250 415.076 Td /F1 9.8 Tf  [(with the recent estimates by Lipsitch et al. [M. Lipsitch, PloS One 4:e6895 \(2009\)]. The number of imported cases from Mexico )] TJ ET
BT 26.250 403.171 Td /F1 9.8 Tf  [(in several countries is found to be in good agreement with the surveillance data.)] TJ ET
BT 26.250 366.569 Td /F4 12.0 Tf  [(Funding Statement)] TJ ET
BT 26.250 346.614 Td /F1 9.8 Tf  [(This work has been partially supported by the NIH, the NSF, the Lilly Endowment Foundation, DTRA, the ERC project EpiFor )] TJ ET
BT 26.250 334.710 Td /F1 9.8 Tf  [(and the FET projects Epiwork and Dynanets. The funders had no role in the preparation of the article.)] TJ ET
BT 26.250 305.607 Td /F4 12.0 Tf  [(Introduction)] TJ ET
BT 26.250 285.653 Td /F1 9.8 Tf  [(An unprecedented global effort in surveillance has been carried out by national and international health agencies for the current )] TJ ET
BT 26.250 273.748 Td /F1 9.8 Tf  [(novel Influenza A \(H1N1\) pandemic )] TJ ET
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BT 193.697 273.748 Td /F1 9.8 Tf  [(. Along with the institutional efforts, a combination of media attention and new )] TJ ET
BT 26.250 261.843 Td /F1 9.8 Tf  [(mechanisms for information retrieval, such as Internet, has allowed the prompt gathering of large amount of data that allow for )] TJ ET
BT 26.250 249.939 Td /F1 9.8 Tf  [(the first time the real-time analysis of a pandemic in such a detailed way. Unfortunately, the access and availability of data does )] TJ ET
BT 26.250 238.034 Td /F1 9.8 Tf  [(not imply reliability or accuracy. A paramount example is provided by the time evolution of the number of cases in each country. )] TJ ET
BT 26.250 226.129 Td /F1 9.8 Tf  [(In the case of influenza, the presence of asymptomatic cases or of cases showing mild symptoms who might not seek for )] TJ ET
BT 26.250 214.224 Td /F1 9.8 Tf  [(medical attention lead to an underascertainment of cases that is hard to estimate. Moreover, the monitoring of cases is )] TJ ET
BT 26.250 202.320 Td /F1 9.8 Tf  [(expected to change with time, from an enhanced surveillance at the start of the epidemic, followed by the ascertainment of more )] TJ ET
BT 26.250 190.415 Td /F1 9.8 Tf  [(severe cases, needing medical attention, hospitalization, and also confirmation of the infection. This is due to the large increase )] TJ ET
BT 26.250 178.510 Td /F1 9.8 Tf  [(in the number of cases overwhelming surveillance systems, which therefore relax their requirements as the epidemic )] TJ ET
BT 26.250 166.605 Td /F1 9.8 Tf  [(progresses due to limited capacity and high costs associated with systematic serological testing. For these reasons, after the )] TJ ET
BT 26.250 154.701 Td /F1 9.8 Tf  [(very initial stage of the outbreak, the number of confirmed cases tends to be a gross underestimation of the actual number of )] TJ ET
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BT 113.513 142.796 Td /F1 9.8 Tf  [(. On the other hand, reliable figures for the actual number of cases is the key to the estimate of parameters )] TJ ET
BT 26.250 130.891 Td /F1 9.8 Tf  [(such as the mortality, morbidity or hospitalization rates that are on their turn crucial in the policy making process. A paramount )] TJ ET
BT 26.250 118.986 Td /F1 9.8 Tf  [(example of this issue is provided by the worries caused by the early estimate of the fatality rate of the current H1N1 pandemic )] TJ ET
BT 26.250 107.082 Td /F1 9.8 Tf  [(from the Mexican data. As it turned out later, this number was inflated because the confirmed cases of infections were grossly )] TJ ET
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BT 150.884 95.177 Td /F1 9.8 Tf  [(. In particular, two studies have assessed the size of the epidemic in Mexico by analyzing the )] TJ ET
BT 26.250 83.272 Td /F1 9.8 Tf  [(number of H1N1 infected travelers arriving from Mexico detected by the surveillance systems of other countries in their attempt )] TJ ET
BT 26.250 71.367 Td /F1 9.8 Tf  [(to contain the epidemic )] TJ ET
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BT 150.904 71.367 Td /F1 9.8 Tf  [(. Both papers find that the estimate for the number of cases in Mexico at the end of April early May )] TJ ET
BT 26.250 59.463 Td /F1 9.8 Tf  [(is orders of magnitude larger than those confirmed by Mexican authorities. In particular, the calculation of Ref. )] TJ ET
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BT 512.882 59.463 Td /F1 9.8 Tf  [( that uses the )] TJ ET
BT 26.250 47.558 Td /F1 9.8 Tf  [(most updated data source gives a lower bound for the number of cases that is between 113,000 and 375,000 cases, to be )] TJ ET
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BT 15.000 693.094 Td /F2 21.0 Tf  [(early stage of the pandemic with a spatially structured epidemic )] TJ ET
BT 15.000 668.146 Td /F2 21.0 Tf  [(model)] TJ ET
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BT 15.000 650.140 Td /F3 9.8 Tf  [(November 17, 2009)] TJ ET
BT 96.510 650.140 Td /F3 9.8 Tf  [(�)] TJ ET
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BT 101.385 650.140 Td /F3 9.8 Tf  [(Influenza)] TJ ET
BT 26.250 638.299 Td /F1 9.8 Tf  [(Vittoria Colizza)] TJ ET
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BT 91.263 638.299 Td /F1 9.8 Tf  [(, )] TJ ET
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BT 96.684 638.299 Td /F1 9.8 Tf  [(Alessandro Vespignani)] TJ ET
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BT 201.818 638.299 Td /F1 9.8 Tf  [(Nicola Perra)] TJ ET
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BT 255.453 638.299 Td /F1 9.8 Tf  [(, )] TJ ET
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BT 260.874 638.299 Td /F1 9.8 Tf  [(Chiara Poletto)] TJ ET
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BT 322.650 638.299 Td /F1 9.8 Tf  [(, )] TJ ET
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BT 328.071 638.299 Td /F1 9.8 Tf  [(Bruno Gon�alves)] TJ ET
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BT 408.274 638.299 Td /F1 9.8 Tf  [(Hao Hu)] TJ ET
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BT 512.863 638.299 Td /F1 9.8 Tf  [(Daniela Paolotti)] TJ ET
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BT 31.671 626.394 Td /F1 9.8 Tf  [(Wouter Van den Broeck)] TJ ET
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BT 135.177 626.394 Td /F1 9.8 Tf  [(, )] TJ ET
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BT 140.598 626.394 Td /F1 9.8 Tf  [(Michele Tizzoni)] TJ ET
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BT 213.197 626.394 Td /F1 9.8 Tf  [(Paolo Bajardi)] TJ ET
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BT 276.601 626.394 Td /F1 9.8 Tf  [(Jose J. Ramasco)] TJ ET
0.271 0.267 0.267 rg
BT 26.250 614.490 Td /F1 9.8 Tf  [(Colizza V, Vespignani A, Perra N, Poletto C, Gon�alves B, Hu H, Balcan D, Paolotti D, Van den Broeck W, Tizzoni M, Bajardi )] TJ ET
BT 568.126 614.490 Td /F1 9.8 Tf  [(P, )] TJ ET
BT 26.250 602.585 Td /F1 9.8 Tf  [(Ramasco JJ. Estimate of Novel Influenza A/H1N1 cases in Mexico at the early stage of the pandemic with a spatially structured )] TJ ET
BT 26.250 590.680 Td /F1 9.8 Tf  [(epidemic model. PLOS Currents Influenza. 2009 Nov 17 . Edition 1. doi: 10.1371/currents.RRN1129.)] TJ ET
q
15.000 33.272 577.500 555.027 re W n
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BT 26.250 561.578 Td /F4 12.0 Tf  [(Abstract)] TJ ET
BT 26.250 541.623 Td /F1 9.8 Tf  [(Determining the number of cases in an epidemic is fundamental to properly evaluate several disease features of high relevance )] TJ ET
BT 26.250 529.719 Td /F1 9.8 Tf  [(for public health policies such as mortality, morbidity or hospitalization rates. Surveillance efforts are however incomplete )] TJ ET
BT 26.250 517.814 Td /F1 9.8 Tf  [(especially at the early stage of an outbreak due to the ongoing learning process about the disease characteristics. An example )] TJ ET
BT 26.250 505.909 Td /F1 9.8 Tf  [(of this is represented by the number of H1N1 influenza cases in Mexico during the first months of the current pandemic. Several )] TJ ET
BT 26.250 494.004 Td /F1 9.8 Tf  [(estimates using backtrack calculation based on imported cases from Mexico in other countries point out that the actual number )] TJ ET
BT 26.250 482.100 Td /F1 9.8 Tf  [(of cases was likely orders of magnitude larger than the number of confirmed cases.)] TJ ET
BT 26.250 462.695 Td /F1 9.8 Tf  [(Realistic computational models fed with the best available estimates of the basic disease parameters can provide an ab-initio )] TJ ET
BT 26.250 450.790 Td /F1 9.8 Tf  [(calculation of the number of cases in Mexico as other countries. Here we use the Global Epidemic and Mobility \(GLEaM\) model )] TJ ET
BT 26.250 438.885 Td /F1 9.8 Tf  [(to obtain estimates of the size of the epidemic in Mexico as well as of imported cases at the end of April and beginning of May. )] TJ ET
BT 26.250 426.981 Td /F1 9.8 Tf  [(We find that the reference range for the number of cases in Mexico on April 30th is 121,000 to 1,394,000 in good agreement )] TJ ET
BT 26.250 415.076 Td /F1 9.8 Tf  [(with the recent estimates by Lipsitch et al. [M. Lipsitch, PloS One 4:e6895 \(2009\)]. The number of imported cases from Mexico )] TJ ET
BT 26.250 403.171 Td /F1 9.8 Tf  [(in several countries is found to be in good agreement with the surveillance data.)] TJ ET
BT 26.250 366.569 Td /F4 12.0 Tf  [(Funding Statement)] TJ ET
BT 26.250 346.614 Td /F1 9.8 Tf  [(This work has been partially supported by the NIH, the NSF, the Lilly Endowment Foundation, DTRA, the ERC project EpiFor )] TJ ET
BT 26.250 334.710 Td /F1 9.8 Tf  [(and the FET projects Epiwork and Dynanets. The funders had no role in the preparation of the article.)] TJ ET
BT 26.250 305.607 Td /F4 12.0 Tf  [(Introduction)] TJ ET
BT 26.250 285.653 Td /F1 9.8 Tf  [(An unprecedented global effort in surveillance has been carried out by national and international health agencies for the current )] TJ ET
BT 26.250 273.748 Td /F1 9.8 Tf  [(novel Influenza A \(H1N1\) pandemic )] TJ ET
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BT 182.855 273.748 Td /F1 9.8 Tf  [([1])] TJ ET
0.271 0.267 0.267 rg
BT 193.697 273.748 Td /F1 9.8 Tf  [(. Along with the institutional efforts, a combination of media attention and new )] TJ ET
BT 26.250 261.843 Td /F1 9.8 Tf  [(mechanisms for information retrieval, such as Internet, has allowed the prompt gathering of large amount of data that allow for )] TJ ET
BT 26.250 249.939 Td /F1 9.8 Tf  [(the first time the real-time analysis of a pandemic in such a detailed way. Unfortunately, the access and availability of data does )] TJ ET
BT 26.250 238.034 Td /F1 9.8 Tf  [(not imply reliability or accuracy. A paramount example is provided by the time evolution of the number of cases in each country. )] TJ ET
BT 26.250 226.129 Td /F1 9.8 Tf  [(In the case of influenza, the presence of asymptomatic cases or of cases showing mild symptoms who might not seek for )] TJ ET
BT 26.250 214.224 Td /F1 9.8 Tf  [(medical attention lead to an underascertainment of cases that is hard to estimate. Moreover, the monitoring of cases is )] TJ ET
BT 26.250 202.320 Td /F1 9.8 Tf  [(expected to change with time, from an enhanced surveillance at the start of the epidemic, followed by the ascertainment of more )] TJ ET
BT 26.250 190.415 Td /F1 9.8 Tf  [(severe cases, needing medical attention, hospitalization, and also confirmation of the infection. This is due to the large increase )] TJ ET
BT 26.250 178.510 Td /F1 9.8 Tf  [(in the number of cases overwhelming surveillance systems, which therefore relax their requirements as the epidemic )] TJ ET
BT 26.250 166.605 Td /F1 9.8 Tf  [(progresses due to limited capacity and high costs associated with systematic serological testing. For these reasons, after the )] TJ ET
BT 26.250 154.701 Td /F1 9.8 Tf  [(very initial stage of the outbreak, the number of confirmed cases tends to be a gross underestimation of the actual number of )] TJ ET
BT 26.250 142.796 Td /F1 9.8 Tf  [(infections )] TJ ET
0.267 0.267 0.267 rg
BT 70.144 142.796 Td /F1 9.8 Tf  [([2])] TJ ET
BT 80.987 142.796 Td /F1 9.8 Tf  [([3])] TJ ET
BT 91.829 142.796 Td /F1 9.8 Tf  [([4])] TJ ET
BT 102.671 142.796 Td /F1 9.8 Tf  [([5])] TJ ET
0.271 0.267 0.267 rg
BT 113.513 142.796 Td /F1 9.8 Tf  [(. On the other hand, reliable figures for the actual number of cases is the key to the estimate of parameters )] TJ ET
BT 26.250 130.891 Td /F1 9.8 Tf  [(such as the mortality, morbidity or hospitalization rates that are on their turn crucial in the policy making process. A paramount )] TJ ET
BT 26.250 118.986 Td /F1 9.8 Tf  [(example of this issue is provided by the worries caused by the early estimate of the fatality rate of the current H1N1 pandemic )] TJ ET
BT 26.250 107.082 Td /F1 9.8 Tf  [(from the Mexican data. As it turned out later, this number was inflated because the confirmed cases of infections were grossly )] TJ ET
BT 26.250 95.177 Td /F1 9.8 Tf  [(underestimated in Mexico )] TJ ET
0.267 0.267 0.267 rg
BT 140.042 95.177 Td /F1 9.8 Tf  [([2])] TJ ET
0.271 0.267 0.267 rg
BT 150.884 95.177 Td /F1 9.8 Tf  [(. In particular, two studies have assessed the size of the epidemic in Mexico by analyzing the )] TJ ET
BT 26.250 83.272 Td /F1 9.8 Tf  [(number of H1N1 infected travelers arriving from Mexico detected by the surveillance systems of other countries in their attempt )] TJ ET
BT 26.250 71.367 Td /F1 9.8 Tf  [(to contain the epidemic )] TJ ET
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BT 129.220 71.367 Td /F1 9.8 Tf  [([5])] TJ ET
BT 140.062 71.367 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 150.904 71.367 Td /F1 9.8 Tf  [(. Both papers find that the estimate for the number of cases in Mexico at the end of April early May )] TJ ET
BT 26.250 59.463 Td /F1 9.8 Tf  [(is orders of magnitude larger than those confirmed by Mexican authorities. In particular, the calculation of Ref. )] TJ ET
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BT 276.601 626.394 Td /F1 9.8 Tf  [(Jose J. Ramasco)] TJ ET
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BT 26.250 561.578 Td /F4 12.0 Tf  [(Abstract)] TJ ET
BT 26.250 541.623 Td /F1 9.8 Tf  [(Determining the number of cases in an epidemic is fundamental to properly evaluate several disease features of high relevance )] TJ ET
BT 26.250 529.719 Td /F1 9.8 Tf  [(for public health policies such as mortality, morbidity or hospitalization rates. Surveillance efforts are however incomplete )] TJ ET
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BT 26.250 366.569 Td /F4 12.0 Tf  [(Funding Statement)] TJ ET
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BT 26.250 305.607 Td /F4 12.0 Tf  [(Introduction)] TJ ET
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0.271 0.267 0.267 rg
q
15.000 31.277 577.500 745.723 re W n
0.271 0.267 0.267 rg
BT 26.250 767.476 Td /F1 9.8 Tf  [(compared with the official report that indicate 3,350 confirmed cases )] TJ ET
0.267 0.267 0.267 rg
BT 323.216 767.476 Td /F1 9.8 Tf  [([7])] TJ ET
0.271 0.267 0.267 rg
BT 334.058 767.476 Td /F1 9.8 Tf  [(.)] TJ ET
BT 26.250 748.071 Td /F1 9.8 Tf  [(Here, we use the Global Epidemic and Mobility \(GLEaM\) model )] TJ ET
0.267 0.267 0.267 rg
BT 302.594 748.071 Td /F1 9.8 Tf  [([8])] TJ ET
BT 313.436 748.071 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 324.278 748.071 Td /F1 9.8 Tf  [( to provide a computational ab-initio evaluation of the early )] TJ ET
BT 26.250 736.167 Td /F1 9.8 Tf  [(size of the outbreak in Mexico and the fluxes of infected travelers to other countries. The GLEaM model is a spatially structured )] TJ ET
BT 26.250 724.262 Td /F1 9.8 Tf  [(metapopulation epidemic model )] TJ ET
0.267 0.267 0.267 rg
BT 166.601 724.262 Td /F1 9.8 Tf  [([8])] TJ ET
BT 177.443 724.262 Td /F1 9.8 Tf  [([9])] TJ ET
BT 188.285 724.262 Td /F1 9.8 Tf  [([10])] TJ ET
BT 204.548 724.262 Td /F1 9.8 Tf  [([11])] TJ ET
BT 220.811 724.262 Td /F1 9.8 Tf  [([12])] TJ ET
BT 237.074 724.262 Td /F1 9.8 Tf  [([13])] TJ ET
BT 253.337 724.262 Td /F1 9.8 Tf  [([14])] TJ ET
BT 269.600 724.262 Td /F1 9.8 Tf  [([15])] TJ ET
BT 285.863 724.262 Td /F1 9.8 Tf  [([16])] TJ ET
BT 302.126 724.262 Td /F1 9.8 Tf  [([17])] TJ ET
BT 318.389 724.262 Td /F1 9.8 Tf  [([18])] TJ ET
BT 334.652 724.262 Td /F1 9.8 Tf  [([19])] TJ ET
BT 350.915 724.262 Td /F1 9.8 Tf  [([20])] TJ ET
BT 367.178 724.262 Td /F1 9.8 Tf  [([21])] TJ ET
0.271 0.267 0.267 rg
BT 383.441 724.262 Td /F1 9.8 Tf  [(, that allows the generation of stochastic )] TJ ET
BT 26.250 712.357 Td /F1 9.8 Tf  [(realizations of the worldwide unfolding of the epidemic, with mobility processes entirely based on real data. Once the disease )] TJ ET
BT 26.250 700.452 Td /F1 9.8 Tf  [(parameters and initial conditions based on available data are defined, the model generates in-silico epidemics for which we can )] TJ ET
BT 26.250 688.548 Td /F1 9.8 Tf  [(gather information such as prevalence, morbidity, number of secondary cases, number of imported cases and many others for )] TJ ET
BT 26.250 676.643 Td /F1 9.8 Tf  [(each subpopulation and with a time resolution of one day. In Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 309.156 676.643 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 319.998 676.643 Td /F1 9.8 Tf  [(, the GLEaM model has been used to perform a Maximum )] TJ ET
BT 26.250 664.738 Td /F1 9.8 Tf  [(Likelihood Estimate \(MLE\) of the transmission potential of the current H1N1 pandemic. Here we use the best estimate )] TJ ET
BT 26.250 652.833 Td /F1 9.8 Tf  [(parameters from Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 121.069 652.833 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 131.911 652.833 Td /F1 9.8 Tf  [( to simulate 2�10 )] TJ ET
BT 209.140 656.722 Td /F1 8.7 Tf  [(3)] TJ ET
BT 213.959 652.833 Td /F1 9.8 Tf  [( stochastic simulations of the current pandemic and provide an estimate of the )] TJ ET
BT 26.250 640.929 Td /F1 9.8 Tf  [(number of H1N1 cases in Mexico at the date of May the 8th. This is an ab-initio computational estimate and to further cross-)] TJ ET
BT 26.250 629.024 Td /F1 9.8 Tf  [(validate our results, we compare the number of infected individuals traveling from Mexico to other countries from our simulations )] TJ ET
BT 26.250 617.119 Td /F1 9.8 Tf  [(and compare these numbers with surveillance reports )] TJ ET
0.267 0.267 0.267 rg
BT 260.338 617.119 Td /F1 9.8 Tf  [([6])] TJ ET
BT 271.180 617.119 Td /F1 9.8 Tf  [([22])] TJ ET
BT 287.443 617.119 Td /F1 9.8 Tf  [([23])] TJ ET
BT 303.706 617.119 Td /F1 9.8 Tf  [([24])] TJ ET
0.271 0.267 0.267 rg
BT 319.969 617.119 Td /F1 9.8 Tf  [(. We find in our simulations that in Mexico as of the date of )] TJ ET
BT 26.250 605.214 Td /F1 9.8 Tf  [(May the 8th the symptomatic cases 95% reference range is 121,000 to 1,394,000. This value is in good agreement with the )] TJ ET
BT 26.250 593.310 Td /F1 9.8 Tf  [(lower bound estimate of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 153.058 593.310 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 163.900 593.310 Td /F1 9.8 Tf  [(. The number of infected individuals with travel history from Mexico in countries such as US, )] TJ ET
BT 26.250 581.405 Td /F1 9.8 Tf  [(Canada, Spain and UK is also within the confidence range of our simulations. These results provide further support to the claim )] TJ ET
BT 26.250 569.500 Td /F1 9.8 Tf  [(that the number of confirmed H1N1 cases in Mexico is only a very small fraction of the actually occurred cases.)] TJ ET
BT 26.250 532.898 Td /F4 12.0 Tf  [(Materials and Methods)] TJ ET
BT 26.250 512.943 Td /F1 9.8 Tf  [(The global epidemic and mobility metapopulation \(GLEaM\) model is based on a geographically structured metapopulation )] TJ ET
BT 26.250 501.039 Td /F1 9.8 Tf  [(approach )] TJ ET
0.267 0.267 0.267 rg
BT 69.608 501.039 Td /F1 9.8 Tf  [([8])] TJ ET
BT 80.450 501.039 Td /F1 9.8 Tf  [([9])] TJ ET
BT 91.292 501.039 Td /F1 9.8 Tf  [([10])] TJ ET
BT 107.555 501.039 Td /F1 9.8 Tf  [([11])] TJ ET
BT 123.818 501.039 Td /F1 9.8 Tf  [([12])] TJ ET
BT 140.081 501.039 Td /F1 9.8 Tf  [([13])] TJ ET
BT 156.344 501.039 Td /F1 9.8 Tf  [([14])] TJ ET
BT 172.607 501.039 Td /F1 9.8 Tf  [([15])] TJ ET
BT 188.870 501.039 Td /F1 9.8 Tf  [([16])] TJ ET
BT 205.133 501.039 Td /F1 9.8 Tf  [([17])] TJ ET
BT 221.396 501.039 Td /F1 9.8 Tf  [([18])] TJ ET
BT 237.659 501.039 Td /F1 9.8 Tf  [([19])] TJ ET
BT 253.922 501.039 Td /F1 9.8 Tf  [([20])] TJ ET
BT 270.185 501.039 Td /F1 9.8 Tf  [([21])] TJ ET
BT 286.448 501.039 Td /F1 9.8 Tf  [([25])] TJ ET
0.271 0.267 0.267 rg
BT 302.711 501.039 Td /F1 9.8 Tf  [(. GLEaM is composed of three layers. The first one is the )] TJ ET
BT 26.250 489.134 Td /F1 9.8 Tf  [(population layer that integrates distinct census areas for a total of 3362 subpopulations in 220 countries of the world. The )] TJ ET
BT 26.250 477.229 Td /F1 9.8 Tf  [(census areas are defined by a Voronoi-like tessellation process that partition the world surface. Given a set of points S in the )] TJ ET
BT 26.250 465.324 Td /F1 9.8 Tf  [(plane, which are the Voronoi sites, each site s has a Voronoi cell V\(s\) consisting of all points closer to s than to any other site. In )] TJ ET
BT 26.250 453.420 Td /F1 9.8 Tf  [(our partition we use 3362 major transportation hubs in the world as the Voronoi sites. The boundaries of each subpopulation are )] TJ ET
BT 26.250 441.515 Td /F1 9.8 Tf  [(defined by all the points in the plane that are equidistant to two sites. For each area defined by the cell boundaries and the )] TJ ET
BT 26.250 429.610 Td /F1 9.8 Tf  [(Voronoi process, the population is obtained from the site of the �Gridded Population of the World� project of SEDAC \(Columbia )] TJ ET
BT 26.250 417.705 Td /F1 9.8 Tf  [(University\) )] TJ ET
0.267 0.267 0.267 rg
BT 75.000 417.705 Td /F1 9.8 Tf  [([26])] TJ ET
0.271 0.267 0.267 rg
BT 91.263 417.705 Td /F1 9.8 Tf  [( that provides population estimates worldwide for cells of 15 � 15 minutes of arc. The second layer of the model )] TJ ET
BT 26.250 405.801 Td /F1 9.8 Tf  [(is composed by the human mobility flows among the census areas. We consider both commuting flows collected from various )] TJ ET
BT 26.250 393.896 Td /F1 9.8 Tf  [(sources in more than 30 countries and the airline traffic provided by IATA )] TJ ET
0.267 0.267 0.267 rg
BT 343.808 393.896 Td /F1 9.8 Tf  [([27])] TJ ET
0.271 0.267 0.267 rg
BT 360.070 393.896 Td /F1 9.8 Tf  [( and OAG )] TJ ET
0.267 0.267 0.267 rg
BT 406.139 393.896 Td /F1 9.8 Tf  [([28])] TJ ET
0.271 0.267 0.267 rg
BT 422.402 393.896 Td /F1 9.8 Tf  [(. Further details concerning the )] TJ ET
BT 26.250 381.991 Td /F1 9.8 Tf  [(composition of GLEaM and the integration of its three layers for a practical simulation of epidemic spreading are given in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 567.609 381.991 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 26.250 370.086 Td /F1 9.8 Tf  [(. The third layer of the model concerns the disease dynamics used to model the disease evolution. We adopt a SEIR-like )] TJ ET
BT 26.250 358.182 Td /F1 9.8 Tf  [(compartmentalization framework in which separate compartments for symptomatic traveling and not traveling, as well as )] TJ ET
BT 26.250 346.277 Td /F1 9.8 Tf  [(asymptomatic individuals are included in each different subpopulations. The infection dynamics takes place within each )] TJ ET
BT 26.250 334.372 Td /F1 9.8 Tf  [(subpopulation and assumes the classic influenza-like-illness compartmentalization in which each individual is classified by one )] TJ ET
BT 26.250 322.467 Td /F1 9.8 Tf  [(of the discrete states such as susceptible, latent, infectious symptomatic, infectious non-symptomatic or permanently )] TJ ET
BT 26.250 310.563 Td /F1 9.8 Tf  [(recovered/removed. All transitions are modeled through binomial and multinomial processes to ensure the discrete and )] TJ ET
BT 26.250 298.658 Td /F1 9.8 Tf  [(stochastic nature of the processes. A full definition of the model is reported in Ref )] TJ ET
0.267 0.267 0.267 rg
BT 379.044 298.658 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 389.886 298.658 Td /F1 9.8 Tf  [(.)] TJ ET
BT 26.250 279.253 Td /F1 9.8 Tf  [(It is also worth stressing here some of the model assumptions. The model is not an agent-based model and does not include )] TJ ET
BT 26.250 267.348 Td /F1 9.8 Tf  [(additional structure within a subpopulation, therefore it cannot provide detailed information at the level of households or )] TJ ET
BT 26.250 255.444 Td /F1 9.8 Tf  [(workplaces. The fraction of infected population is likely overestimated because of the assumptions of an entirely susceptible )] TJ ET
BT 26.250 243.539 Td /F1 9.8 Tf  [(populations and of subpopulations with homogeneous mixing. Current data on the severity of the pandemic has revealed an age )] TJ ET
BT 26.250 231.634 Td /F1 9.8 Tf  [(pattern for influenza attack rate shifted towards the younger age classes of the population )] TJ ET
0.267 0.267 0.267 rg
BT 414.836 231.634 Td /F1 9.8 Tf  [([5])] TJ ET
BT 425.678 231.634 Td /F1 9.8 Tf  [([29])] TJ ET
BT 441.941 231.634 Td /F1 9.8 Tf  [([30])] TJ ET
BT 458.204 231.634 Td /F1 9.8 Tf  [([31])] TJ ET
BT 474.467 231.634 Td /F1 9.8 Tf  [([32])] TJ ET
BT 490.730 231.634 Td /F1 9.8 Tf  [([33])] TJ ET
BT 506.993 231.634 Td /F1 9.8 Tf  [([34])] TJ ET
0.271 0.267 0.267 rg
BT 523.256 231.634 Td /F1 9.8 Tf  [(, suggesting )] TJ ET
BT 26.250 219.729 Td /F1 9.8 Tf  [(a possible presence of cross-immunity between the H1N1 pandemic strain and preexisting influenza viruses in the elderly )] TJ ET
0.267 0.267 0.267 rg
BT 551.872 219.729 Td /F1 9.8 Tf  [([35])] TJ ET
BT 26.250 207.825 Td /F1 9.8 Tf  [([36])] TJ ET
BT 42.513 207.825 Td /F1 9.8 Tf  [([37])] TJ ET
0.271 0.267 0.267 rg
BT 58.776 207.825 Td /F1 9.8 Tf  [(, besides other mechanisms. This possibility is however still under exploration and no reliable estimates are available, )] TJ ET
BT 26.250 195.920 Td /F1 9.8 Tf  [(therefore we assumed a fully susceptible population to study the initial stage of the outbreak, following previous studies on )] TJ ET
BT 26.250 184.015 Td /F1 9.8 Tf  [(H1N1 pandemic )] TJ ET
0.267 0.267 0.267 rg
BT 98.858 184.015 Td /F1 9.8 Tf  [([5])] TJ ET
BT 109.700 184.015 Td /F1 9.8 Tf  [([6])] TJ ET
BT 120.542 184.015 Td /F1 9.8 Tf  [([38])] TJ ET
BT 136.805 184.015 Td /F1 9.8 Tf  [([39])] TJ ET
0.271 0.267 0.267 rg
BT 153.068 184.015 Td /F1 9.8 Tf  [(.)] TJ ET
BT 26.250 164.610 Td /F1 9.8 Tf  [(The spreading rate of the epidemic is governed by the basic reproduction number and the generation interval of the specific viral )] TJ ET
BT 26.250 152.706 Td /F1 9.8 Tf  [(strain considered. In order to obtain best estimate for these parameters the model has been used to perform a MLE of the )] TJ ET
BT 26.250 140.801 Td /F1 9.8 Tf  [(parameters against the actual chronology of newly infected countries )] TJ ET
0.267 0.267 0.267 rg
BT 325.390 140.801 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 336.232 140.801 Td /F1 9.8 Tf  [(. This methodology considers a Monte Carlo generation )] TJ ET
BT 26.250 128.896 Td /F1 9.8 Tf  [(of the distribution of arrival time of the infection in each country based on the analysis of one million worldwide simulations of the )] TJ ET
BT 26.250 116.991 Td /F1 9.8 Tf  [(pandemic evolution with the GLEaM model. This analysis provides the maximum likelihood estimates for the basic parameters )] TJ ET
BT 26.250 105.087 Td /F1 9.8 Tf  [(of the H1N1 such as the reproductive number R )] TJ ET
BT 235.427 103.022 Td /F1 8.7 Tf  [(0)] TJ ET
BT 240.245 105.087 Td /F1 9.8 Tf  [( and the basic model parameters e and � defining the inverse average )] TJ ET
BT 26.250 93.182 Td /F1 9.8 Tf  [(exposed and infectious time durations, respectively. In the following we consider as the baseline case the set of parameters )] TJ ET
BT 26.250 81.277 Td /F1 9.8 Tf  [(defined by the best estimates: ?)] TJ ET
BT 163.910 85.165 Td /F1 8.7 Tf  [(-1)] TJ ET
BT 171.615 81.277 Td /F1 9.8 Tf  [(=1.1 days, �)] TJ ET
BT 225.006 85.165 Td /F1 8.7 Tf  [(-1)] TJ ET
BT 232.711 81.277 Td /F1 9.8 Tf  [(=2.5 days, R)] TJ ET
BT 287.720 79.213 Td /F1 8.7 Tf  [(0)] TJ ET
BT 292.539 81.277 Td /F1 9.8 Tf  [( =1.75 )] TJ ET
0.267 0.267 0.267 rg
BT 322.627 81.277 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 333.469 81.277 Td /F1 9.8 Tf  [(, consistent with the estimates of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 497.669 81.277 Td /F1 9.8 Tf  [([38])] TJ ET
0.271 0.267 0.267 rg
BT 513.932 81.277 Td /F1 9.8 Tf  [(. )] TJ ET
BT 26.250 69.372 Td /F1 9.8 Tf  [(Asymptomatic individuals are assumed to represent 1/3 of the total cases, and have a reduced transmissibility of � with respect )] TJ ET
BT 26.250 57.468 Td /F1 9.8 Tf  [(to symptomatic individuals )] TJ ET
0.267 0.267 0.267 rg
BT 142.743 57.468 Td /F1 9.8 Tf  [([9])] TJ ET
BT 153.585 57.468 Td /F1 9.8 Tf  [([38])] TJ ET
BT 169.848 57.468 Td /F1 9.8 Tf  [([40])] TJ ET
BT 186.111 57.468 Td /F1 9.8 Tf  [([41])] TJ ET
0.271 0.267 0.267 rg
BT 202.374 57.468 Td /F1 9.8 Tf  [(. The sensitivity analysis and confidence interval for those values are reported in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 26.250 45.563 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 37.092 45.563 Td /F1 9.8 Tf  [(. For this set of parameters the model generates quantities of interest such as the profile of the epidemic behavior in each )] TJ ET
Q
q
15.000 31.277 577.500 745.723 re W n
0.271 0.267 0.267 rg
BT 26.250 767.476 Td /F1 9.8 Tf  [(compared with the official report that indicate 3,350 confirmed cases )] TJ ET
0.267 0.267 0.267 rg
BT 323.216 767.476 Td /F1 9.8 Tf  [([7])] TJ ET
0.271 0.267 0.267 rg
BT 334.058 767.476 Td /F1 9.8 Tf  [(.)] TJ ET
BT 26.250 748.071 Td /F1 9.8 Tf  [(Here, we use the Global Epidemic and Mobility \(GLEaM\) model )] TJ ET
0.267 0.267 0.267 rg
BT 302.594 748.071 Td /F1 9.8 Tf  [([8])] TJ ET
BT 313.436 748.071 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 324.278 748.071 Td /F1 9.8 Tf  [( to provide a computational ab-initio evaluation of the early )] TJ ET
BT 26.250 736.167 Td /F1 9.8 Tf  [(size of the outbreak in Mexico and the fluxes of infected travelers to other countries. The GLEaM model is a spatially structured )] TJ ET
BT 26.250 724.262 Td /F1 9.8 Tf  [(metapopulation epidemic model )] TJ ET
0.267 0.267 0.267 rg
BT 166.601 724.262 Td /F1 9.8 Tf  [([8])] TJ ET
BT 177.443 724.262 Td /F1 9.8 Tf  [([9])] TJ ET
BT 188.285 724.262 Td /F1 9.8 Tf  [([10])] TJ ET
BT 204.548 724.262 Td /F1 9.8 Tf  [([11])] TJ ET
BT 220.811 724.262 Td /F1 9.8 Tf  [([12])] TJ ET
BT 237.074 724.262 Td /F1 9.8 Tf  [([13])] TJ ET
BT 253.337 724.262 Td /F1 9.8 Tf  [([14])] TJ ET
BT 269.600 724.262 Td /F1 9.8 Tf  [([15])] TJ ET
BT 285.863 724.262 Td /F1 9.8 Tf  [([16])] TJ ET
BT 302.126 724.262 Td /F1 9.8 Tf  [([17])] TJ ET
BT 318.389 724.262 Td /F1 9.8 Tf  [([18])] TJ ET
BT 334.652 724.262 Td /F1 9.8 Tf  [([19])] TJ ET
BT 350.915 724.262 Td /F1 9.8 Tf  [([20])] TJ ET
BT 367.178 724.262 Td /F1 9.8 Tf  [([21])] TJ ET
0.271 0.267 0.267 rg
BT 383.441 724.262 Td /F1 9.8 Tf  [(, that allows the generation of stochastic )] TJ ET
BT 26.250 712.357 Td /F1 9.8 Tf  [(realizations of the worldwide unfolding of the epidemic, with mobility processes entirely based on real data. Once the disease )] TJ ET
BT 26.250 700.452 Td /F1 9.8 Tf  [(parameters and initial conditions based on available data are defined, the model generates in-silico epidemics for which we can )] TJ ET
BT 26.250 688.548 Td /F1 9.8 Tf  [(gather information such as prevalence, morbidity, number of secondary cases, number of imported cases and many others for )] TJ ET
BT 26.250 676.643 Td /F1 9.8 Tf  [(each subpopulation and with a time resolution of one day. In Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 309.156 676.643 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 319.998 676.643 Td /F1 9.8 Tf  [(, the GLEaM model has been used to perform a Maximum )] TJ ET
BT 26.250 664.738 Td /F1 9.8 Tf  [(Likelihood Estimate \(MLE\) of the transmission potential of the current H1N1 pandemic. Here we use the best estimate )] TJ ET
BT 26.250 652.833 Td /F1 9.8 Tf  [(parameters from Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 121.069 652.833 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 131.911 652.833 Td /F1 9.8 Tf  [( to simulate 2�10 )] TJ ET
BT 209.140 656.722 Td /F1 8.7 Tf  [(3)] TJ ET
BT 213.959 652.833 Td /F1 9.8 Tf  [( stochastic simulations of the current pandemic and provide an estimate of the )] TJ ET
BT 26.250 640.929 Td /F1 9.8 Tf  [(number of H1N1 cases in Mexico at the date of May the 8th. This is an ab-initio computational estimate and to further cross-)] TJ ET
BT 26.250 629.024 Td /F1 9.8 Tf  [(validate our results, we compare the number of infected individuals traveling from Mexico to other countries from our simulations )] TJ ET
BT 26.250 617.119 Td /F1 9.8 Tf  [(and compare these numbers with surveillance reports )] TJ ET
0.267 0.267 0.267 rg
BT 260.338 617.119 Td /F1 9.8 Tf  [([6])] TJ ET
BT 271.180 617.119 Td /F1 9.8 Tf  [([22])] TJ ET
BT 287.443 617.119 Td /F1 9.8 Tf  [([23])] TJ ET
BT 303.706 617.119 Td /F1 9.8 Tf  [([24])] TJ ET
0.271 0.267 0.267 rg
BT 319.969 617.119 Td /F1 9.8 Tf  [(. We find in our simulations that in Mexico as of the date of )] TJ ET
BT 26.250 605.214 Td /F1 9.8 Tf  [(May the 8th the symptomatic cases 95% reference range is 121,000 to 1,394,000. This value is in good agreement with the )] TJ ET
BT 26.250 593.310 Td /F1 9.8 Tf  [(lower bound estimate of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 153.058 593.310 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 163.900 593.310 Td /F1 9.8 Tf  [(. The number of infected individuals with travel history from Mexico in countries such as US, )] TJ ET
BT 26.250 581.405 Td /F1 9.8 Tf  [(Canada, Spain and UK is also within the confidence range of our simulations. These results provide further support to the claim )] TJ ET
BT 26.250 569.500 Td /F1 9.8 Tf  [(that the number of confirmed H1N1 cases in Mexico is only a very small fraction of the actually occurred cases.)] TJ ET
BT 26.250 532.898 Td /F4 12.0 Tf  [(Materials and Methods)] TJ ET
BT 26.250 512.943 Td /F1 9.8 Tf  [(The global epidemic and mobility metapopulation \(GLEaM\) model is based on a geographically structured metapopulation )] TJ ET
BT 26.250 501.039 Td /F1 9.8 Tf  [(approach )] TJ ET
0.267 0.267 0.267 rg
BT 69.608 501.039 Td /F1 9.8 Tf  [([8])] TJ ET
BT 80.450 501.039 Td /F1 9.8 Tf  [([9])] TJ ET
BT 91.292 501.039 Td /F1 9.8 Tf  [([10])] TJ ET
BT 107.555 501.039 Td /F1 9.8 Tf  [([11])] TJ ET
BT 123.818 501.039 Td /F1 9.8 Tf  [([12])] TJ ET
BT 140.081 501.039 Td /F1 9.8 Tf  [([13])] TJ ET
BT 156.344 501.039 Td /F1 9.8 Tf  [([14])] TJ ET
BT 172.607 501.039 Td /F1 9.8 Tf  [([15])] TJ ET
BT 188.870 501.039 Td /F1 9.8 Tf  [([16])] TJ ET
BT 205.133 501.039 Td /F1 9.8 Tf  [([17])] TJ ET
BT 221.396 501.039 Td /F1 9.8 Tf  [([18])] TJ ET
BT 237.659 501.039 Td /F1 9.8 Tf  [([19])] TJ ET
BT 253.922 501.039 Td /F1 9.8 Tf  [([20])] TJ ET
BT 270.185 501.039 Td /F1 9.8 Tf  [([21])] TJ ET
BT 286.448 501.039 Td /F1 9.8 Tf  [([25])] TJ ET
0.271 0.267 0.267 rg
BT 302.711 501.039 Td /F1 9.8 Tf  [(. GLEaM is composed of three layers. The first one is the )] TJ ET
BT 26.250 489.134 Td /F1 9.8 Tf  [(population layer that integrates distinct census areas for a total of 3362 subpopulations in 220 countries of the world. The )] TJ ET
BT 26.250 477.229 Td /F1 9.8 Tf  [(census areas are defined by a Voronoi-like tessellation process that partition the world surface. Given a set of points S in the )] TJ ET
BT 26.250 465.324 Td /F1 9.8 Tf  [(plane, which are the Voronoi sites, each site s has a Voronoi cell V\(s\) consisting of all points closer to s than to any other site. In )] TJ ET
BT 26.250 453.420 Td /F1 9.8 Tf  [(our partition we use 3362 major transportation hubs in the world as the Voronoi sites. The boundaries of each subpopulation are )] TJ ET
BT 26.250 441.515 Td /F1 9.8 Tf  [(defined by all the points in the plane that are equidistant to two sites. For each area defined by the cell boundaries and the )] TJ ET
BT 26.250 429.610 Td /F1 9.8 Tf  [(Voronoi process, the population is obtained from the site of the �Gridded Population of the World� project of SEDAC \(Columbia )] TJ ET
BT 26.250 417.705 Td /F1 9.8 Tf  [(University\) )] TJ ET
0.267 0.267 0.267 rg
BT 75.000 417.705 Td /F1 9.8 Tf  [([26])] TJ ET
0.271 0.267 0.267 rg
BT 91.263 417.705 Td /F1 9.8 Tf  [( that provides population estimates worldwide for cells of 15 � 15 minutes of arc. The second layer of the model )] TJ ET
BT 26.250 405.801 Td /F1 9.8 Tf  [(is composed by the human mobility flows among the census areas. We consider both commuting flows collected from various )] TJ ET
BT 26.250 393.896 Td /F1 9.8 Tf  [(sources in more than 30 countries and the airline traffic provided by IATA )] TJ ET
0.267 0.267 0.267 rg
BT 343.808 393.896 Td /F1 9.8 Tf  [([27])] TJ ET
0.271 0.267 0.267 rg
BT 360.070 393.896 Td /F1 9.8 Tf  [( and OAG )] TJ ET
0.267 0.267 0.267 rg
BT 406.139 393.896 Td /F1 9.8 Tf  [([28])] TJ ET
0.271 0.267 0.267 rg
BT 422.402 393.896 Td /F1 9.8 Tf  [(. Further details concerning the )] TJ ET
BT 26.250 381.991 Td /F1 9.8 Tf  [(composition of GLEaM and the integration of its three layers for a practical simulation of epidemic spreading are given in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 567.609 381.991 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 26.250 370.086 Td /F1 9.8 Tf  [(. The third layer of the model concerns the disease dynamics used to model the disease evolution. We adopt a SEIR-like )] TJ ET
BT 26.250 358.182 Td /F1 9.8 Tf  [(compartmentalization framework in which separate compartments for symptomatic traveling and not traveling, as well as )] TJ ET
BT 26.250 346.277 Td /F1 9.8 Tf  [(asymptomatic individuals are included in each different subpopulations. The infection dynamics takes place within each )] TJ ET
BT 26.250 334.372 Td /F1 9.8 Tf  [(subpopulation and assumes the classic influenza-like-illness compartmentalization in which each individual is classified by one )] TJ ET
BT 26.250 322.467 Td /F1 9.8 Tf  [(of the discrete states such as susceptible, latent, infectious symptomatic, infectious non-symptomatic or permanently )] TJ ET
BT 26.250 310.563 Td /F1 9.8 Tf  [(recovered/removed. All transitions are modeled through binomial and multinomial processes to ensure the discrete and )] TJ ET
BT 26.250 298.658 Td /F1 9.8 Tf  [(stochastic nature of the processes. A full definition of the model is reported in Ref )] TJ ET
0.267 0.267 0.267 rg
BT 379.044 298.658 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 389.886 298.658 Td /F1 9.8 Tf  [(.)] TJ ET
BT 26.250 279.253 Td /F1 9.8 Tf  [(It is also worth stressing here some of the model assumptions. The model is not an agent-based model and does not include )] TJ ET
BT 26.250 267.348 Td /F1 9.8 Tf  [(additional structure within a subpopulation, therefore it cannot provide detailed information at the level of households or )] TJ ET
BT 26.250 255.444 Td /F1 9.8 Tf  [(workplaces. The fraction of infected population is likely overestimated because of the assumptions of an entirely susceptible )] TJ ET
BT 26.250 243.539 Td /F1 9.8 Tf  [(populations and of subpopulations with homogeneous mixing. Current data on the severity of the pandemic has revealed an age )] TJ ET
BT 26.250 231.634 Td /F1 9.8 Tf  [(pattern for influenza attack rate shifted towards the younger age classes of the population )] TJ ET
0.267 0.267 0.267 rg
BT 414.836 231.634 Td /F1 9.8 Tf  [([5])] TJ ET
BT 425.678 231.634 Td /F1 9.8 Tf  [([29])] TJ ET
BT 441.941 231.634 Td /F1 9.8 Tf  [([30])] TJ ET
BT 458.204 231.634 Td /F1 9.8 Tf  [([31])] TJ ET
BT 474.467 231.634 Td /F1 9.8 Tf  [([32])] TJ ET
BT 490.730 231.634 Td /F1 9.8 Tf  [([33])] TJ ET
BT 506.993 231.634 Td /F1 9.8 Tf  [([34])] TJ ET
0.271 0.267 0.267 rg
BT 523.256 231.634 Td /F1 9.8 Tf  [(, suggesting )] TJ ET
BT 26.250 219.729 Td /F1 9.8 Tf  [(a possible presence of cross-immunity between the H1N1 pandemic strain and preexisting influenza viruses in the elderly )] TJ ET
0.267 0.267 0.267 rg
BT 551.872 219.729 Td /F1 9.8 Tf  [([35])] TJ ET
BT 26.250 207.825 Td /F1 9.8 Tf  [([36])] TJ ET
BT 42.513 207.825 Td /F1 9.8 Tf  [([37])] TJ ET
0.271 0.267 0.267 rg
BT 58.776 207.825 Td /F1 9.8 Tf  [(, besides other mechanisms. This possibility is however still under exploration and no reliable estimates are available, )] TJ ET
BT 26.250 195.920 Td /F1 9.8 Tf  [(therefore we assumed a fully susceptible population to study the initial stage of the outbreak, following previous studies on )] TJ ET
BT 26.250 184.015 Td /F1 9.8 Tf  [(H1N1 pandemic )] TJ ET
0.267 0.267 0.267 rg
BT 98.858 184.015 Td /F1 9.8 Tf  [([5])] TJ ET
BT 109.700 184.015 Td /F1 9.8 Tf  [([6])] TJ ET
BT 120.542 184.015 Td /F1 9.8 Tf  [([38])] TJ ET
BT 136.805 184.015 Td /F1 9.8 Tf  [([39])] TJ ET
0.271 0.267 0.267 rg
BT 153.068 184.015 Td /F1 9.8 Tf  [(.)] TJ ET
BT 26.250 164.610 Td /F1 9.8 Tf  [(The spreading rate of the epidemic is governed by the basic reproduction number and the generation interval of the specific viral )] TJ ET
BT 26.250 152.706 Td /F1 9.8 Tf  [(strain considered. In order to obtain best estimate for these parameters the model has been used to perform a MLE of the )] TJ ET
BT 26.250 140.801 Td /F1 9.8 Tf  [(parameters against the actual chronology of newly infected countries )] TJ ET
0.267 0.267 0.267 rg
BT 325.390 140.801 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 336.232 140.801 Td /F1 9.8 Tf  [(. This methodology considers a Monte Carlo generation )] TJ ET
BT 26.250 128.896 Td /F1 9.8 Tf  [(of the distribution of arrival time of the infection in each country based on the analysis of one million worldwide simulations of the )] TJ ET
BT 26.250 116.991 Td /F1 9.8 Tf  [(pandemic evolution with the GLEaM model. This analysis provides the maximum likelihood estimates for the basic parameters )] TJ ET
BT 26.250 105.087 Td /F1 9.8 Tf  [(of the H1N1 such as the reproductive number R )] TJ ET
BT 235.427 103.022 Td /F1 8.7 Tf  [(0)] TJ ET
BT 240.245 105.087 Td /F1 9.8 Tf  [( and the basic model parameters e and � defining the inverse average )] TJ ET
BT 26.250 93.182 Td /F1 9.8 Tf  [(exposed and infectious time durations, respectively. In the following we consider as the baseline case the set of parameters )] TJ ET
BT 26.250 81.277 Td /F1 9.8 Tf  [(defined by the best estimates: ?)] TJ ET
BT 163.910 85.165 Td /F1 8.7 Tf  [(-1)] TJ ET
BT 171.615 81.277 Td /F1 9.8 Tf  [(=1.1 days, �)] TJ ET
BT 225.006 85.165 Td /F1 8.7 Tf  [(-1)] TJ ET
BT 232.711 81.277 Td /F1 9.8 Tf  [(=2.5 days, R)] TJ ET
BT 287.720 79.213 Td /F1 8.7 Tf  [(0)] TJ ET
BT 292.539 81.277 Td /F1 9.8 Tf  [( =1.75 )] TJ ET
0.267 0.267 0.267 rg
BT 322.627 81.277 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 333.469 81.277 Td /F1 9.8 Tf  [(, consistent with the estimates of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 497.669 81.277 Td /F1 9.8 Tf  [([38])] TJ ET
0.271 0.267 0.267 rg
BT 513.932 81.277 Td /F1 9.8 Tf  [(. )] TJ ET
BT 26.250 69.372 Td /F1 9.8 Tf  [(Asymptomatic individuals are assumed to represent 1/3 of the total cases, and have a reduced transmissibility of � with respect )] TJ ET
BT 26.250 57.468 Td /F1 9.8 Tf  [(to symptomatic individuals )] TJ ET
0.267 0.267 0.267 rg
BT 142.743 57.468 Td /F1 9.8 Tf  [([9])] TJ ET
BT 153.585 57.468 Td /F1 9.8 Tf  [([38])] TJ ET
BT 169.848 57.468 Td /F1 9.8 Tf  [([40])] TJ ET
BT 186.111 57.468 Td /F1 9.8 Tf  [([41])] TJ ET
0.271 0.267 0.267 rg
BT 202.374 57.468 Td /F1 9.8 Tf  [(. The sensitivity analysis and confidence interval for those values are reported in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 26.250 45.563 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 37.092 45.563 Td /F1 9.8 Tf  [(. For this set of parameters the model generates quantities of interest such as the profile of the epidemic behavior in each )] TJ ET
Q
q
15.000 31.277 577.500 745.723 re W n
0.271 0.267 0.267 rg
BT 26.250 767.476 Td /F1 9.8 Tf  [(compared with the official report that indicate 3,350 confirmed cases )] TJ ET
0.267 0.267 0.267 rg
BT 323.216 767.476 Td /F1 9.8 Tf  [([7])] TJ ET
0.271 0.267 0.267 rg
BT 334.058 767.476 Td /F1 9.8 Tf  [(.)] TJ ET
BT 26.250 748.071 Td /F1 9.8 Tf  [(Here, we use the Global Epidemic and Mobility \(GLEaM\) model )] TJ ET
0.267 0.267 0.267 rg
BT 302.594 748.071 Td /F1 9.8 Tf  [([8])] TJ ET
BT 313.436 748.071 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 324.278 748.071 Td /F1 9.8 Tf  [( to provide a computational ab-initio evaluation of the early )] TJ ET
BT 26.250 736.167 Td /F1 9.8 Tf  [(size of the outbreak in Mexico and the fluxes of infected travelers to other countries. The GLEaM model is a spatially structured )] TJ ET
BT 26.250 724.262 Td /F1 9.8 Tf  [(metapopulation epidemic model )] TJ ET
0.267 0.267 0.267 rg
BT 166.601 724.262 Td /F1 9.8 Tf  [([8])] TJ ET
BT 177.443 724.262 Td /F1 9.8 Tf  [([9])] TJ ET
BT 188.285 724.262 Td /F1 9.8 Tf  [([10])] TJ ET
BT 204.548 724.262 Td /F1 9.8 Tf  [([11])] TJ ET
BT 220.811 724.262 Td /F1 9.8 Tf  [([12])] TJ ET
BT 237.074 724.262 Td /F1 9.8 Tf  [([13])] TJ ET
BT 253.337 724.262 Td /F1 9.8 Tf  [([14])] TJ ET
BT 269.600 724.262 Td /F1 9.8 Tf  [([15])] TJ ET
BT 285.863 724.262 Td /F1 9.8 Tf  [([16])] TJ ET
BT 302.126 724.262 Td /F1 9.8 Tf  [([17])] TJ ET
BT 318.389 724.262 Td /F1 9.8 Tf  [([18])] TJ ET
BT 334.652 724.262 Td /F1 9.8 Tf  [([19])] TJ ET
BT 350.915 724.262 Td /F1 9.8 Tf  [([20])] TJ ET
BT 367.178 724.262 Td /F1 9.8 Tf  [([21])] TJ ET
0.271 0.267 0.267 rg
BT 383.441 724.262 Td /F1 9.8 Tf  [(, that allows the generation of stochastic )] TJ ET
BT 26.250 712.357 Td /F1 9.8 Tf  [(realizations of the worldwide unfolding of the epidemic, with mobility processes entirely based on real data. Once the disease )] TJ ET
BT 26.250 700.452 Td /F1 9.8 Tf  [(parameters and initial conditions based on available data are defined, the model generates in-silico epidemics for which we can )] TJ ET
BT 26.250 688.548 Td /F1 9.8 Tf  [(gather information such as prevalence, morbidity, number of secondary cases, number of imported cases and many others for )] TJ ET
BT 26.250 676.643 Td /F1 9.8 Tf  [(each subpopulation and with a time resolution of one day. In Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 309.156 676.643 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 319.998 676.643 Td /F1 9.8 Tf  [(, the GLEaM model has been used to perform a Maximum )] TJ ET
BT 26.250 664.738 Td /F1 9.8 Tf  [(Likelihood Estimate \(MLE\) of the transmission potential of the current H1N1 pandemic. Here we use the best estimate )] TJ ET
BT 26.250 652.833 Td /F1 9.8 Tf  [(parameters from Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 121.069 652.833 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 131.911 652.833 Td /F1 9.8 Tf  [( to simulate 2�10 )] TJ ET
BT 209.140 656.722 Td /F1 8.7 Tf  [(3)] TJ ET
BT 213.959 652.833 Td /F1 9.8 Tf  [( stochastic simulations of the current pandemic and provide an estimate of the )] TJ ET
BT 26.250 640.929 Td /F1 9.8 Tf  [(number of H1N1 cases in Mexico at the date of May the 8th. This is an ab-initio computational estimate and to further cross-)] TJ ET
BT 26.250 629.024 Td /F1 9.8 Tf  [(validate our results, we compare the number of infected individuals traveling from Mexico to other countries from our simulations )] TJ ET
BT 26.250 617.119 Td /F1 9.8 Tf  [(and compare these numbers with surveillance reports )] TJ ET
0.267 0.267 0.267 rg
BT 260.338 617.119 Td /F1 9.8 Tf  [([6])] TJ ET
BT 271.180 617.119 Td /F1 9.8 Tf  [([22])] TJ ET
BT 287.443 617.119 Td /F1 9.8 Tf  [([23])] TJ ET
BT 303.706 617.119 Td /F1 9.8 Tf  [([24])] TJ ET
0.271 0.267 0.267 rg
BT 319.969 617.119 Td /F1 9.8 Tf  [(. We find in our simulations that in Mexico as of the date of )] TJ ET
BT 26.250 605.214 Td /F1 9.8 Tf  [(May the 8th the symptomatic cases 95% reference range is 121,000 to 1,394,000. This value is in good agreement with the )] TJ ET
BT 26.250 593.310 Td /F1 9.8 Tf  [(lower bound estimate of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 153.058 593.310 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 163.900 593.310 Td /F1 9.8 Tf  [(. The number of infected individuals with travel history from Mexico in countries such as US, )] TJ ET
BT 26.250 581.405 Td /F1 9.8 Tf  [(Canada, Spain and UK is also within the confidence range of our simulations. These results provide further support to the claim )] TJ ET
BT 26.250 569.500 Td /F1 9.8 Tf  [(that the number of confirmed H1N1 cases in Mexico is only a very small fraction of the actually occurred cases.)] TJ ET
BT 26.250 532.898 Td /F4 12.0 Tf  [(Materials and Methods)] TJ ET
BT 26.250 512.943 Td /F1 9.8 Tf  [(The global epidemic and mobility metapopulation \(GLEaM\) model is based on a geographically structured metapopulation )] TJ ET
BT 26.250 501.039 Td /F1 9.8 Tf  [(approach )] TJ ET
0.267 0.267 0.267 rg
BT 69.608 501.039 Td /F1 9.8 Tf  [([8])] TJ ET
BT 80.450 501.039 Td /F1 9.8 Tf  [([9])] TJ ET
BT 91.292 501.039 Td /F1 9.8 Tf  [([10])] TJ ET
BT 107.555 501.039 Td /F1 9.8 Tf  [([11])] TJ ET
BT 123.818 501.039 Td /F1 9.8 Tf  [([12])] TJ ET
BT 140.081 501.039 Td /F1 9.8 Tf  [([13])] TJ ET
BT 156.344 501.039 Td /F1 9.8 Tf  [([14])] TJ ET
BT 172.607 501.039 Td /F1 9.8 Tf  [([15])] TJ ET
BT 188.870 501.039 Td /F1 9.8 Tf  [([16])] TJ ET
BT 205.133 501.039 Td /F1 9.8 Tf  [([17])] TJ ET
BT 221.396 501.039 Td /F1 9.8 Tf  [([18])] TJ ET
BT 237.659 501.039 Td /F1 9.8 Tf  [([19])] TJ ET
BT 253.922 501.039 Td /F1 9.8 Tf  [([20])] TJ ET
BT 270.185 501.039 Td /F1 9.8 Tf  [([21])] TJ ET
BT 286.448 501.039 Td /F1 9.8 Tf  [([25])] TJ ET
0.271 0.267 0.267 rg
BT 302.711 501.039 Td /F1 9.8 Tf  [(. GLEaM is composed of three layers. The first one is the )] TJ ET
BT 26.250 489.134 Td /F1 9.8 Tf  [(population layer that integrates distinct census areas for a total of 3362 subpopulations in 220 countries of the world. The )] TJ ET
BT 26.250 477.229 Td /F1 9.8 Tf  [(census areas are defined by a Voronoi-like tessellation process that partition the world surface. Given a set of points S in the )] TJ ET
BT 26.250 465.324 Td /F1 9.8 Tf  [(plane, which are the Voronoi sites, each site s has a Voronoi cell V\(s\) consisting of all points closer to s than to any other site. In )] TJ ET
BT 26.250 453.420 Td /F1 9.8 Tf  [(our partition we use 3362 major transportation hubs in the world as the Voronoi sites. The boundaries of each subpopulation are )] TJ ET
BT 26.250 441.515 Td /F1 9.8 Tf  [(defined by all the points in the plane that are equidistant to two sites. For each area defined by the cell boundaries and the )] TJ ET
BT 26.250 429.610 Td /F1 9.8 Tf  [(Voronoi process, the population is obtained from the site of the �Gridded Population of the World� project of SEDAC \(Columbia )] TJ ET
BT 26.250 417.705 Td /F1 9.8 Tf  [(University\) )] TJ ET
0.267 0.267 0.267 rg
BT 75.000 417.705 Td /F1 9.8 Tf  [([26])] TJ ET
0.271 0.267 0.267 rg
BT 91.263 417.705 Td /F1 9.8 Tf  [( that provides population estimates worldwide for cells of 15 � 15 minutes of arc. The second layer of the model )] TJ ET
BT 26.250 405.801 Td /F1 9.8 Tf  [(is composed by the human mobility flows among the census areas. We consider both commuting flows collected from various )] TJ ET
BT 26.250 393.896 Td /F1 9.8 Tf  [(sources in more than 30 countries and the airline traffic provided by IATA )] TJ ET
0.267 0.267 0.267 rg
BT 343.808 393.896 Td /F1 9.8 Tf  [([27])] TJ ET
0.271 0.267 0.267 rg
BT 360.070 393.896 Td /F1 9.8 Tf  [( and OAG )] TJ ET
0.267 0.267 0.267 rg
BT 406.139 393.896 Td /F1 9.8 Tf  [([28])] TJ ET
0.271 0.267 0.267 rg
BT 422.402 393.896 Td /F1 9.8 Tf  [(. Further details concerning the )] TJ ET
BT 26.250 381.991 Td /F1 9.8 Tf  [(composition of GLEaM and the integration of its three layers for a practical simulation of epidemic spreading are given in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 567.609 381.991 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 26.250 370.086 Td /F1 9.8 Tf  [(. The third layer of the model concerns the disease dynamics used to model the disease evolution. We adopt a SEIR-like )] TJ ET
BT 26.250 358.182 Td /F1 9.8 Tf  [(compartmentalization framework in which separate compartments for symptomatic traveling and not traveling, as well as )] TJ ET
BT 26.250 346.277 Td /F1 9.8 Tf  [(asymptomatic individuals are included in each different subpopulations. The infection dynamics takes place within each )] TJ ET
BT 26.250 334.372 Td /F1 9.8 Tf  [(subpopulation and assumes the classic influenza-like-illness compartmentalization in which each individual is classified by one )] TJ ET
BT 26.250 322.467 Td /F1 9.8 Tf  [(of the discrete states such as susceptible, latent, infectious symptomatic, infectious non-symptomatic or permanently )] TJ ET
BT 26.250 310.563 Td /F1 9.8 Tf  [(recovered/removed. All transitions are modeled through binomial and multinomial processes to ensure the discrete and )] TJ ET
BT 26.250 298.658 Td /F1 9.8 Tf  [(stochastic nature of the processes. A full definition of the model is reported in Ref )] TJ ET
0.267 0.267 0.267 rg
BT 379.044 298.658 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 389.886 298.658 Td /F1 9.8 Tf  [(.)] TJ ET
BT 26.250 279.253 Td /F1 9.8 Tf  [(It is also worth stressing here some of the model assumptions. The model is not an agent-based model and does not include )] TJ ET
BT 26.250 267.348 Td /F1 9.8 Tf  [(additional structure within a subpopulation, therefore it cannot provide detailed information at the level of households or )] TJ ET
BT 26.250 255.444 Td /F1 9.8 Tf  [(workplaces. The fraction of infected population is likely overestimated because of the assumptions of an entirely susceptible )] TJ ET
BT 26.250 243.539 Td /F1 9.8 Tf  [(populations and of subpopulations with homogeneous mixing. Current data on the severity of the pandemic has revealed an age )] TJ ET
BT 26.250 231.634 Td /F1 9.8 Tf  [(pattern for influenza attack rate shifted towards the younger age classes of the population )] TJ ET
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BT 425.678 231.634 Td /F1 9.8 Tf  [([29])] TJ ET
BT 441.941 231.634 Td /F1 9.8 Tf  [([30])] TJ ET
BT 458.204 231.634 Td /F1 9.8 Tf  [([31])] TJ ET
BT 474.467 231.634 Td /F1 9.8 Tf  [([32])] TJ ET
BT 490.730 231.634 Td /F1 9.8 Tf  [([33])] TJ ET
BT 506.993 231.634 Td /F1 9.8 Tf  [([34])] TJ ET
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BT 523.256 231.634 Td /F1 9.8 Tf  [(, suggesting )] TJ ET
BT 26.250 219.729 Td /F1 9.8 Tf  [(a possible presence of cross-immunity between the H1N1 pandemic strain and preexisting influenza viruses in the elderly )] TJ ET
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BT 551.872 219.729 Td /F1 9.8 Tf  [([35])] TJ ET
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BT 42.513 207.825 Td /F1 9.8 Tf  [([37])] TJ ET
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BT 58.776 207.825 Td /F1 9.8 Tf  [(, besides other mechanisms. This possibility is however still under exploration and no reliable estimates are available, )] TJ ET
BT 26.250 195.920 Td /F1 9.8 Tf  [(therefore we assumed a fully susceptible population to study the initial stage of the outbreak, following previous studies on )] TJ ET
BT 26.250 184.015 Td /F1 9.8 Tf  [(H1N1 pandemic )] TJ ET
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BT 109.700 184.015 Td /F1 9.8 Tf  [([6])] TJ ET
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BT 153.068 184.015 Td /F1 9.8 Tf  [(.)] TJ ET
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BT 26.250 152.706 Td /F1 9.8 Tf  [(strain considered. In order to obtain best estimate for these parameters the model has been used to perform a MLE of the )] TJ ET
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BT 26.250 116.991 Td /F1 9.8 Tf  [(pandemic evolution with the GLEaM model. This analysis provides the maximum likelihood estimates for the basic parameters )] TJ ET
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BT 235.427 103.022 Td /F1 8.7 Tf  [(0)] TJ ET
BT 240.245 105.087 Td /F1 9.8 Tf  [( and the basic model parameters e and � defining the inverse average )] TJ ET
BT 26.250 93.182 Td /F1 9.8 Tf  [(exposed and infectious time durations, respectively. In the following we consider as the baseline case the set of parameters )] TJ ET
BT 26.250 81.277 Td /F1 9.8 Tf  [(defined by the best estimates: ?)] TJ ET
BT 163.910 85.165 Td /F1 8.7 Tf  [(-1)] TJ ET
BT 171.615 81.277 Td /F1 9.8 Tf  [(=1.1 days, �)] TJ ET
BT 225.006 85.165 Td /F1 8.7 Tf  [(-1)] TJ ET
BT 232.711 81.277 Td /F1 9.8 Tf  [(=2.5 days, R)] TJ ET
BT 287.720 79.213 Td /F1 8.7 Tf  [(0)] TJ ET
BT 292.539 81.277 Td /F1 9.8 Tf  [( =1.75 )] TJ ET
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BT 322.627 81.277 Td /F1 9.8 Tf  [([9])] TJ ET
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BT 333.469 81.277 Td /F1 9.8 Tf  [(, consistent with the estimates of Ref. )] TJ ET
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BT 497.669 81.277 Td /F1 9.8 Tf  [([38])] TJ ET
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BT 513.932 81.277 Td /F1 9.8 Tf  [(. )] TJ ET
BT 26.250 69.372 Td /F1 9.8 Tf  [(Asymptomatic individuals are assumed to represent 1/3 of the total cases, and have a reduced transmissibility of � with respect )] TJ ET
BT 26.250 57.468 Td /F1 9.8 Tf  [(to symptomatic individuals )] TJ ET
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BT 142.743 57.468 Td /F1 9.8 Tf  [([9])] TJ ET
BT 153.585 57.468 Td /F1 9.8 Tf  [([38])] TJ ET
BT 169.848 57.468 Td /F1 9.8 Tf  [([40])] TJ ET
BT 186.111 57.468 Td /F1 9.8 Tf  [([41])] TJ ET
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BT 202.374 57.468 Td /F1 9.8 Tf  [(. The sensitivity analysis and confidence interval for those values are reported in Ref. )] TJ ET
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BT 26.250 45.563 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 37.092 45.563 Td /F1 9.8 Tf  [(. For this set of parameters the model generates quantities of interest such as the profile of the epidemic behavior in each )] TJ ET
Q
q
0.000 0.000 0.000 rg
BT 291.710 19.825 Td /F1 11.0 Tf  [(2)] TJ ET
BT 25.000 19.825 Td /F1 11.0 Tf  [(PLOS Currents Influenza)] TJ ET

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BT 26.250 767.476 Td /F1 9.8 Tf  [(subpopulation or the number of imported cases. In the following, simulation results are aggregated at the level of the country for )] TJ ET
BT 26.250 755.571 Td /F1 9.8 Tf  [(a direct comparison with the empirical data available. The initial conditions of the epidemic are defined by setting the onset of )] TJ ET
BT 26.250 743.667 Td /F1 9.8 Tf  [(the outbreak near La Gloria in Mexico on February 18 )] TJ ET
BT 260.357 747.555 Td /F1 8.7 Tf  [(th)] TJ ET
BT 267.585 743.667 Td /F1 9.8 Tf  [( , 2009, as reported by official sources )] TJ ET
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BT 435.042 743.667 Td /F1 9.8 Tf  [([36])] TJ ET
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BT 451.305 743.667 Td /F1 9.8 Tf  [( and analogously to other )] TJ ET
BT 26.250 731.762 Td /F1 9.8 Tf  [(works )] TJ ET
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BT 54.418 731.762 Td /F1 9.8 Tf  [([8])] TJ ET
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BT 65.260 731.762 Td /F1 9.8 Tf  [(. We tested different localization of the first cases in census areas close to La Gloria without observing relevant )] TJ ET
BT 26.250 719.857 Td /F1 9.8 Tf  [(variations with respect to the observed results. In Mexico we also consider the control measures implemented in the country )] TJ ET
BT 26.250 707.952 Td /F1 9.8 Tf  [(starting April 24 )] TJ ET
BT 96.694 711.841 Td /F1 8.7 Tf  [(th)] TJ ET
BT 103.922 707.952 Td /F1 9.8 Tf  [( and ending May 10th following Ref. )] TJ ET
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BT 261.628 707.952 Td /F1 9.8 Tf  [([2])] TJ ET
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BT 272.470 707.952 Td /F1 9.8 Tf  [(, as those might affect the spreading to other countries )] TJ ET
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BT 510.390 707.952 Td /F1 9.8 Tf  [([9])] TJ ET
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BT 521.232 707.952 Td /F1 9.8 Tf  [(. Here we )] TJ ET
BT 26.250 696.048 Td /F1 9.8 Tf  [(focus on the cumulative number of cases observed in Mexico at the date of April the 30 )] TJ ET
BT 404.521 699.936 Td /F1 8.7 Tf  [(th)] TJ ET
BT 411.749 696.048 Td /F1 9.8 Tf  [( and the imported cases in the UK, )] TJ ET
BT 26.250 684.143 Td /F1 9.8 Tf  [(US, Brazil, Germany and France. Each simulation represents a stochastic realization of the process and we aggregate data on )] TJ ET
BT 26.250 672.238 Td /F1 9.8 Tf  [(2�10 )] TJ ET
BT 50.918 676.126 Td /F1 8.7 Tf  [(3)] TJ ET
BT 55.736 672.238 Td /F1 9.8 Tf  [( realizations providing reference ranges for all quantities. The data of imported cases are compared with those reported )] TJ ET
BT 26.250 660.333 Td /F1 9.8 Tf  [(in Ref. )] TJ ET
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BT 57.138 660.333 Td /F1 9.8 Tf  [([6])] TJ ET
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BT 67.980 660.333 Td /F1 9.8 Tf  [( for the UK and the US. The data for France was obtained from Ref. )] TJ ET
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BT 362.791 660.333 Td /F1 9.8 Tf  [([23])] TJ ET
0.271 0.267 0.267 rg
BT 379.054 660.333 Td /F1 9.8 Tf  [(, those for Germany from Ref. )] TJ ET
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BT 510.727 660.333 Td /F1 9.8 Tf  [([22])] TJ ET
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BT 526.990 660.333 Td /F1 9.8 Tf  [( and those )] TJ ET
BT 26.250 648.429 Td /F1 9.8 Tf  [(for Brazil from the reports at the site of the Health Department of the Brazilian Government )] TJ ET
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BT 419.126 648.429 Td /F1 9.8 Tf  [([24])] TJ ET
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BT 435.389 648.429 Td /F1 9.8 Tf  [(.)] TJ ET
BT 26.250 611.826 Td /F4 12.0 Tf  [(Results and Discussion)] TJ ET
BT 26.250 591.872 Td /F1 9.8 Tf  [(By using GLEaM it is possible to provide a model estimate of the number of imported cases arriving from Mexico to a set of )] TJ ET
BT 26.250 579.967 Td /F1 9.8 Tf  [(selected countries. The estimated 99% reference range is shown in Table 1. The dates and target countries are chosen to )] TJ ET
BT 26.250 568.062 Td /F1 9.8 Tf  [(facilitate the comparison with the numbers found in the literature )] TJ ET
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BT 305.334 568.062 Td /F1 9.8 Tf  [([6])] TJ ET
BT 316.176 568.062 Td /F1 9.8 Tf  [([22])] TJ ET
BT 332.439 568.062 Td /F1 9.8 Tf  [([23])] TJ ET
BT 348.702 568.062 Td /F1 9.8 Tf  [([24])] TJ ET
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BT 364.965 568.062 Td /F1 9.8 Tf  [(. The numbers shown in the Table refer to the )] TJ ET
BT 26.250 556.158 Td /F1 9.8 Tf  [(importantion of infected/exposed individual traveling from Mexico in one of the listed countries as of the date of May the 8)] TJ ET
BT 548.129 560.046 Td /F1 8.7 Tf  [(th)] TJ ET
BT 555.357 556.158 Td /F1 9.8 Tf  [(. )] TJ ET
BT 26.250 544.253 Td /F1 9.8 Tf  [(Only 2/3 of the exposed travelers are then considered in the cumulative number of cases as only this fraction will eventually )] TJ ET
BT 26.250 532.348 Td /F1 9.8 Tf  [(develop symptoms, according to the model assumptions. The numbers of imported cases to each country are typically small, )] TJ ET
BT 26.250 520.443 Td /F1 9.8 Tf  [(and as such prone to large stochastic fluctuations. However the surveillance values are all within the 99% reference ranges of )] TJ ET
BT 26.250 508.539 Td /F1 9.8 Tf  [(the 2,000 realizations of our model. We will provide elsewhere a full sensitivity analysis of the results but we observe very small )] TJ ET
BT 26.250 496.634 Td /F1 9.8 Tf  [(variations with respect to the presented results in the range of parameters explored. This is because any MLE for R)] TJ ET
BT 522.632 494.570 Td /F5 8.7 Tf  [(0)] TJ ET
BT 527.451 496.634 Td /F1 9.8 Tf  [( and )] TJ ET
BT 26.250 484.729 Td /F1 9.8 Tf  [(generation interval tend to optimize the growth rate with respect to the epidemic timeline thus producing very similar results in )] TJ ET
BT 26.250 472.824 Td /F1 9.8 Tf  [(the early spreading of the epidemic. We have also considered that in the US the travel history is known only for 50% of the )] TJ ET
BT 26.250 460.920 Td /F1 9.8 Tf  [(confirmed cases. The simple extrapolation that provides a twofold estimate of imported cases \(in brackets in Table 1\) is )] TJ ET
BT 26.250 449.015 Td /F1 9.8 Tf  [(however still compatible with the reference range of our stochastic simulations.)] TJ ET
BT 26.250 429.610 Td /F1 9.8 Tf  [(Table 2 shows GLEaM predictions for the size of the epidemic in Mexico on April 30)] TJ ET
BT 387.146 433.498 Td /F1 8.7 Tf  [(th)] TJ ET
BT 394.374 429.610 Td /F1 9.8 Tf  [( and compare the results with the )] TJ ET
BT 26.250 417.705 Td /F1 9.8 Tf  [(estimations of Refs. )] TJ ET
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BT 114.575 417.705 Td /F1 9.8 Tf  [([5])] TJ ET
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BT 125.417 417.705 Td /F1 9.8 Tf  [( and )] TJ ET
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BT 147.101 417.705 Td /F1 9.8 Tf  [([6])] TJ ET
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BT 157.943 417.705 Td /F1 9.8 Tf  [(. We provide the 95% reference range over 2,000 realizations. The obtained range includes the )] TJ ET
BT 26.250 405.801 Td /F1 9.8 Tf  [(lower bound estimate of Ref )] TJ ET
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BT 150.348 405.801 Td /F1 9.8 Tf  [([6])] TJ ET
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BT 161.190 405.801 Td /F1 9.8 Tf  [(. Our median value for the number of asymptomatic cases is 734,000 that is again compatible )] TJ ET
BT 26.250 393.896 Td /F1 9.8 Tf  [(with the range of values reported in Ref. )] TJ ET
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BT 201.838 393.896 Td /F1 9.8 Tf  [([6])] TJ ET
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BT 212.680 393.896 Td /F1 9.8 Tf  [(. While the estimates presented in Refs. )] TJ ET
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BT 387.712 393.896 Td /F1 9.8 Tf  [([5])] TJ ET
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BT 398.554 393.896 Td /F1 9.8 Tf  [( and )] TJ ET
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BT 420.238 393.896 Td /F1 9.8 Tf  [([6])] TJ ET
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BT 431.080 393.896 Td /F1 9.8 Tf  [( are based on a homogeneous )] TJ ET
BT 26.250 381.991 Td /F1 9.8 Tf  [(mixing approach within the entire Mexico, the approach used here is a spatially structured model that just in Mexico counts 65 )] TJ ET
BT 26.250 370.086 Td /F1 9.8 Tf  [(different census areas. These census areas are not equally connected internationally and between them. The number of cases )] TJ ET
BT 26.250 358.182 Td /F1 9.8 Tf  [(relevant for the international spread of infected individuals are mostly in census areas close to international transportation hubs. )] TJ ET
BT 26.250 346.277 Td /F1 9.8 Tf  [(Poorly connected regions of Mexico on the other hand, while experiencing a considerable number of cases, would contribute )] TJ ET
BT 26.250 334.372 Td /F1 9.8 Tf  [(only marginally to the International spread of cases. This observation readily explains why single population calculations that )] TJ ET
BT 26.250 322.467 Td /F1 9.8 Tf  [(match the detection of imported cases with the local prevalence are necessarily underestimating the latter quantity.)] TJ ET
BT 26.250 303.063 Td /F1 9.8 Tf  [(While GLEaM takes into account a higher level of geographical organization than previous approaches, its estimates still )] TJ ET
BT 26.250 291.158 Td /F1 9.8 Tf  [(contain a number of assumptions and approximations. The contagion within each census area is approximated by means of a )] TJ ET
BT 26.250 279.253 Td /F1 9.8 Tf  [(homogeneous mixing process. Once a person arrives at a census area by plane, he/she comes integrated into the local )] TJ ET
BT 26.250 267.348 Td /F1 9.8 Tf  [(population. This implies that, as in )] TJ ET
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BT 175.815 267.348 Td /F1 9.8 Tf  [([6])] TJ ET
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BT 186.657 267.348 Td /F1 9.8 Tf  [(, the travelers and the local population are equally exposed to the disease. Finally, the )] TJ ET
BT 26.250 255.444 Td /F1 9.8 Tf  [(model considers each individual as independent and the possibility of cluster cases is not considered. Despite these )] TJ ET
BT 26.250 243.539 Td /F1 9.8 Tf  [(shortcomings and other necessary uncertainties, GLEaM predictions might provide additional information for a better )] TJ ET
BT 26.250 231.634 Td /F1 9.8 Tf  [(understanding of the early evolution of the present pandemic. Despite the different approximations used here and in Ref. )] TJ ET
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BT 548.148 231.634 Td /F1 9.8 Tf  [([6])] TJ ET
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BT 558.990 231.634 Td /F1 9.8 Tf  [(, )] TJ ET
BT 26.250 219.729 Td /F1 9.8 Tf  [(both approaches are providing support to the possibility of a reporting ratio of infected cases in Mexico as low as 1 in 100, in )] TJ ET
BT 26.250 207.825 Td /F1 9.8 Tf  [(agreement with prior estimates )] TJ ET
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BT 162.253 207.825 Td /F1 9.8 Tf  [([2])] TJ ET
0.271 0.267 0.267 rg
BT 173.095 207.825 Td /F1 9.8 Tf  [(. This finding is important when evaluating the massive amount of data which are now being )] TJ ET
BT 26.250 195.920 Td /F1 9.8 Tf  [(collected in a large number of countries around the world. We can easily imagine that the reporting rate as well as any estimate )] TJ ET
BT 26.250 184.015 Td /F1 9.8 Tf  [(of the cumulative attack rate in most of the countries could be easily underestimated by orders of magnitude.)] TJ ET
BT 26.250 147.413 Td /F4 12.0 Tf  [(Competing interests)] TJ ET
BT 26.250 127.458 Td /F1 9.8 Tf  [(AV is consulting and has a research agreement with Abbott for the modeling of H1N1 diffusion. The other authors have declared )] TJ ET
BT 26.250 115.554 Td /F1 9.8 Tf  [(that no competing interests exist.)] TJ ET
BT 26.250 78.951 Td /F4 12.0 Tf  [(Tables)] TJ ET
1.000 1.000 1.000 rg
26.250 67.021 555.000 1.500 re f
Q
q
15.000 67.021 577.500 709.979 re W n
0.271 0.267 0.267 rg
BT 26.250 767.476 Td /F1 9.8 Tf  [(subpopulation or the number of imported cases. In the following, simulation results are aggregated at the level of the country for )] TJ ET
BT 26.250 755.571 Td /F1 9.8 Tf  [(a direct comparison with the empirical data available. The initial conditions of the epidemic are defined by setting the onset of )] TJ ET
BT 26.250 743.667 Td /F1 9.8 Tf  [(the outbreak near La Gloria in Mexico on February 18 )] TJ ET
BT 260.357 747.555 Td /F1 8.7 Tf  [(th)] TJ ET
BT 267.585 743.667 Td /F1 9.8 Tf  [( , 2009, as reported by official sources )] TJ ET
0.267 0.267 0.267 rg
BT 435.042 743.667 Td /F1 9.8 Tf  [([36])] TJ ET
0.271 0.267 0.267 rg
BT 451.305 743.667 Td /F1 9.8 Tf  [( and analogously to other )] TJ ET
BT 26.250 731.762 Td /F1 9.8 Tf  [(works )] TJ ET
0.267 0.267 0.267 rg
BT 54.418 731.762 Td /F1 9.8 Tf  [([8])] TJ ET
0.271 0.267 0.267 rg
BT 65.260 731.762 Td /F1 9.8 Tf  [(. We tested different localization of the first cases in census areas close to La Gloria without observing relevant )] TJ ET
BT 26.250 719.857 Td /F1 9.8 Tf  [(variations with respect to the observed results. In Mexico we also consider the control measures implemented in the country )] TJ ET
BT 26.250 707.952 Td /F1 9.8 Tf  [(starting April 24 )] TJ ET
BT 96.694 711.841 Td /F1 8.7 Tf  [(th)] TJ ET
BT 103.922 707.952 Td /F1 9.8 Tf  [( and ending May 10th following Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 261.628 707.952 Td /F1 9.8 Tf  [([2])] TJ ET
0.271 0.267 0.267 rg
BT 272.470 707.952 Td /F1 9.8 Tf  [(, as those might affect the spreading to other countries )] TJ ET
0.267 0.267 0.267 rg
BT 510.390 707.952 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 521.232 707.952 Td /F1 9.8 Tf  [(. Here we )] TJ ET
BT 26.250 696.048 Td /F1 9.8 Tf  [(focus on the cumulative number of cases observed in Mexico at the date of April the 30 )] TJ ET
BT 404.521 699.936 Td /F1 8.7 Tf  [(th)] TJ ET
BT 411.749 696.048 Td /F1 9.8 Tf  [( and the imported cases in the UK, )] TJ ET
BT 26.250 684.143 Td /F1 9.8 Tf  [(US, Brazil, Germany and France. Each simulation represents a stochastic realization of the process and we aggregate data on )] TJ ET
BT 26.250 672.238 Td /F1 9.8 Tf  [(2�10 )] TJ ET
BT 50.918 676.126 Td /F1 8.7 Tf  [(3)] TJ ET
BT 55.736 672.238 Td /F1 9.8 Tf  [( realizations providing reference ranges for all quantities. The data of imported cases are compared with those reported )] TJ ET
BT 26.250 660.333 Td /F1 9.8 Tf  [(in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 57.138 660.333 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 67.980 660.333 Td /F1 9.8 Tf  [( for the UK and the US. The data for France was obtained from Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 362.791 660.333 Td /F1 9.8 Tf  [([23])] TJ ET
0.271 0.267 0.267 rg
BT 379.054 660.333 Td /F1 9.8 Tf  [(, those for Germany from Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 510.727 660.333 Td /F1 9.8 Tf  [([22])] TJ ET
0.271 0.267 0.267 rg
BT 526.990 660.333 Td /F1 9.8 Tf  [( and those )] TJ ET
BT 26.250 648.429 Td /F1 9.8 Tf  [(for Brazil from the reports at the site of the Health Department of the Brazilian Government )] TJ ET
0.267 0.267 0.267 rg
BT 419.126 648.429 Td /F1 9.8 Tf  [([24])] TJ ET
0.271 0.267 0.267 rg
BT 435.389 648.429 Td /F1 9.8 Tf  [(.)] TJ ET
BT 26.250 611.826 Td /F4 12.0 Tf  [(Results and Discussion)] TJ ET
BT 26.250 591.872 Td /F1 9.8 Tf  [(By using GLEaM it is possible to provide a model estimate of the number of imported cases arriving from Mexico to a set of )] TJ ET
BT 26.250 579.967 Td /F1 9.8 Tf  [(selected countries. The estimated 99% reference range is shown in Table 1. The dates and target countries are chosen to )] TJ ET
BT 26.250 568.062 Td /F1 9.8 Tf  [(facilitate the comparison with the numbers found in the literature )] TJ ET
0.267 0.267 0.267 rg
BT 305.334 568.062 Td /F1 9.8 Tf  [([6])] TJ ET
BT 316.176 568.062 Td /F1 9.8 Tf  [([22])] TJ ET
BT 332.439 568.062 Td /F1 9.8 Tf  [([23])] TJ ET
BT 348.702 568.062 Td /F1 9.8 Tf  [([24])] TJ ET
0.271 0.267 0.267 rg
BT 364.965 568.062 Td /F1 9.8 Tf  [(. The numbers shown in the Table refer to the )] TJ ET
BT 26.250 556.158 Td /F1 9.8 Tf  [(importantion of infected/exposed individual traveling from Mexico in one of the listed countries as of the date of May the 8)] TJ ET
BT 548.129 560.046 Td /F1 8.7 Tf  [(th)] TJ ET
BT 555.357 556.158 Td /F1 9.8 Tf  [(. )] TJ ET
BT 26.250 544.253 Td /F1 9.8 Tf  [(Only 2/3 of the exposed travelers are then considered in the cumulative number of cases as only this fraction will eventually )] TJ ET
BT 26.250 532.348 Td /F1 9.8 Tf  [(develop symptoms, according to the model assumptions. The numbers of imported cases to each country are typically small, )] TJ ET
BT 26.250 520.443 Td /F1 9.8 Tf  [(and as such prone to large stochastic fluctuations. However the surveillance values are all within the 99% reference ranges of )] TJ ET
BT 26.250 508.539 Td /F1 9.8 Tf  [(the 2,000 realizations of our model. We will provide elsewhere a full sensitivity analysis of the results but we observe very small )] TJ ET
BT 26.250 496.634 Td /F1 9.8 Tf  [(variations with respect to the presented results in the range of parameters explored. This is because any MLE for R)] TJ ET
BT 522.632 494.570 Td /F5 8.7 Tf  [(0)] TJ ET
BT 527.451 496.634 Td /F1 9.8 Tf  [( and )] TJ ET
BT 26.250 484.729 Td /F1 9.8 Tf  [(generation interval tend to optimize the growth rate with respect to the epidemic timeline thus producing very similar results in )] TJ ET
BT 26.250 472.824 Td /F1 9.8 Tf  [(the early spreading of the epidemic. We have also considered that in the US the travel history is known only for 50% of the )] TJ ET
BT 26.250 460.920 Td /F1 9.8 Tf  [(confirmed cases. The simple extrapolation that provides a twofold estimate of imported cases \(in brackets in Table 1\) is )] TJ ET
BT 26.250 449.015 Td /F1 9.8 Tf  [(however still compatible with the reference range of our stochastic simulations.)] TJ ET
BT 26.250 429.610 Td /F1 9.8 Tf  [(Table 2 shows GLEaM predictions for the size of the epidemic in Mexico on April 30)] TJ ET
BT 387.146 433.498 Td /F1 8.7 Tf  [(th)] TJ ET
BT 394.374 429.610 Td /F1 9.8 Tf  [( and compare the results with the )] TJ ET
BT 26.250 417.705 Td /F1 9.8 Tf  [(estimations of Refs. )] TJ ET
0.267 0.267 0.267 rg
BT 114.575 417.705 Td /F1 9.8 Tf  [([5])] TJ ET
0.271 0.267 0.267 rg
BT 125.417 417.705 Td /F1 9.8 Tf  [( and )] TJ ET
0.267 0.267 0.267 rg
BT 147.101 417.705 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 157.943 417.705 Td /F1 9.8 Tf  [(. We provide the 95% reference range over 2,000 realizations. The obtained range includes the )] TJ ET
BT 26.250 405.801 Td /F1 9.8 Tf  [(lower bound estimate of Ref )] TJ ET
0.267 0.267 0.267 rg
BT 150.348 405.801 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 161.190 405.801 Td /F1 9.8 Tf  [(. Our median value for the number of asymptomatic cases is 734,000 that is again compatible )] TJ ET
BT 26.250 393.896 Td /F1 9.8 Tf  [(with the range of values reported in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 201.838 393.896 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 212.680 393.896 Td /F1 9.8 Tf  [(. While the estimates presented in Refs. )] TJ ET
0.267 0.267 0.267 rg
BT 387.712 393.896 Td /F1 9.8 Tf  [([5])] TJ ET
0.271 0.267 0.267 rg
BT 398.554 393.896 Td /F1 9.8 Tf  [( and )] TJ ET
0.267 0.267 0.267 rg
BT 420.238 393.896 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 431.080 393.896 Td /F1 9.8 Tf  [( are based on a homogeneous )] TJ ET
BT 26.250 381.991 Td /F1 9.8 Tf  [(mixing approach within the entire Mexico, the approach used here is a spatially structured model that just in Mexico counts 65 )] TJ ET
BT 26.250 370.086 Td /F1 9.8 Tf  [(different census areas. These census areas are not equally connected internationally and between them. The number of cases )] TJ ET
BT 26.250 358.182 Td /F1 9.8 Tf  [(relevant for the international spread of infected individuals are mostly in census areas close to international transportation hubs. )] TJ ET
BT 26.250 346.277 Td /F1 9.8 Tf  [(Poorly connected regions of Mexico on the other hand, while experiencing a considerable number of cases, would contribute )] TJ ET
BT 26.250 334.372 Td /F1 9.8 Tf  [(only marginally to the International spread of cases. This observation readily explains why single population calculations that )] TJ ET
BT 26.250 322.467 Td /F1 9.8 Tf  [(match the detection of imported cases with the local prevalence are necessarily underestimating the latter quantity.)] TJ ET
BT 26.250 303.063 Td /F1 9.8 Tf  [(While GLEaM takes into account a higher level of geographical organization than previous approaches, its estimates still )] TJ ET
BT 26.250 291.158 Td /F1 9.8 Tf  [(contain a number of assumptions and approximations. The contagion within each census area is approximated by means of a )] TJ ET
BT 26.250 279.253 Td /F1 9.8 Tf  [(homogeneous mixing process. Once a person arrives at a census area by plane, he/she comes integrated into the local )] TJ ET
BT 26.250 267.348 Td /F1 9.8 Tf  [(population. This implies that, as in )] TJ ET
0.267 0.267 0.267 rg
BT 175.815 267.348 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 186.657 267.348 Td /F1 9.8 Tf  [(, the travelers and the local population are equally exposed to the disease. Finally, the )] TJ ET
BT 26.250 255.444 Td /F1 9.8 Tf  [(model considers each individual as independent and the possibility of cluster cases is not considered. Despite these )] TJ ET
BT 26.250 243.539 Td /F1 9.8 Tf  [(shortcomings and other necessary uncertainties, GLEaM predictions might provide additional information for a better )] TJ ET
BT 26.250 231.634 Td /F1 9.8 Tf  [(understanding of the early evolution of the present pandemic. Despite the different approximations used here and in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 548.148 231.634 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 558.990 231.634 Td /F1 9.8 Tf  [(, )] TJ ET
BT 26.250 219.729 Td /F1 9.8 Tf  [(both approaches are providing support to the possibility of a reporting ratio of infected cases in Mexico as low as 1 in 100, in )] TJ ET
BT 26.250 207.825 Td /F1 9.8 Tf  [(agreement with prior estimates )] TJ ET
0.267 0.267 0.267 rg
BT 162.253 207.825 Td /F1 9.8 Tf  [([2])] TJ ET
0.271 0.267 0.267 rg
BT 173.095 207.825 Td /F1 9.8 Tf  [(. This finding is important when evaluating the massive amount of data which are now being )] TJ ET
BT 26.250 195.920 Td /F1 9.8 Tf  [(collected in a large number of countries around the world. We can easily imagine that the reporting rate as well as any estimate )] TJ ET
BT 26.250 184.015 Td /F1 9.8 Tf  [(of the cumulative attack rate in most of the countries could be easily underestimated by orders of magnitude.)] TJ ET
BT 26.250 147.413 Td /F4 12.0 Tf  [(Competing interests)] TJ ET
BT 26.250 127.458 Td /F1 9.8 Tf  [(AV is consulting and has a research agreement with Abbott for the modeling of H1N1 diffusion. The other authors have declared )] TJ ET
BT 26.250 115.554 Td /F1 9.8 Tf  [(that no competing interests exist.)] TJ ET
BT 26.250 78.951 Td /F4 12.0 Tf  [(Tables)] TJ ET
1.000 1.000 1.000 rg
26.250 67.021 555.000 1.500 re f
Q
q
15.000 67.021 577.500 709.979 re W n
0.271 0.267 0.267 rg
BT 26.250 767.476 Td /F1 9.8 Tf  [(subpopulation or the number of imported cases. In the following, simulation results are aggregated at the level of the country for )] TJ ET
BT 26.250 755.571 Td /F1 9.8 Tf  [(a direct comparison with the empirical data available. The initial conditions of the epidemic are defined by setting the onset of )] TJ ET
BT 26.250 743.667 Td /F1 9.8 Tf  [(the outbreak near La Gloria in Mexico on February 18 )] TJ ET
BT 260.357 747.555 Td /F1 8.7 Tf  [(th)] TJ ET
BT 267.585 743.667 Td /F1 9.8 Tf  [( , 2009, as reported by official sources )] TJ ET
0.267 0.267 0.267 rg
BT 435.042 743.667 Td /F1 9.8 Tf  [([36])] TJ ET
0.271 0.267 0.267 rg
BT 451.305 743.667 Td /F1 9.8 Tf  [( and analogously to other )] TJ ET
BT 26.250 731.762 Td /F1 9.8 Tf  [(works )] TJ ET
0.267 0.267 0.267 rg
BT 54.418 731.762 Td /F1 9.8 Tf  [([8])] TJ ET
0.271 0.267 0.267 rg
BT 65.260 731.762 Td /F1 9.8 Tf  [(. We tested different localization of the first cases in census areas close to La Gloria without observing relevant )] TJ ET
BT 26.250 719.857 Td /F1 9.8 Tf  [(variations with respect to the observed results. In Mexico we also consider the control measures implemented in the country )] TJ ET
BT 26.250 707.952 Td /F1 9.8 Tf  [(starting April 24 )] TJ ET
BT 96.694 711.841 Td /F1 8.7 Tf  [(th)] TJ ET
BT 103.922 707.952 Td /F1 9.8 Tf  [( and ending May 10th following Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 261.628 707.952 Td /F1 9.8 Tf  [([2])] TJ ET
0.271 0.267 0.267 rg
BT 272.470 707.952 Td /F1 9.8 Tf  [(, as those might affect the spreading to other countries )] TJ ET
0.267 0.267 0.267 rg
BT 510.390 707.952 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 521.232 707.952 Td /F1 9.8 Tf  [(. Here we )] TJ ET
BT 26.250 696.048 Td /F1 9.8 Tf  [(focus on the cumulative number of cases observed in Mexico at the date of April the 30 )] TJ ET
BT 404.521 699.936 Td /F1 8.7 Tf  [(th)] TJ ET
BT 411.749 696.048 Td /F1 9.8 Tf  [( and the imported cases in the UK, )] TJ ET
BT 26.250 684.143 Td /F1 9.8 Tf  [(US, Brazil, Germany and France. Each simulation represents a stochastic realization of the process and we aggregate data on )] TJ ET
BT 26.250 672.238 Td /F1 9.8 Tf  [(2�10 )] TJ ET
BT 50.918 676.126 Td /F1 8.7 Tf  [(3)] TJ ET
BT 55.736 672.238 Td /F1 9.8 Tf  [( realizations providing reference ranges for all quantities. The data of imported cases are compared with those reported )] TJ ET
BT 26.250 660.333 Td /F1 9.8 Tf  [(in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 57.138 660.333 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 67.980 660.333 Td /F1 9.8 Tf  [( for the UK and the US. The data for France was obtained from Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 362.791 660.333 Td /F1 9.8 Tf  [([23])] TJ ET
0.271 0.267 0.267 rg
BT 379.054 660.333 Td /F1 9.8 Tf  [(, those for Germany from Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 510.727 660.333 Td /F1 9.8 Tf  [([22])] TJ ET
0.271 0.267 0.267 rg
BT 526.990 660.333 Td /F1 9.8 Tf  [( and those )] TJ ET
BT 26.250 648.429 Td /F1 9.8 Tf  [(for Brazil from the reports at the site of the Health Department of the Brazilian Government )] TJ ET
0.267 0.267 0.267 rg
BT 419.126 648.429 Td /F1 9.8 Tf  [([24])] TJ ET
0.271 0.267 0.267 rg
BT 435.389 648.429 Td /F1 9.8 Tf  [(.)] TJ ET
BT 26.250 611.826 Td /F4 12.0 Tf  [(Results and Discussion)] TJ ET
BT 26.250 591.872 Td /F1 9.8 Tf  [(By using GLEaM it is possible to provide a model estimate of the number of imported cases arriving from Mexico to a set of )] TJ ET
BT 26.250 579.967 Td /F1 9.8 Tf  [(selected countries. The estimated 99% reference range is shown in Table 1. The dates and target countries are chosen to )] TJ ET
BT 26.250 568.062 Td /F1 9.8 Tf  [(facilitate the comparison with the numbers found in the literature )] TJ ET
0.267 0.267 0.267 rg
BT 305.334 568.062 Td /F1 9.8 Tf  [([6])] TJ ET
BT 316.176 568.062 Td /F1 9.8 Tf  [([22])] TJ ET
BT 332.439 568.062 Td /F1 9.8 Tf  [([23])] TJ ET
BT 348.702 568.062 Td /F1 9.8 Tf  [([24])] TJ ET
0.271 0.267 0.267 rg
BT 364.965 568.062 Td /F1 9.8 Tf  [(. The numbers shown in the Table refer to the )] TJ ET
BT 26.250 556.158 Td /F1 9.8 Tf  [(importantion of infected/exposed individual traveling from Mexico in one of the listed countries as of the date of May the 8)] TJ ET
BT 548.129 560.046 Td /F1 8.7 Tf  [(th)] TJ ET
BT 555.357 556.158 Td /F1 9.8 Tf  [(. )] TJ ET
BT 26.250 544.253 Td /F1 9.8 Tf  [(Only 2/3 of the exposed travelers are then considered in the cumulative number of cases as only this fraction will eventually )] TJ ET
BT 26.250 532.348 Td /F1 9.8 Tf  [(develop symptoms, according to the model assumptions. The numbers of imported cases to each country are typically small, )] TJ ET
BT 26.250 520.443 Td /F1 9.8 Tf  [(and as such prone to large stochastic fluctuations. However the surveillance values are all within the 99% reference ranges of )] TJ ET
BT 26.250 508.539 Td /F1 9.8 Tf  [(the 2,000 realizations of our model. We will provide elsewhere a full sensitivity analysis of the results but we observe very small )] TJ ET
BT 26.250 496.634 Td /F1 9.8 Tf  [(variations with respect to the presented results in the range of parameters explored. This is because any MLE for R)] TJ ET
BT 522.632 494.570 Td /F5 8.7 Tf  [(0)] TJ ET
BT 527.451 496.634 Td /F1 9.8 Tf  [( and )] TJ ET
BT 26.250 484.729 Td /F1 9.8 Tf  [(generation interval tend to optimize the growth rate with respect to the epidemic timeline thus producing very similar results in )] TJ ET
BT 26.250 472.824 Td /F1 9.8 Tf  [(the early spreading of the epidemic. We have also considered that in the US the travel history is known only for 50% of the )] TJ ET
BT 26.250 460.920 Td /F1 9.8 Tf  [(confirmed cases. The simple extrapolation that provides a twofold estimate of imported cases \(in brackets in Table 1\) is )] TJ ET
BT 26.250 449.015 Td /F1 9.8 Tf  [(however still compatible with the reference range of our stochastic simulations.)] TJ ET
BT 26.250 429.610 Td /F1 9.8 Tf  [(Table 2 shows GLEaM predictions for the size of the epidemic in Mexico on April 30)] TJ ET
BT 387.146 433.498 Td /F1 8.7 Tf  [(th)] TJ ET
BT 394.374 429.610 Td /F1 9.8 Tf  [( and compare the results with the )] TJ ET
BT 26.250 417.705 Td /F1 9.8 Tf  [(estimations of Refs. )] TJ ET
0.267 0.267 0.267 rg
BT 114.575 417.705 Td /F1 9.8 Tf  [([5])] TJ ET
0.271 0.267 0.267 rg
BT 125.417 417.705 Td /F1 9.8 Tf  [( and )] TJ ET
0.267 0.267 0.267 rg
BT 147.101 417.705 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 157.943 417.705 Td /F1 9.8 Tf  [(. We provide the 95% reference range over 2,000 realizations. The obtained range includes the )] TJ ET
BT 26.250 405.801 Td /F1 9.8 Tf  [(lower bound estimate of Ref )] TJ ET
0.267 0.267 0.267 rg
BT 150.348 405.801 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 161.190 405.801 Td /F1 9.8 Tf  [(. Our median value for the number of asymptomatic cases is 734,000 that is again compatible )] TJ ET
BT 26.250 393.896 Td /F1 9.8 Tf  [(with the range of values reported in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 201.838 393.896 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 212.680 393.896 Td /F1 9.8 Tf  [(. While the estimates presented in Refs. )] TJ ET
0.267 0.267 0.267 rg
BT 387.712 393.896 Td /F1 9.8 Tf  [([5])] TJ ET
0.271 0.267 0.267 rg
BT 398.554 393.896 Td /F1 9.8 Tf  [( and )] TJ ET
0.267 0.267 0.267 rg
BT 420.238 393.896 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 431.080 393.896 Td /F1 9.8 Tf  [( are based on a homogeneous )] TJ ET
BT 26.250 381.991 Td /F1 9.8 Tf  [(mixing approach within the entire Mexico, the approach used here is a spatially structured model that just in Mexico counts 65 )] TJ ET
BT 26.250 370.086 Td /F1 9.8 Tf  [(different census areas. These census areas are not equally connected internationally and between them. The number of cases )] TJ ET
BT 26.250 358.182 Td /F1 9.8 Tf  [(relevant for the international spread of infected individuals are mostly in census areas close to international transportation hubs. )] TJ ET
BT 26.250 346.277 Td /F1 9.8 Tf  [(Poorly connected regions of Mexico on the other hand, while experiencing a considerable number of cases, would contribute )] TJ ET
BT 26.250 334.372 Td /F1 9.8 Tf  [(only marginally to the International spread of cases. This observation readily explains why single population calculations that )] TJ ET
BT 26.250 322.467 Td /F1 9.8 Tf  [(match the detection of imported cases with the local prevalence are necessarily underestimating the latter quantity.)] TJ ET
BT 26.250 303.063 Td /F1 9.8 Tf  [(While GLEaM takes into account a higher level of geographical organization than previous approaches, its estimates still )] TJ ET
BT 26.250 291.158 Td /F1 9.8 Tf  [(contain a number of assumptions and approximations. The contagion within each census area is approximated by means of a )] TJ ET
BT 26.250 279.253 Td /F1 9.8 Tf  [(homogeneous mixing process. Once a person arrives at a census area by plane, he/she comes integrated into the local )] TJ ET
BT 26.250 267.348 Td /F1 9.8 Tf  [(population. This implies that, as in )] TJ ET
0.267 0.267 0.267 rg
BT 175.815 267.348 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
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129.973 705.975 90.780 0.750 re f
129.973 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 157.208 712.001 Td /F1 9.8 Tf  [(85 \(170\))] TJ ET
0.267 0.267 0.267 rg
220.003 721.856 90.780 0.750 re f
220.003 705.975 90.780 0.750 re f
220.003 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 259.972 712.001 Td /F1 9.8 Tf  [(17)] TJ ET
0.267 0.267 0.267 rg
310.034 721.856 90.780 0.750 re f
310.034 705.975 90.780 0.750 re f
310.034 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 350.003 712.001 Td /F1 9.8 Tf  [(11)] TJ ET
0.267 0.267 0.267 rg
400.064 721.856 90.780 0.750 re f
400.064 705.975 90.780 0.750 re f
400.064 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 442.744 712.001 Td /F1 9.8 Tf  [(9)] TJ ET
0.267 0.267 0.267 rg
490.095 721.856 90.780 0.750 re f
490.095 705.975 90.780 0.750 re f
490.095 705.975 0.750 16.631 re f
580.125 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 532.774 712.001 Td /F1 9.8 Tf  [(3)] TJ ET
BT 26.250 658.576 Td /F4 9.8 Tf  [(Table 1: Cumulative number of imported cases from Mexico shown as the 99% reference range over 2,000 realizations )] TJ ET
BT 26.250 646.671 Td /F4 9.8 Tf  [(on May 8 for a few countries.)] TJ ET
BT 160.078 646.671 Td /F1 9.8 Tf  [( The simulations are obtained with the best estimate parameters of the baseline case of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 560.560 646.671 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 26.250 634.767 Td /F1 9.8 Tf  [(and R0=1.75 [95%CI 1.64 to 1.88]. The number of imported infected individuals and of independent clusters correspond to the )] TJ ET
BT 26.250 622.862 Td /F1 9.8 Tf  [(data given in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 104.835 622.862 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 115.677 622.862 Td /F1 9.8 Tf  [( for US, and UK and the values in )] TJ ET
0.267 0.267 0.267 rg
BT 263.087 622.862 Td /F1 9.8 Tf  [([23])] TJ ET
0.271 0.267 0.267 rg
BT 279.350 622.862 Td /F1 9.8 Tf  [( for France, in )] TJ ET
0.267 0.267 0.267 rg
BT 342.208 622.862 Td /F1 9.8 Tf  [([22])] TJ ET
0.271 0.267 0.267 rg
BT 358.471 622.862 Td /F1 9.8 Tf  [( for Germany and in )] TJ ET
0.267 0.267 0.267 rg
BT 447.343 622.862 Td /F1 9.8 Tf  [([24])] TJ ET
0.271 0.267 0.267 rg
BT 463.606 622.862 Td /F1 9.8 Tf  [( for Brazil. No data was )] TJ ET
BT 26.250 610.957 Td /F1 9.8 Tf  [(available to assess the possible presence of clusters in Germany and France. In the USA we report in parentheses the revised )] TJ ET
BT 26.250 599.052 Td /F1 9.8 Tf  [(number considering the rate of unknown travel history in confirmed cases.)] TJ ET
1.000 1.000 1.000 rg
26.250 508.265 555.000 80.906 re f
0.267 0.267 0.267 rg
26.625 588.046 246.478 0.750 re f
26.625 572.165 0.750 16.631 re f
272.353 588.046 308.522 0.750 re f
272.353 572.165 0.750 16.631 re f
580.125 572.165 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 297.938 578.192 Td /F4 9.8 Tf  [(Number of symptomatic cases in Mexico \(Apr. the 30th\))] TJ ET
0.267 0.267 0.267 rg
26.625 572.165 246.478 0.750 re f
26.625 556.284 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 109.499 562.310 Td /F1 9.8 Tf  [(Simulation Results)] TJ ET
0.267 0.267 0.267 rg
272.353 572.165 308.522 0.750 re f
272.353 556.284 0.750 16.631 re f
580.125 556.284 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 379.180 562.310 Td /F1 9.8 Tf  [([121,000 � 1,394,000])] TJ ET
0.267 0.267 0.267 rg
26.625 556.284 246.478 0.750 re f
26.625 540.403 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 85.368 546.429 Td /F1 9.8 Tf  [(Lower bound range of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 203.518 546.429 Td /F1 9.8 Tf  [([6])] TJ ET
272.353 556.284 308.522 0.750 re f
272.353 540.403 0.750 16.631 re f
580.125 540.403 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 389.754 546.429 Td /F1 9.8 Tf  [(113,000-375,000)] TJ ET
0.267 0.267 0.267 rg
26.625 540.403 246.478 0.750 re f
26.625 524.521 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 105.155 530.548 Td /F1 9.8 Tf  [(Estimate of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 177.227 530.548 Td /F1 9.8 Tf  [([5])] TJ ET
0.271 0.267 0.267 rg
BT 188.069 530.548 Td /F1 9.8 Tf  [( *)] TJ ET
0.267 0.267 0.267 rg
272.353 540.403 308.522 0.750 re f
272.353 524.521 0.750 16.631 re f
580.125 524.521 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 391.378 530.548 Td /F1 9.8 Tf  [(2,000 � 280,000)] TJ ET
0.267 0.267 0.267 rg
26.625 524.521 246.478 0.750 re f
26.625 508.640 246.478 0.750 re f
26.625 508.640 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 55.586 514.667 Td /F1 9.8 Tf  [(Mexican official report )] TJ ET
0.267 0.267 0.267 rg
BT 153.116 514.667 Td /F1 9.8 Tf  [([7])] TJ ET
0.271 0.267 0.267 rg
BT 163.958 514.667 Td /F1 9.8 Tf  [( \(confirmed cases\))] TJ ET
0.267 0.267 0.267 rg
272.353 524.521 308.522 0.750 re f
272.353 508.640 308.522 0.750 re f
272.353 508.640 0.750 16.631 re f
580.125 508.640 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 414.417 514.667 Td /F1 9.8 Tf  [(3,350)] TJ ET
BT 26.250 461.241 Td /F4 9.8 Tf  [(Table 2: Predictions of GLEaM for the size of the epidemic in Mexico on April 30 in thousands of cases and )] TJ ET
BT 26.250 449.337 Td /F4 9.8 Tf  [(comparison with other approaches and with empirical data.)] TJ ET
BT 301.493 449.337 Td /F1 9.8 Tf  [( The simulations are obtained with the best estimate parameters )] TJ ET
BT 26.250 437.432 Td /F1 9.8 Tf  [(of the baseline case of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 147.111 437.432 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 157.953 437.432 Td /F1 9.8 Tf  [( and show the 95% reference range over 2,000 stochastic realizations. The results are compared )] TJ ET
BT 26.250 425.527 Td /F1 9.8 Tf  [(with the lower bound estimate range in )] TJ ET
0.267 0.267 0.267 rg
BT 195.871 425.527 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 206.713 425.527 Td /F1 9.8 Tf  [(, the estimate provided in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 338.942 425.527 Td /F1 9.8 Tf  [([5])] TJ ET
0.271 0.267 0.267 rg
BT 349.784 425.527 Td /F1 9.8 Tf  [( and the number of confirmed cases given by official )] TJ ET
BT 26.250 413.622 Td /F1 9.8 Tf  [(reports )] TJ ET
0.267 0.267 0.267 rg
BT 59.303 413.622 Td /F1 9.8 Tf  [([27])] TJ ET
0.271 0.267 0.267 rg
BT 75.566 413.622 Td /F1 9.8 Tf  [(. *The interval provided for Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 213.206 413.622 Td /F1 9.8 Tf  [([5])] TJ ET
0.271 0.267 0.267 rg
BT 224.048 413.622 Td /F1 9.8 Tf  [( is obtained by merging the results reported in the paper under different )] TJ ET
BT 26.250 401.718 Td /F1 9.8 Tf  [(assumptions and including the 95% CI.)] TJ ET
BT 26.250 365.115 Td /F4 12.0 Tf  [(Acknowledgements)] TJ ET
BT 26.250 345.161 Td /F1 9.8 Tf  [(The authors thank IATA and OAG for providing their databases. We are also grateful to the Staff of the Big Red Computer and )] TJ ET
BT 26.250 333.256 Td /F1 9.8 Tf  [(the Computational Facilities at Indiana University, as well as to Ciro Cattuto for his support with the computational infrastructure )] TJ ET
BT 26.250 321.351 Td /F1 9.8 Tf  [(at the ISI Foundation.)] TJ ET
BT 26.250 292.249 Td /F4 12.0 Tf  [(References)] TJ ET
BT 26.250 264.795 Td /F1 9.8 Tf  [(1.)] TJ ET
BT 38.132 264.795 Td /F1 9.8 Tf  [(World Health Organization \(WHO\) pandemic \(H1N1\) situation update 66. Technical report. )] TJ ET
BT 26.250 252.890 Td /F1 9.8 Tf  [(http://www.who.int/csr/don/2009_09_18/en/index.html)] TJ ET
BT 26.250 233.485 Td /F1 9.8 Tf  [(2.)] TJ ET
BT 38.132 233.485 Td /F1 9.8 Tf  [(Cruz-Pacheco G, Duran L, Esteva L, Minzoni A, Lopez-Cervantes M, et al. \(2009\) Modelling of the in?uenza A\(H1N1\)v )] TJ ET
BT 26.250 221.580 Td /F1 9.8 Tf  [(outbreak in Mexico City, April-May 2009, with control sanitary measures. Euro Surveill 14: 19254.)] TJ ET
BT 26.250 202.176 Td /F1 9.8 Tf  [(3.)] TJ ET
BT 38.132 202.176 Td /F1 9.8 Tf  [(Garske T, Legrand J, Donnelly CA, Ward H, Cauchemez S, Fraser C, Ferguson NM, Ghani AC: Assessing the severity of the )] TJ ET
BT 26.250 190.271 Td /F1 9.8 Tf  [(novel A/H1N1 pandemic. BMJ 2009, 339:b2840.)] TJ ET
BT 26.250 170.866 Td /F1 9.8 Tf  [(4.)] TJ ET
BT 38.132 170.866 Td /F1 9.8 Tf  [(Lipsitch M, Hayden FG, Cowling BJ, Leung GM: How to maintain surveillance for novel influenza A H1N1 when there are too )] TJ ET
BT 26.250 158.961 Td /F1 9.8 Tf  [(many cases to count. The Lancet 2009, 374:1209 - 1211)] TJ ET
BT 26.250 139.557 Td /F1 9.8 Tf  [(5.)] TJ ET
BT 38.132 139.557 Td /F1 9.8 Tf  [(Fraser C, Donnelly CA, Cauchemez S, Hanage WP, Van Kerkhove MD, et al. \(2009\) Pandemic Potential of a Strain of )] TJ ET
BT 26.250 127.652 Td /F1 9.8 Tf  [(In?uenza A \(H1N1\): Early Findings. Science 324: 1557-1561.)] TJ ET
BT 26.250 108.247 Td /F1 9.8 Tf  [(6.)] TJ ET
BT 38.132 108.247 Td /F1 9.8 Tf  [(Lipsitch M, La jous M, O�Hagan JJ, Cohen T, Miller JC, et al. \(2009\) Use of Cumulative Incidence of Novel In?uenza A/H1N1 )] TJ ET
BT 26.250 96.342 Td /F1 9.8 Tf  [(in Foreign Travelers to Estimate Lower Bounds on Cumulative Incidence in Mexico. PLoS ONE 4: e6895.)] TJ ET
BT 26.250 76.938 Td /F1 9.8 Tf  [(7.)] TJ ET
BT 38.132 76.938 Td /F1 9.8 Tf  [(Secretaria de Salud, Mexico. Situation actual de la epidemia, Oct 12, 2009. )] TJ ET
BT 26.250 65.033 Td /F1 9.8 Tf  [(http://portal.salud.gob.mx/sites/salud/descargas/pdf/influenza/situacion_actual_epidemia_121009.pdf)] TJ ET
BT 26.250 45.628 Td /F1 9.8 Tf  [(8.)] TJ ET
BT 38.132 45.628 Td /F1 9.8 Tf  [(Balcan D, Colizza V, Goncalves B, Hu H, Ramasco JJ, Vespigani A \(2009\) Multiscale mobility networks and the large scale )] TJ ET
Q
q
15.000 31.342 577.500 745.658 re W n
1.000 1.000 1.000 rg
26.250 705.600 555.000 71.400 re f
0.267 0.267 0.267 rg
26.625 776.625 104.098 0.750 re f
26.625 737.737 0.750 39.638 re f
0.271 0.267 0.267 rg
BT 36.690 766.770 Td /F4 9.8 Tf  [(Number imported )] TJ ET
BT 42.370 759.139 Td /F4 9.8 Tf  [(cases \(May 8th\))] TJ ET
0.267 0.267 0.267 rg
129.973 776.625 90.780 0.750 re f
129.973 737.737 0.750 39.638 re f
0.271 0.267 0.267 rg
BT 165.072 766.770 Td /F4 9.8 Tf  [(USA)] TJ ET
0.267 0.267 0.267 rg
220.003 776.625 90.780 0.750 re f
220.003 737.737 0.750 39.638 re f
0.271 0.267 0.267 rg
BT 258.354 766.770 Td /F4 9.8 Tf  [(UK)] TJ ET
0.267 0.267 0.267 rg
310.034 776.625 90.780 0.750 re f
310.034 737.737 0.750 39.638 re f
0.271 0.267 0.267 rg
BT 339.439 766.770 Td /F4 9.8 Tf  [(France)] TJ ET
0.267 0.267 0.267 rg
400.064 776.625 90.780 0.750 re f
400.064 737.737 0.750 39.638 re f
0.271 0.267 0.267 rg
BT 424.321 766.770 Td /F4 9.8 Tf  [(Germany)] TJ ET
0.267 0.267 0.267 rg
490.095 776.625 90.780 0.750 re f
490.095 737.737 0.750 39.638 re f
580.125 737.737 0.750 39.638 re f
0.271 0.267 0.267 rg
BT 522.210 766.770 Td /F4 9.8 Tf  [(Brazil)] TJ ET
0.267 0.267 0.267 rg
26.625 737.737 104.098 0.750 re f
26.625 721.856 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 38.309 727.883 Td /F1 9.8 Tf  [(Simulation Results)] TJ ET
0.267 0.267 0.267 rg
129.973 737.737 90.780 0.750 re f
129.973 721.856 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 159.100 727.883 Td /F1 9.8 Tf  [(0 � 534)] TJ ET
0.267 0.267 0.267 rg
220.003 737.737 90.780 0.750 re f
220.003 721.856 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 251.841 727.883 Td /F1 9.8 Tf  [(0 � 44)] TJ ET
0.267 0.267 0.267 rg
310.034 737.737 90.780 0.750 re f
310.034 721.856 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 341.871 727.883 Td /F1 9.8 Tf  [(0 � 62)] TJ ET
0.267 0.267 0.267 rg
400.064 737.737 90.780 0.750 re f
400.064 721.856 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 431.902 727.883 Td /F1 9.8 Tf  [(0 � 55)] TJ ET
0.267 0.267 0.267 rg
490.095 737.737 90.780 0.750 re f
490.095 721.856 0.750 16.631 re f
580.125 721.856 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 521.932 727.883 Td /F1 9.8 Tf  [(0 � 45)] TJ ET
0.267 0.267 0.267 rg
26.625 721.856 104.098 0.750 re f
26.625 705.975 104.098 0.750 re f
26.625 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 41.283 712.001 Td /F1 9.8 Tf  [(Surveillance data)] TJ ET
0.267 0.267 0.267 rg
129.973 721.856 90.780 0.750 re f
129.973 705.975 90.780 0.750 re f
129.973 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 157.208 712.001 Td /F1 9.8 Tf  [(85 \(170\))] TJ ET
0.267 0.267 0.267 rg
220.003 721.856 90.780 0.750 re f
220.003 705.975 90.780 0.750 re f
220.003 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 259.972 712.001 Td /F1 9.8 Tf  [(17)] TJ ET
0.267 0.267 0.267 rg
310.034 721.856 90.780 0.750 re f
310.034 705.975 90.780 0.750 re f
310.034 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 350.003 712.001 Td /F1 9.8 Tf  [(11)] TJ ET
0.267 0.267 0.267 rg
400.064 721.856 90.780 0.750 re f
400.064 705.975 90.780 0.750 re f
400.064 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 442.744 712.001 Td /F1 9.8 Tf  [(9)] TJ ET
0.267 0.267 0.267 rg
490.095 721.856 90.780 0.750 re f
490.095 705.975 90.780 0.750 re f
490.095 705.975 0.750 16.631 re f
580.125 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 532.774 712.001 Td /F1 9.8 Tf  [(3)] TJ ET
BT 26.250 658.576 Td /F4 9.8 Tf  [(Table 1: Cumulative number of imported cases from Mexico shown as the 99% reference range over 2,000 realizations )] TJ ET
BT 26.250 646.671 Td /F4 9.8 Tf  [(on May 8 for a few countries.)] TJ ET
BT 160.078 646.671 Td /F1 9.8 Tf  [( The simulations are obtained with the best estimate parameters of the baseline case of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 560.560 646.671 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 26.250 634.767 Td /F1 9.8 Tf  [(and R0=1.75 [95%CI 1.64 to 1.88]. The number of imported infected individuals and of independent clusters correspond to the )] TJ ET
BT 26.250 622.862 Td /F1 9.8 Tf  [(data given in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 104.835 622.862 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 115.677 622.862 Td /F1 9.8 Tf  [( for US, and UK and the values in )] TJ ET
0.267 0.267 0.267 rg
BT 263.087 622.862 Td /F1 9.8 Tf  [([23])] TJ ET
0.271 0.267 0.267 rg
BT 279.350 622.862 Td /F1 9.8 Tf  [( for France, in )] TJ ET
0.267 0.267 0.267 rg
BT 342.208 622.862 Td /F1 9.8 Tf  [([22])] TJ ET
0.271 0.267 0.267 rg
BT 358.471 622.862 Td /F1 9.8 Tf  [( for Germany and in )] TJ ET
0.267 0.267 0.267 rg
BT 447.343 622.862 Td /F1 9.8 Tf  [([24])] TJ ET
0.271 0.267 0.267 rg
BT 463.606 622.862 Td /F1 9.8 Tf  [( for Brazil. No data was )] TJ ET
BT 26.250 610.957 Td /F1 9.8 Tf  [(available to assess the possible presence of clusters in Germany and France. In the USA we report in parentheses the revised )] TJ ET
BT 26.250 599.052 Td /F1 9.8 Tf  [(number considering the rate of unknown travel history in confirmed cases.)] TJ ET
1.000 1.000 1.000 rg
26.250 508.265 555.000 80.906 re f
0.267 0.267 0.267 rg
26.625 588.046 246.478 0.750 re f
26.625 572.165 0.750 16.631 re f
272.353 588.046 308.522 0.750 re f
272.353 572.165 0.750 16.631 re f
580.125 572.165 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 297.938 578.192 Td /F4 9.8 Tf  [(Number of symptomatic cases in Mexico \(Apr. the 30th\))] TJ ET
0.267 0.267 0.267 rg
26.625 572.165 246.478 0.750 re f
26.625 556.284 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 109.499 562.310 Td /F1 9.8 Tf  [(Simulation Results)] TJ ET
0.267 0.267 0.267 rg
272.353 572.165 308.522 0.750 re f
272.353 556.284 0.750 16.631 re f
580.125 556.284 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 379.180 562.310 Td /F1 9.8 Tf  [([121,000 � 1,394,000])] TJ ET
0.267 0.267 0.267 rg
26.625 556.284 246.478 0.750 re f
26.625 540.403 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 85.368 546.429 Td /F1 9.8 Tf  [(Lower bound range of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 203.518 546.429 Td /F1 9.8 Tf  [([6])] TJ ET
272.353 556.284 308.522 0.750 re f
272.353 540.403 0.750 16.631 re f
580.125 540.403 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 389.754 546.429 Td /F1 9.8 Tf  [(113,000-375,000)] TJ ET
0.267 0.267 0.267 rg
26.625 540.403 246.478 0.750 re f
26.625 524.521 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 105.155 530.548 Td /F1 9.8 Tf  [(Estimate of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 177.227 530.548 Td /F1 9.8 Tf  [([5])] TJ ET
0.271 0.267 0.267 rg
BT 188.069 530.548 Td /F1 9.8 Tf  [( *)] TJ ET
0.267 0.267 0.267 rg
272.353 540.403 308.522 0.750 re f
272.353 524.521 0.750 16.631 re f
580.125 524.521 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 391.378 530.548 Td /F1 9.8 Tf  [(2,000 � 280,000)] TJ ET
0.267 0.267 0.267 rg
26.625 524.521 246.478 0.750 re f
26.625 508.640 246.478 0.750 re f
26.625 508.640 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 55.586 514.667 Td /F1 9.8 Tf  [(Mexican official report )] TJ ET
0.267 0.267 0.267 rg
BT 153.116 514.667 Td /F1 9.8 Tf  [([7])] TJ ET
0.271 0.267 0.267 rg
BT 163.958 514.667 Td /F1 9.8 Tf  [( \(confirmed cases\))] TJ ET
0.267 0.267 0.267 rg
272.353 524.521 308.522 0.750 re f
272.353 508.640 308.522 0.750 re f
272.353 508.640 0.750 16.631 re f
580.125 508.640 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 414.417 514.667 Td /F1 9.8 Tf  [(3,350)] TJ ET
BT 26.250 461.241 Td /F4 9.8 Tf  [(Table 2: Predictions of GLEaM for the size of the epidemic in Mexico on April 30 in thousands of cases and )] TJ ET
BT 26.250 449.337 Td /F4 9.8 Tf  [(comparison with other approaches and with empirical data.)] TJ ET
BT 301.493 449.337 Td /F1 9.8 Tf  [( The simulations are obtained with the best estimate parameters )] TJ ET
BT 26.250 437.432 Td /F1 9.8 Tf  [(of the baseline case of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 147.111 437.432 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 157.953 437.432 Td /F1 9.8 Tf  [( and show the 95% reference range over 2,000 stochastic realizations. The results are compared )] TJ ET
BT 26.250 425.527 Td /F1 9.8 Tf  [(with the lower bound estimate range in )] TJ ET
0.267 0.267 0.267 rg
BT 195.871 425.527 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 206.713 425.527 Td /F1 9.8 Tf  [(, the estimate provided in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 338.942 425.527 Td /F1 9.8 Tf  [([5])] TJ ET
0.271 0.267 0.267 rg
BT 349.784 425.527 Td /F1 9.8 Tf  [( and the number of confirmed cases given by official )] TJ ET
BT 26.250 413.622 Td /F1 9.8 Tf  [(reports )] TJ ET
0.267 0.267 0.267 rg
BT 59.303 413.622 Td /F1 9.8 Tf  [([27])] TJ ET
0.271 0.267 0.267 rg
BT 75.566 413.622 Td /F1 9.8 Tf  [(. *The interval provided for Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 213.206 413.622 Td /F1 9.8 Tf  [([5])] TJ ET
0.271 0.267 0.267 rg
BT 224.048 413.622 Td /F1 9.8 Tf  [( is obtained by merging the results reported in the paper under different )] TJ ET
BT 26.250 401.718 Td /F1 9.8 Tf  [(assumptions and including the 95% CI.)] TJ ET
BT 26.250 365.115 Td /F4 12.0 Tf  [(Acknowledgements)] TJ ET
BT 26.250 345.161 Td /F1 9.8 Tf  [(The authors thank IATA and OAG for providing their databases. We are also grateful to the Staff of the Big Red Computer and )] TJ ET
BT 26.250 333.256 Td /F1 9.8 Tf  [(the Computational Facilities at Indiana University, as well as to Ciro Cattuto for his support with the computational infrastructure )] TJ ET
BT 26.250 321.351 Td /F1 9.8 Tf  [(at the ISI Foundation.)] TJ ET
BT 26.250 292.249 Td /F4 12.0 Tf  [(References)] TJ ET
BT 26.250 264.795 Td /F1 9.8 Tf  [(1.)] TJ ET
BT 38.132 264.795 Td /F1 9.8 Tf  [(World Health Organization \(WHO\) pandemic \(H1N1\) situation update 66. Technical report. )] TJ ET
BT 26.250 252.890 Td /F1 9.8 Tf  [(http://www.who.int/csr/don/2009_09_18/en/index.html)] TJ ET
BT 26.250 233.485 Td /F1 9.8 Tf  [(2.)] TJ ET
BT 38.132 233.485 Td /F1 9.8 Tf  [(Cruz-Pacheco G, Duran L, Esteva L, Minzoni A, Lopez-Cervantes M, et al. \(2009\) Modelling of the in?uenza A\(H1N1\)v )] TJ ET
BT 26.250 221.580 Td /F1 9.8 Tf  [(outbreak in Mexico City, April-May 2009, with control sanitary measures. Euro Surveill 14: 19254.)] TJ ET
BT 26.250 202.176 Td /F1 9.8 Tf  [(3.)] TJ ET
BT 38.132 202.176 Td /F1 9.8 Tf  [(Garske T, Legrand J, Donnelly CA, Ward H, Cauchemez S, Fraser C, Ferguson NM, Ghani AC: Assessing the severity of the )] TJ ET
BT 26.250 190.271 Td /F1 9.8 Tf  [(novel A/H1N1 pandemic. BMJ 2009, 339:b2840.)] TJ ET
BT 26.250 170.866 Td /F1 9.8 Tf  [(4.)] TJ ET
BT 38.132 170.866 Td /F1 9.8 Tf  [(Lipsitch M, Hayden FG, Cowling BJ, Leung GM: How to maintain surveillance for novel influenza A H1N1 when there are too )] TJ ET
BT 26.250 158.961 Td /F1 9.8 Tf  [(many cases to count. The Lancet 2009, 374:1209 - 1211)] TJ ET
BT 26.250 139.557 Td /F1 9.8 Tf  [(5.)] TJ ET
BT 38.132 139.557 Td /F1 9.8 Tf  [(Fraser C, Donnelly CA, Cauchemez S, Hanage WP, Van Kerkhove MD, et al. \(2009\) Pandemic Potential of a Strain of )] TJ ET
BT 26.250 127.652 Td /F1 9.8 Tf  [(In?uenza A \(H1N1\): Early Findings. Science 324: 1557-1561.)] TJ ET
BT 26.250 108.247 Td /F1 9.8 Tf  [(6.)] TJ ET
BT 38.132 108.247 Td /F1 9.8 Tf  [(Lipsitch M, La jous M, O�Hagan JJ, Cohen T, Miller JC, et al. \(2009\) Use of Cumulative Incidence of Novel In?uenza A/H1N1 )] TJ ET
BT 26.250 96.342 Td /F1 9.8 Tf  [(in Foreign Travelers to Estimate Lower Bounds on Cumulative Incidence in Mexico. PLoS ONE 4: e6895.)] TJ ET
BT 26.250 76.938 Td /F1 9.8 Tf  [(7.)] TJ ET
BT 38.132 76.938 Td /F1 9.8 Tf  [(Secretaria de Salud, Mexico. Situation actual de la epidemia, Oct 12, 2009. )] TJ ET
BT 26.250 65.033 Td /F1 9.8 Tf  [(http://portal.salud.gob.mx/sites/salud/descargas/pdf/influenza/situacion_actual_epidemia_121009.pdf)] TJ ET
BT 26.250 45.628 Td /F1 9.8 Tf  [(8.)] TJ ET
BT 38.132 45.628 Td /F1 9.8 Tf  [(Balcan D, Colizza V, Goncalves B, Hu H, Ramasco JJ, Vespigani A \(2009\) Multiscale mobility networks and the large scale )] TJ ET
Q
q
15.000 31.342 577.500 745.658 re W n
1.000 1.000 1.000 rg
26.250 705.600 555.000 71.400 re f
0.267 0.267 0.267 rg
26.625 776.625 104.098 0.750 re f
26.625 737.737 0.750 39.638 re f
0.271 0.267 0.267 rg
BT 36.690 766.770 Td /F4 9.8 Tf  [(Number imported )] TJ ET
BT 42.370 759.139 Td /F4 9.8 Tf  [(cases \(May 8th\))] TJ ET
0.267 0.267 0.267 rg
129.973 776.625 90.780 0.750 re f
129.973 737.737 0.750 39.638 re f
0.271 0.267 0.267 rg
BT 165.072 766.770 Td /F4 9.8 Tf  [(USA)] TJ ET
0.267 0.267 0.267 rg
220.003 776.625 90.780 0.750 re f
220.003 737.737 0.750 39.638 re f
0.271 0.267 0.267 rg
BT 258.354 766.770 Td /F4 9.8 Tf  [(UK)] TJ ET
0.267 0.267 0.267 rg
310.034 776.625 90.780 0.750 re f
310.034 737.737 0.750 39.638 re f
0.271 0.267 0.267 rg
BT 339.439 766.770 Td /F4 9.8 Tf  [(France)] TJ ET
0.267 0.267 0.267 rg
400.064 776.625 90.780 0.750 re f
400.064 737.737 0.750 39.638 re f
0.271 0.267 0.267 rg
BT 424.321 766.770 Td /F4 9.8 Tf  [(Germany)] TJ ET
0.267 0.267 0.267 rg
490.095 776.625 90.780 0.750 re f
490.095 737.737 0.750 39.638 re f
580.125 737.737 0.750 39.638 re f
0.271 0.267 0.267 rg
BT 522.210 766.770 Td /F4 9.8 Tf  [(Brazil)] TJ ET
0.267 0.267 0.267 rg
26.625 737.737 104.098 0.750 re f
26.625 721.856 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 38.309 727.883 Td /F1 9.8 Tf  [(Simulation Results)] TJ ET
0.267 0.267 0.267 rg
129.973 737.737 90.780 0.750 re f
129.973 721.856 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 159.100 727.883 Td /F1 9.8 Tf  [(0 � 534)] TJ ET
0.267 0.267 0.267 rg
220.003 737.737 90.780 0.750 re f
220.003 721.856 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 251.841 727.883 Td /F1 9.8 Tf  [(0 � 44)] TJ ET
0.267 0.267 0.267 rg
310.034 737.737 90.780 0.750 re f
310.034 721.856 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 341.871 727.883 Td /F1 9.8 Tf  [(0 � 62)] TJ ET
0.267 0.267 0.267 rg
400.064 737.737 90.780 0.750 re f
400.064 721.856 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 431.902 727.883 Td /F1 9.8 Tf  [(0 � 55)] TJ ET
0.267 0.267 0.267 rg
490.095 737.737 90.780 0.750 re f
490.095 721.856 0.750 16.631 re f
580.125 721.856 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 521.932 727.883 Td /F1 9.8 Tf  [(0 � 45)] TJ ET
0.267 0.267 0.267 rg
26.625 721.856 104.098 0.750 re f
26.625 705.975 104.098 0.750 re f
26.625 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 41.283 712.001 Td /F1 9.8 Tf  [(Surveillance data)] TJ ET
0.267 0.267 0.267 rg
129.973 721.856 90.780 0.750 re f
129.973 705.975 90.780 0.750 re f
129.973 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 157.208 712.001 Td /F1 9.8 Tf  [(85 \(170\))] TJ ET
0.267 0.267 0.267 rg
220.003 721.856 90.780 0.750 re f
220.003 705.975 90.780 0.750 re f
220.003 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 259.972 712.001 Td /F1 9.8 Tf  [(17)] TJ ET
0.267 0.267 0.267 rg
310.034 721.856 90.780 0.750 re f
310.034 705.975 90.780 0.750 re f
310.034 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 350.003 712.001 Td /F1 9.8 Tf  [(11)] TJ ET
0.267 0.267 0.267 rg
400.064 721.856 90.780 0.750 re f
400.064 705.975 90.780 0.750 re f
400.064 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 442.744 712.001 Td /F1 9.8 Tf  [(9)] TJ ET
0.267 0.267 0.267 rg
490.095 721.856 90.780 0.750 re f
490.095 705.975 90.780 0.750 re f
490.095 705.975 0.750 16.631 re f
580.125 705.975 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 532.774 712.001 Td /F1 9.8 Tf  [(3)] TJ ET
BT 26.250 658.576 Td /F4 9.8 Tf  [(Table 1: Cumulative number of imported cases from Mexico shown as the 99% reference range over 2,000 realizations )] TJ ET
BT 26.250 646.671 Td /F4 9.8 Tf  [(on May 8 for a few countries.)] TJ ET
BT 160.078 646.671 Td /F1 9.8 Tf  [( The simulations are obtained with the best estimate parameters of the baseline case of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 560.560 646.671 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 26.250 634.767 Td /F1 9.8 Tf  [(and R0=1.75 [95%CI 1.64 to 1.88]. The number of imported infected individuals and of independent clusters correspond to the )] TJ ET
BT 26.250 622.862 Td /F1 9.8 Tf  [(data given in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 104.835 622.862 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 115.677 622.862 Td /F1 9.8 Tf  [( for US, and UK and the values in )] TJ ET
0.267 0.267 0.267 rg
BT 263.087 622.862 Td /F1 9.8 Tf  [([23])] TJ ET
0.271 0.267 0.267 rg
BT 279.350 622.862 Td /F1 9.8 Tf  [( for France, in )] TJ ET
0.267 0.267 0.267 rg
BT 342.208 622.862 Td /F1 9.8 Tf  [([22])] TJ ET
0.271 0.267 0.267 rg
BT 358.471 622.862 Td /F1 9.8 Tf  [( for Germany and in )] TJ ET
0.267 0.267 0.267 rg
BT 447.343 622.862 Td /F1 9.8 Tf  [([24])] TJ ET
0.271 0.267 0.267 rg
BT 463.606 622.862 Td /F1 9.8 Tf  [( for Brazil. No data was )] TJ ET
BT 26.250 610.957 Td /F1 9.8 Tf  [(available to assess the possible presence of clusters in Germany and France. In the USA we report in parentheses the revised )] TJ ET
BT 26.250 599.052 Td /F1 9.8 Tf  [(number considering the rate of unknown travel history in confirmed cases.)] TJ ET
1.000 1.000 1.000 rg
26.250 508.265 555.000 80.906 re f
0.267 0.267 0.267 rg
26.625 588.046 246.478 0.750 re f
26.625 572.165 0.750 16.631 re f
272.353 588.046 308.522 0.750 re f
272.353 572.165 0.750 16.631 re f
580.125 572.165 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 297.938 578.192 Td /F4 9.8 Tf  [(Number of symptomatic cases in Mexico \(Apr. the 30th\))] TJ ET
0.267 0.267 0.267 rg
26.625 572.165 246.478 0.750 re f
26.625 556.284 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 109.499 562.310 Td /F1 9.8 Tf  [(Simulation Results)] TJ ET
0.267 0.267 0.267 rg
272.353 572.165 308.522 0.750 re f
272.353 556.284 0.750 16.631 re f
580.125 556.284 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 379.180 562.310 Td /F1 9.8 Tf  [([121,000 � 1,394,000])] TJ ET
0.267 0.267 0.267 rg
26.625 556.284 246.478 0.750 re f
26.625 540.403 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 85.368 546.429 Td /F1 9.8 Tf  [(Lower bound range of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 203.518 546.429 Td /F1 9.8 Tf  [([6])] TJ ET
272.353 556.284 308.522 0.750 re f
272.353 540.403 0.750 16.631 re f
580.125 540.403 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 389.754 546.429 Td /F1 9.8 Tf  [(113,000-375,000)] TJ ET
0.267 0.267 0.267 rg
26.625 540.403 246.478 0.750 re f
26.625 524.521 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 105.155 530.548 Td /F1 9.8 Tf  [(Estimate of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 177.227 530.548 Td /F1 9.8 Tf  [([5])] TJ ET
0.271 0.267 0.267 rg
BT 188.069 530.548 Td /F1 9.8 Tf  [( *)] TJ ET
0.267 0.267 0.267 rg
272.353 540.403 308.522 0.750 re f
272.353 524.521 0.750 16.631 re f
580.125 524.521 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 391.378 530.548 Td /F1 9.8 Tf  [(2,000 � 280,000)] TJ ET
0.267 0.267 0.267 rg
26.625 524.521 246.478 0.750 re f
26.625 508.640 246.478 0.750 re f
26.625 508.640 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 55.586 514.667 Td /F1 9.8 Tf  [(Mexican official report )] TJ ET
0.267 0.267 0.267 rg
BT 153.116 514.667 Td /F1 9.8 Tf  [([7])] TJ ET
0.271 0.267 0.267 rg
BT 163.958 514.667 Td /F1 9.8 Tf  [( \(confirmed cases\))] TJ ET
0.267 0.267 0.267 rg
272.353 524.521 308.522 0.750 re f
272.353 508.640 308.522 0.750 re f
272.353 508.640 0.750 16.631 re f
580.125 508.640 0.750 16.631 re f
0.271 0.267 0.267 rg
BT 414.417 514.667 Td /F1 9.8 Tf  [(3,350)] TJ ET
BT 26.250 461.241 Td /F4 9.8 Tf  [(Table 2: Predictions of GLEaM for the size of the epidemic in Mexico on April 30 in thousands of cases and )] TJ ET
BT 26.250 449.337 Td /F4 9.8 Tf  [(comparison with other approaches and with empirical data.)] TJ ET
BT 301.493 449.337 Td /F1 9.8 Tf  [( The simulations are obtained with the best estimate parameters )] TJ ET
BT 26.250 437.432 Td /F1 9.8 Tf  [(of the baseline case of Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 147.111 437.432 Td /F1 9.8 Tf  [([9])] TJ ET
0.271 0.267 0.267 rg
BT 157.953 437.432 Td /F1 9.8 Tf  [( and show the 95% reference range over 2,000 stochastic realizations. The results are compared )] TJ ET
BT 26.250 425.527 Td /F1 9.8 Tf  [(with the lower bound estimate range in )] TJ ET
0.267 0.267 0.267 rg
BT 195.871 425.527 Td /F1 9.8 Tf  [([6])] TJ ET
0.271 0.267 0.267 rg
BT 206.713 425.527 Td /F1 9.8 Tf  [(, the estimate provided in Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 338.942 425.527 Td /F1 9.8 Tf  [([5])] TJ ET
0.271 0.267 0.267 rg
BT 349.784 425.527 Td /F1 9.8 Tf  [( and the number of confirmed cases given by official )] TJ ET
BT 26.250 413.622 Td /F1 9.8 Tf  [(reports )] TJ ET
0.267 0.267 0.267 rg
BT 59.303 413.622 Td /F1 9.8 Tf  [([27])] TJ ET
0.271 0.267 0.267 rg
BT 75.566 413.622 Td /F1 9.8 Tf  [(. *The interval provided for Ref. )] TJ ET
0.267 0.267 0.267 rg
BT 213.206 413.622 Td /F1 9.8 Tf  [([5])] TJ ET
0.271 0.267 0.267 rg
BT 224.048 413.622 Td /F1 9.8 Tf  [( is obtained by merging the results reported in the paper under different )] TJ ET
BT 26.250 401.718 Td /F1 9.8 Tf  [(assumptions and including the 95% CI.)] TJ ET
BT 26.250 365.115 Td /F4 12.0 Tf  [(Acknowledgements)] TJ ET
BT 26.250 345.161 Td /F1 9.8 Tf  [(The authors thank IATA and OAG for providing their databases. We are also grateful to the Staff of the Big Red Computer and )] TJ ET
BT 26.250 333.256 Td /F1 9.8 Tf  [(the Computational Facilities at Indiana University, as well as to Ciro Cattuto for his support with the computational infrastructure )] TJ ET
BT 26.250 321.351 Td /F1 9.8 Tf  [(at the ISI Foundation.)] TJ ET
BT 26.250 292.249 Td /F4 12.0 Tf  [(References)] TJ ET
BT 26.250 264.795 Td /F1 9.8 Tf  [(1.)] TJ ET
BT 38.132 264.795 Td /F1 9.8 Tf  [(World Health Organization \(WHO\) pandemic \(H1N1\) situation update 66. Technical report. )] TJ ET
BT 26.250 252.890 Td /F1 9.8 Tf  [(http://www.who.int/csr/don/2009_09_18/en/index.html)] TJ ET
BT 26.250 233.485 Td /F1 9.8 Tf  [(2.)] TJ ET
BT 38.132 233.485 Td /F1 9.8 Tf  [(Cruz-Pacheco G, Duran L, Esteva L, Minzoni A, Lopez-Cervantes M, et al. \(2009\) Modelling of the in?uenza A\(H1N1\)v )] TJ ET
BT 26.250 221.580 Td /F1 9.8 Tf  [(outbreak in Mexico City, April-May 2009, with control sanitary measures. Euro Surveill 14: 19254.)] TJ ET
BT 26.250 202.176 Td /F1 9.8 Tf  [(3.)] TJ ET
BT 38.132 202.176 Td /F1 9.8 Tf  [(Garske T, Legrand J, Donnelly CA, Ward H, Cauchemez S, Fraser C, Ferguson NM, Ghani AC: Assessing the severity of the )] TJ ET
BT 26.250 190.271 Td /F1 9.8 Tf  [(novel A/H1N1 pandemic. BMJ 2009, 339:b2840.)] TJ ET
BT 26.250 170.866 Td /F1 9.8 Tf  [(4.)] TJ ET
BT 38.132 170.866 Td /F1 9.8 Tf  [(Lipsitch M, Hayden FG, Cowling BJ, Leung GM: How to maintain surveillance for novel influenza A H1N1 when there are too )] TJ ET
BT 26.250 158.961 Td /F1 9.8 Tf  [(many cases to count. The Lancet 2009, 374:1209 - 1211)] TJ ET
BT 26.250 139.557 Td /F1 9.8 Tf  [(5.)] TJ ET
BT 38.132 139.557 Td /F1 9.8 Tf  [(Fraser C, Donnelly CA, Cauchemez S, Hanage WP, Van Kerkhove MD, et al. \(2009\) Pandemic Potential of a Strain of )] TJ ET
BT 26.250 127.652 Td /F1 9.8 Tf  [(In?uenza A \(H1N1\): Early Findings. Science 324: 1557-1561.)] TJ ET
BT 26.250 108.247 Td /F1 9.8 Tf  [(6.)] TJ ET
BT 38.132 108.247 Td /F1 9.8 Tf  [(Lipsitch M, La jous M, O�Hagan JJ, Cohen T, Miller JC, et al. \(2009\) Use of Cumulative Incidence of Novel In?uenza A/H1N1 )] TJ ET
BT 26.250 96.342 Td /F1 9.8 Tf  [(in Foreign Travelers to Estimate Lower Bounds on Cumulative Incidence in Mexico. PLoS ONE 4: e6895.)] TJ ET
BT 26.250 76.938 Td /F1 9.8 Tf  [(7.)] TJ ET
BT 38.132 76.938 Td /F1 9.8 Tf  [(Secretaria de Salud, Mexico. Situation actual de la epidemia, Oct 12, 2009. )] TJ ET
BT 26.250 65.033 Td /F1 9.8 Tf  [(http://portal.salud.gob.mx/sites/salud/descargas/pdf/influenza/situacion_actual_epidemia_121009.pdf)] TJ ET
BT 26.250 45.628 Td /F1 9.8 Tf  [(8.)] TJ ET
BT 38.132 45.628 Td /F1 9.8 Tf  [(Balcan D, Colizza V, Goncalves B, Hu H, Ramasco JJ, Vespigani A \(2009\) Multiscale mobility networks and the large scale )] 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 Influenza)] TJ ET

Q
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BT 26.250 270.929 Td /F1 9.8 Tf  [(25.)] TJ ET
BT 43.553 270.929 Td /F1 9.8 Tf  [(Colizza V, Barrat A, Barth�lemy M, Vespignani A \(2007\) Predictability and epidemic pathways in global outbreaks of )] TJ ET
BT 26.250 259.024 Td /F1 9.8 Tf  [(infectious diseases: the SARS case study. BMC Med, 5:34.)] TJ ET
BT 26.250 239.619 Td /F1 9.8 Tf  [(26.)] TJ ET
BT 43.553 239.619 Td /F1 9.8 Tf  [(Center for International Earth Science Information Network \(CIESIN\), Columbia University; International Food Policy )] TJ ET
BT 26.250 227.715 Td /F1 9.8 Tf  [(Research Institute \(IFPRI\); The World Bank; and Centro Internacional de Agricultura Tropical \(CIAT\). The Gridded Population of )] TJ ET
BT 26.250 215.810 Td /F1 9.8 Tf  [(the World Version 3 \(GPWv3\) and the Global Rural-Urban Mapping Project \(GRUMP\), Alpha Version. )] TJ ET
BT 26.250 203.905 Td /F1 9.8 Tf  [(http://sedac.ciesin.columbia.edu/gpw)] TJ ET
BT 26.250 184.500 Td /F1 9.8 Tf  [(27.)] TJ ET
BT 43.553 184.500 Td /F1 9.8 Tf  [(International Air Transport Association \(IATA\). http://www.iata.org)] TJ ET
BT 26.250 165.096 Td /F1 9.8 Tf  [(28.)] TJ ET
BT 43.553 165.096 Td /F1 9.8 Tf  [(Official Airline Guide \(OAG\). http://www.oag.com)] TJ ET
BT 26.250 145.691 Td /F1 9.8 Tf  [(29.)] TJ ET
BT 43.553 145.691 Td /F1 9.8 Tf  [(Chowell G et al \(2009\): Severe respiratory disease concurrent with the circulation of H1N1 influenza. New Engl J Med )] TJ ET
BT 26.250 133.786 Td /F1 9.8 Tf  [(361:674-679.)] TJ ET
BT 26.250 114.381 Td /F1 9.8 Tf  [(30.)] TJ ET
BT 43.553 114.381 Td /F1 9.8 Tf  [(The ANZIC Influenza Investigators \(2009\) Critical care services and 2009 H1N1 inluenza in Australia and New Zealand. )] TJ ET
BT 26.250 102.477 Td /F1 9.8 Tf  [(New Engl. J Med 10.1056/NEJMoa0908481.)] TJ ET
BT 26.250 83.072 Td /F1 9.8 Tf  [(31.)] TJ ET
BT 43.553 83.072 Td /F1 9.8 Tf  [(Rello J et al. \(2009\) Intensive Care adult patients with severe respiratory failure caused by influenza A\(H1N1\) in Spain. )] TJ ET
BT 26.250 71.167 Td /F1 9.8 Tf  [(Critical care 13:R148.)] TJ ET
BT 26.250 51.762 Td /F1 9.8 Tf  [(32.)] TJ ET
BT 43.553 51.762 Td /F1 9.8 Tf  [(Perez-Padilla R et al \(2009\) Pneumonia and Respiratory failure from swine-origin influenza A\(H1N1\) in Mexico. New Engl J )] TJ ET
Q
q
15.000 37.477 577.500 739.523 re W n
0.271 0.267 0.267 rg
BT 26.250 767.476 Td /F1 9.8 Tf  [(spreading of infectious diseases. ArXiv : 0907.3304.)] TJ ET
BT 26.250 748.071 Td /F1 9.8 Tf  [(9.)] TJ ET
BT 38.132 748.071 Td /F1 9.8 Tf  [(Balcan D, Hu H, Goncalves B, Bajardi P, Poletto C, et al. \(2009\) Seasonal transmission potential and activity peaks of the )] TJ ET
BT 26.250 736.167 Td /F1 9.8 Tf  [(new in?uenza A\(H1N1\): a Monte Carlo likelihood analysis based on human mobility. BMC Medicine 7: 45.)] TJ ET
BT 26.250 716.762 Td /F1 9.8 Tf  [(10.)] TJ ET
BT 43.553 716.762 Td /F1 9.8 Tf  [(Rvachev L, Longini I \(1985\) A mathematical model for the global spread of in?uenza. Mathematical Biosciences 75: 3-22.)] TJ ET
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BT 43.553 697.357 Td /F1 9.8 Tf  [(Grais R, Hugh Ellis J, Glass G \(2003\) Assessing the impact of airline travel on the geographic spread of pandemic )] TJ ET
BT 26.250 685.452 Td /F1 9.8 Tf  [(in?uenza. Eur J Epidemiol 18: 1065-1072.)] TJ ET
BT 26.250 666.048 Td /F1 9.8 Tf  [(12.)] TJ ET
BT 43.553 666.048 Td /F1 9.8 Tf  [(Hufnagel L, Brockmann D, Geisel T \(2004\) Forecast and control of epidemics in a globalized world. Proc Natl Acad Sci )] TJ ET
BT 26.250 654.143 Td /F1 9.8 Tf  [(\(USA\) 101: 15124-15129.)] TJ ET
BT 26.250 634.738 Td /F1 9.8 Tf  [(13.)] TJ ET
BT 43.553 634.738 Td /F1 9.8 Tf  [(Cooper BS, Pitman RJ, Edmunds WJ, Gay NJ \(2006\) Delaying the international spread of pandemic in?uenza. PLoS Med )] TJ ET
BT 26.250 622.833 Td /F1 9.8 Tf  [(3: e212.)] TJ ET
BT 26.250 603.429 Td /F1 9.8 Tf  [(14.)] TJ ET
BT 43.553 603.429 Td /F1 9.8 Tf  [(Epstein JM, Goedecke DM, Yu F, Morris RJ, Wagener DK, et al. \(2007\) Controlling pandemic ?u: The value of international )] TJ ET
BT 26.250 591.524 Td /F1 9.8 Tf  [(air travel restrictions. PLoS ONE 2: e401.)] TJ ET
BT 26.250 572.119 Td /F1 9.8 Tf  [(15.)] TJ ET
BT 43.553 572.119 Td /F1 9.8 Tf  [(Flahault A, Vergu E, Coudeville L, Grais R \(2006\) Strategies for containing a global in?uenza pandemic. Vaccine 24: 6751-)] TJ ET
BT 26.250 560.214 Td /F1 9.8 Tf  [(6755.)] TJ ET
BT 26.250 540.810 Td /F1 9.8 Tf  [(16.)] TJ ET
BT 43.553 540.810 Td /F1 9.8 Tf  [(Viboud C, Bjornstad ON, Smith DL, Simonsen L, Miller MA, et al. \(2006\) Synchrony, Waves, and Spatial Hierarchies in the )] TJ ET
BT 26.250 528.905 Td /F1 9.8 Tf  [(Spread of In?uenza. Science 312: 447-451.)] TJ ET
BT 26.250 509.500 Td /F1 9.8 Tf  [(17.)] TJ ET
BT 43.553 509.500 Td /F1 9.8 Tf  [(Flahault A, Valleron AJ \(1991\) A method for assessing the global spread of HIV-1 infection based on air-travel. Math Popul )] TJ ET
BT 26.250 497.595 Td /F1 9.8 Tf  [(Stud 3: 1-11.)] TJ ET
BT 26.250 478.191 Td /F1 9.8 Tf  [(18.)] TJ ET
BT 43.553 478.191 Td /F1 9.8 Tf  [(Colizza V, Barrat A, Barthelemy M, Vespignani A \(2006\) The role of airline transportation network in the prediction and )] TJ ET
BT 26.250 466.286 Td /F1 9.8 Tf  [(predictability of global epidemics. Proc Natl Acad Sci \(USA\) 103: 2015-2020.)] TJ ET
BT 26.250 446.881 Td /F1 9.8 Tf  [(19.)] TJ ET
BT 43.553 446.881 Td /F1 9.8 Tf  [(Colizza V, Barrat A, Barthelemy M, Valleron AJ, Vespignani A \(2007\) Modeling the Worldwide spread of pandemic )] TJ ET
BT 26.250 434.976 Td /F1 9.8 Tf  [(in?uenza: baseline case and containment interventions. PloS Medicine 4: e13.)] TJ ET
BT 26.250 415.572 Td /F1 9.8 Tf  [(20.)] TJ ET
BT 43.553 415.572 Td /F1 9.8 Tf  [(Keeling M, Rohani P \(2002\) Estimating spatial coupling in epidemiological systems: a mechanistic approach. Ecology )] TJ ET
BT 26.250 403.667 Td /F1 9.8 Tf  [(Letters 5: 20-29.)] TJ ET
BT 26.250 384.262 Td /F1 9.8 Tf  [(21.)] TJ ET
BT 43.553 384.262 Td /F1 9.8 Tf  [(Sattenspiel L, Dietz K \(1995\) A structured epidemic model incorporating geographic mobility among regions. Math Biosci )] TJ ET
BT 26.250 372.357 Td /F1 9.8 Tf  [(128: 71-91.)] TJ ET
BT 26.250 352.953 Td /F1 9.8 Tf  [(22.)] TJ ET
BT 43.553 352.953 Td /F1 9.8 Tf  [(German team for investigation of the Novel in?uenza A\(H1N1\) \(2009\) Description of the early stage of pandemic \(H1N1\) )] TJ ET
BT 26.250 341.048 Td /F1 9.8 Tf  [(2009 in Germany, 27 April-16 June 2009. Euro Surveill 14: 19295.)] TJ ET
BT 26.250 321.643 Td /F1 9.8 Tf  [(23.)] TJ ET
BT 43.553 321.643 Td /F1 9.8 Tf  [(French team for investigation of the Novel in?uenza A\(H1N1\) \(2009\) New in?uenza A\(H1N1\) virus infections in France, )] TJ ET
BT 26.250 309.738 Td /F1 9.8 Tf  [(April-May 2009. Euro Surveill 14: 19221.)] TJ ET
BT 26.250 290.334 Td /F1 9.8 Tf  [(24.)] TJ ET
BT 43.553 290.334 Td /F1 9.8 Tf  [(Reports of the Brazilian Health Department \(Ministerio da Saude\). http://portal.saude.gov.br/portal/saude)] TJ ET
BT 26.250 270.929 Td /F1 9.8 Tf  [(25.)] TJ ET
BT 43.553 270.929 Td /F1 9.8 Tf  [(Colizza V, Barrat A, Barth�lemy M, Vespignani A \(2007\) Predictability and epidemic pathways in global outbreaks of )] TJ ET
BT 26.250 259.024 Td /F1 9.8 Tf  [(infectious diseases: the SARS case study. BMC Med, 5:34.)] TJ ET
BT 26.250 239.619 Td /F1 9.8 Tf  [(26.)] TJ ET
BT 43.553 239.619 Td /F1 9.8 Tf  [(Center for International Earth Science Information Network \(CIESIN\), Columbia University; International Food Policy )] TJ ET
BT 26.250 227.715 Td /F1 9.8 Tf  [(Research Institute \(IFPRI\); The World Bank; and Centro Internacional de Agricultura Tropical \(CIAT\). The Gridded Population of )] TJ ET
BT 26.250 215.810 Td /F1 9.8 Tf  [(the World Version 3 \(GPWv3\) and the Global Rural-Urban Mapping Project \(GRUMP\), Alpha Version. )] TJ ET
BT 26.250 203.905 Td /F1 9.8 Tf  [(http://sedac.ciesin.columbia.edu/gpw)] TJ ET
BT 26.250 184.500 Td /F1 9.8 Tf  [(27.)] TJ ET
BT 43.553 184.500 Td /F1 9.8 Tf  [(International Air Transport Association \(IATA\). http://www.iata.org)] TJ ET
BT 26.250 165.096 Td /F1 9.8 Tf  [(28.)] TJ ET
BT 43.553 165.096 Td /F1 9.8 Tf  [(Official Airline Guide \(OAG\). http://www.oag.com)] TJ ET
BT 26.250 145.691 Td /F1 9.8 Tf  [(29.)] TJ ET
BT 43.553 145.691 Td /F1 9.8 Tf  [(Chowell G et al \(2009\): Severe respiratory disease concurrent with the circulation of H1N1 influenza. New Engl J Med )] TJ ET
BT 26.250 133.786 Td /F1 9.8 Tf  [(361:674-679.)] TJ ET
BT 26.250 114.381 Td /F1 9.8 Tf  [(30.)] TJ ET
BT 43.553 114.381 Td /F1 9.8 Tf  [(The ANZIC Influenza Investigators \(2009\) Critical care services and 2009 H1N1 inluenza in Australia and New Zealand. )] TJ ET
BT 26.250 102.477 Td /F1 9.8 Tf  [(New Engl. J Med 10.1056/NEJMoa0908481.)] TJ ET
BT 26.250 83.072 Td /F1 9.8 Tf  [(31.)] TJ ET
BT 43.553 83.072 Td /F1 9.8 Tf  [(Rello J et al. \(2009\) Intensive Care adult patients with severe respiratory failure caused by influenza A\(H1N1\) in Spain. )] TJ ET
BT 26.250 71.167 Td /F1 9.8 Tf  [(Critical care 13:R148.)] TJ ET
BT 26.250 51.762 Td /F1 9.8 Tf  [(32.)] TJ ET
BT 43.553 51.762 Td /F1 9.8 Tf  [(Perez-Padilla R et al \(2009\) Pneumonia and Respiratory failure from swine-origin influenza A\(H1N1\) in Mexico. New Engl J )] TJ ET
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 Influenza)] TJ ET

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q
15.000 504.024 577.500 272.976 re W n
0.271 0.267 0.267 rg
BT 26.250 767.476 Td /F1 9.8 Tf  [(Med 361: 680-689.)] TJ ET
BT 26.250 748.071 Td /F1 9.8 Tf  [(33.)] TJ ET
BT 43.553 748.071 Td /F1 9.8 Tf  [(Presanis et al \(2009\) The severity of pandemic H1N1 influenza in the United States, April � July 2009. PLoS Currents )] TJ ET
BT 26.250 736.167 Td /F1 9.8 Tf  [(Influenza. 2009 Sep 25 [revised 2009 Oct 2]:RRN1042.)] TJ ET
BT 26.250 716.762 Td /F1 9.8 Tf  [(34.)] TJ ET
BT 43.553 716.762 Td /F1 9.8 Tf  [(Centers for Disease Control and Prevention \(2009\) Bacterial Coinfections in Lung Tissue Specimens from Fatal Cases of )] TJ ET
BT 26.250 704.857 Td /F1 9.8 Tf  [(2009 Pandemic Influenza A \(H1N1\) --- United States, May--August 2009. Morb. Mortal. Wkly. Rep. 58: 1)] TJ ET
BT 26.250 685.452 Td /F1 9.8 Tf  [(35.)] TJ ET
BT 43.553 685.452 Td /F1 9.8 Tf  [(McCaw JM, McVernon J, McBryde ES, Mathews JD \(2009\) Influenza: accounting for prior immunity. Science 325, 1071.)] TJ ET
BT 26.250 666.048 Td /F1 9.8 Tf  [(36.)] TJ ET
BT 43.553 666.048 Td /F1 9.8 Tf  [(Centers for Disease Control and Prevention \(2009\) Morb. Mortal. Wkly. Rep. 58: 521.)] TJ ET
BT 26.250 646.643 Td /F1 9.8 Tf  [(37.)] TJ ET
BT 43.553 646.643 Td /F1 9.8 Tf  [(Katriel, Guy; Stone, Lewi. Pandemic influenza dynamics and the breakdown of herd immunity. PLoS Currents Influenza. )] TJ ET
BT 26.250 634.738 Td /F1 9.8 Tf  [(2009 Oct 2:RRN1046.)] TJ ET
BT 26.250 615.333 Td /F1 9.8 Tf  [(38.)] TJ ET
BT 43.553 615.333 Td /F1 9.8 Tf  [(Yang Y, Sugimoto JD, Halloran ME, Basta NE, Chao DL, Matrajt L, Potter G, Kenah E, Longini IM \(2009\) The )] TJ ET
BT 26.250 603.429 Td /F1 9.8 Tf  [(transmissibility and control of pandemic influenza A\(H1N1\) virus. Science 10.1126/science.1177373)] TJ ET
BT 26.250 584.024 Td /F1 9.8 Tf  [(39.)] TJ ET
BT 43.553 584.024 Td /F1 9.8 Tf  [(Flahault A, Vergu E, Boelle P-Y \(2009\) Potential for a global dynamic of influenza A\(H1N1\). BMC Infect Dis 9: 129.)] TJ ET
BT 26.250 564.619 Td /F1 9.8 Tf  [(40.)] TJ ET
BT 43.553 564.619 Td /F1 9.8 Tf  [(Halloran ME, Hayden FG, Yang Y, Longini IM, Monto AS \(2007\): Antiviral Effects on Influenza Viral Transmission and )] TJ ET
BT 26.250 552.714 Td /F1 9.8 Tf  [(Pathogenicity: Observations from Household-based Trials. Am J Epidemiol 165:212.)] TJ ET
BT 26.250 533.310 Td /F1 9.8 Tf  [(41.)] TJ ET
BT 43.553 533.310 Td /F1 9.8 Tf  [(Carrat F, Vergu E, Ferguson NM, Lemaitre M, Cauchemez S, Leach S, Valleron AJ: Time lines of infection and disease in )] TJ ET
BT 26.250 521.405 Td /F1 9.8 Tf  [(human influenza: a review of volunteer challenge studies. Am J Epidemiol 2008, 167:775-785.)] TJ ET
Q
q
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BT 26.250 767.476 Td /F1 9.8 Tf  [(Med 361: 680-689.)] TJ ET
BT 26.250 748.071 Td /F1 9.8 Tf  [(33.)] TJ ET
BT 43.553 748.071 Td /F1 9.8 Tf  [(Presanis et al \(2009\) The severity of pandemic H1N1 influenza in the United States, April � July 2009. PLoS Currents )] TJ ET
BT 26.250 736.167 Td /F1 9.8 Tf  [(Influenza. 2009 Sep 25 [revised 2009 Oct 2]:RRN1042.)] TJ ET
BT 26.250 716.762 Td /F1 9.8 Tf  [(34.)] TJ ET
BT 43.553 716.762 Td /F1 9.8 Tf  [(Centers for Disease Control and Prevention \(2009\) Bacterial Coinfections in Lung Tissue Specimens from Fatal Cases of )] TJ ET
BT 26.250 704.857 Td /F1 9.8 Tf  [(2009 Pandemic Influenza A \(H1N1\) --- United States, May--August 2009. Morb. Mortal. Wkly. Rep. 58: 1)] TJ ET
BT 26.250 685.452 Td /F1 9.8 Tf  [(35.)] TJ ET
BT 43.553 685.452 Td /F1 9.8 Tf  [(McCaw JM, McVernon J, McBryde ES, Mathews JD \(2009\) Influenza: accounting for prior immunity. Science 325, 1071.)] TJ ET
BT 26.250 666.048 Td /F1 9.8 Tf  [(36.)] TJ ET
BT 43.553 666.048 Td /F1 9.8 Tf  [(Centers for Disease Control and Prevention \(2009\) Morb. Mortal. Wkly. Rep. 58: 521.)] TJ ET
BT 26.250 646.643 Td /F1 9.8 Tf  [(37.)] TJ ET
BT 43.553 646.643 Td /F1 9.8 Tf  [(Katriel, Guy; Stone, Lewi. Pandemic influenza dynamics and the breakdown of herd immunity. PLoS Currents Influenza. )] TJ ET
BT 26.250 634.738 Td /F1 9.8 Tf  [(2009 Oct 2:RRN1046.)] TJ ET
BT 26.250 615.333 Td /F1 9.8 Tf  [(38.)] TJ ET
BT 43.553 615.333 Td /F1 9.8 Tf  [(Yang Y, Sugimoto JD, Halloran ME, Basta NE, Chao DL, Matrajt L, Potter G, Kenah E, Longini IM \(2009\) The )] TJ ET
BT 26.250 603.429 Td /F1 9.8 Tf  [(transmissibility and control of pandemic influenza A\(H1N1\) virus. Science 10.1126/science.1177373)] TJ ET
BT 26.250 584.024 Td /F1 9.8 Tf  [(39.)] TJ ET
BT 43.553 584.024 Td /F1 9.8 Tf  [(Flahault A, Vergu E, Boelle P-Y \(2009\) Potential for a global dynamic of influenza A\(H1N1\). BMC Infect Dis 9: 129.)] TJ ET
BT 26.250 564.619 Td /F1 9.8 Tf  [(40.)] TJ ET
BT 43.553 564.619 Td /F1 9.8 Tf  [(Halloran ME, Hayden FG, Yang Y, Longini IM, Monto AS \(2007\): Antiviral Effects on Influenza Viral Transmission and )] TJ ET
BT 26.250 552.714 Td /F1 9.8 Tf  [(Pathogenicity: Observations from Household-based Trials. Am J Epidemiol 165:212.)] TJ ET
BT 26.250 533.310 Td /F1 9.8 Tf  [(41.)] TJ ET
BT 43.553 533.310 Td /F1 9.8 Tf  [(Carrat F, Vergu E, Ferguson NM, Lemaitre M, Cauchemez S, Leach S, Valleron AJ: Time lines of infection and disease in )] TJ ET
BT 26.250 521.405 Td /F1 9.8 Tf  [(human influenza: a review of volunteer challenge studies. Am J Epidemiol 2008, 167:775-785.)] TJ ET
Q
q
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BT 26.250 767.476 Td /F1 9.8 Tf  [(Med 361: 680-689.)] TJ ET
BT 26.250 748.071 Td /F1 9.8 Tf  [(33.)] TJ ET
BT 43.553 748.071 Td /F1 9.8 Tf  [(Presanis et al \(2009\) The severity of pandemic H1N1 influenza in the United States, April � July 2009. PLoS Currents )] TJ ET
BT 26.250 736.167 Td /F1 9.8 Tf  [(Influenza. 2009 Sep 25 [revised 2009 Oct 2]:RRN1042.)] TJ ET
BT 26.250 716.762 Td /F1 9.8 Tf  [(34.)] TJ ET
BT 43.553 716.762 Td /F1 9.8 Tf  [(Centers for Disease Control and Prevention \(2009\) Bacterial Coinfections in Lung Tissue Specimens from Fatal Cases of )] TJ ET
BT 26.250 704.857 Td /F1 9.8 Tf  [(2009 Pandemic Influenza A \(H1N1\) --- United States, May--August 2009. Morb. Mortal. Wkly. Rep. 58: 1)] TJ ET
BT 26.250 685.452 Td /F1 9.8 Tf  [(35.)] TJ ET
BT 43.553 685.452 Td /F1 9.8 Tf  [(McCaw JM, McVernon J, McBryde ES, Mathews JD \(2009\) Influenza: accounting for prior immunity. Science 325, 1071.)] TJ ET
BT 26.250 666.048 Td /F1 9.8 Tf  [(36.)] TJ ET
BT 43.553 666.048 Td /F1 9.8 Tf  [(Centers for Disease Control and Prevention \(2009\) Morb. Mortal. Wkly. Rep. 58: 521.)] TJ ET
BT 26.250 646.643 Td /F1 9.8 Tf  [(37.)] TJ ET
BT 43.553 646.643 Td /F1 9.8 Tf  [(Katriel, Guy; Stone, Lewi. Pandemic influenza dynamics and the breakdown of herd immunity. PLoS Currents Influenza. )] TJ ET
BT 26.250 634.738 Td /F1 9.8 Tf  [(2009 Oct 2:RRN1046.)] TJ ET
BT 26.250 615.333 Td /F1 9.8 Tf  [(38.)] TJ ET
BT 43.553 615.333 Td /F1 9.8 Tf  [(Yang Y, Sugimoto JD, Halloran ME, Basta NE, Chao DL, Matrajt L, Potter G, Kenah E, Longini IM \(2009\) The )] TJ ET
BT 26.250 603.429 Td /F1 9.8 Tf  [(transmissibility and control of pandemic influenza A\(H1N1\) virus. Science 10.1126/science.1177373)] TJ ET
BT 26.250 584.024 Td /F1 9.8 Tf  [(39.)] TJ ET
BT 43.553 584.024 Td /F1 9.8 Tf  [(Flahault A, Vergu E, Boelle P-Y \(2009\) Potential for a global dynamic of influenza A\(H1N1\). BMC Infect Dis 9: 129.)] TJ ET
BT 26.250 564.619 Td /F1 9.8 Tf  [(40.)] TJ ET
BT 43.553 564.619 Td /F1 9.8 Tf  [(Halloran ME, Hayden FG, Yang Y, Longini IM, Monto AS \(2007\): Antiviral Effects on Influenza Viral Transmission and )] TJ ET
BT 26.250 552.714 Td /F1 9.8 Tf  [(Pathogenicity: Observations from Household-based Trials. Am J Epidemiol 165:212.)] TJ ET
BT 26.250 533.310 Td /F1 9.8 Tf  [(41.)] TJ ET
BT 43.553 533.310 Td /F1 9.8 Tf  [(Carrat F, Vergu E, Ferguson NM, Lemaitre M, Cauchemez S, Leach S, Valleron AJ: Time lines of infection and disease in )] TJ ET
BT 26.250 521.405 Td /F1 9.8 Tf  [(human influenza: a review of volunteer challenge studies. Am J Epidemiol 2008, 167:775-785.)] TJ ET
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BT 25.000 19.825 Td /F1 11.0 Tf  [(PLOS Currents Influenza)] TJ ET

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trailer
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