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Temporal Variations in the Effective Reproduction Number of the 2014 West )] TJ ET BT 26.250 639.438 Td /F1 9.8 Tf [(Africa Ebola Outbreak. PLOS Currents Outbreaks. 2014 Sep 18 . Edition 1. doi: )] TJ ET BT 26.250 627.533 Td /F1 9.8 Tf [(10.1371/currents.outbreaks.9e4c4294ec8ce1adad283172b16bc908.)] TJ ET q 15.000 23.815 577.500 601.337 re W n 0.271 0.267 0.267 rg BT 26.250 598.430 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 578.476 Td /F1 9.8 Tf [(Background)] TJ ET BT 26.250 566.571 Td /F1 9.8 Tf [(The rapidly evolving 2014 Ebola virus disease \(EVD\) outbreak in West Africa is the largest documented in history, both in terms )] TJ ET BT 26.250 554.667 Td /F1 9.8 Tf [(of the number of people infected and in the geographic spread. The high morbidity and mortality have inspired response )] TJ ET BT 26.250 542.762 Td /F1 9.8 Tf [(strategies to the outbreak at the individual, regional, and national levels. Methods to provide real-time assessment of changing )] TJ ET BT 26.250 530.857 Td /F1 9.8 Tf [(transmission dynamics are critical to the understanding of how these adaptive intervention measures have affected the spread )] TJ ET BT 26.250 518.952 Td /F1 9.8 Tf [(of the outbreak.)] TJ ET BT 26.250 499.548 Td /F1 9.8 Tf [(Methods)] TJ ET BT 26.250 487.643 Td /F1 9.8 Tf [(In this analysis, we use the time series of EVD cases in Guinea, Sierra Leone, and Liberia up to September 8, 2014, and )] TJ ET BT 26.250 475.738 Td /F1 9.8 Tf [(employ novel methodology to estimate how the rate of exponential rise of new cases has changed over the outbreak using )] TJ ET BT 26.250 463.833 Td /F1 9.8 Tf [(piecewise fits of exponential curves to the outbreak data.)] TJ ET BT 26.250 444.429 Td /F1 9.8 Tf [(Results)] TJ ET BT 26.250 432.524 Td /F1 9.8 Tf [(We find that for Liberia and Guinea, the effective reproduction number rose, rather than fell, around the time that the outbreak )] TJ ET BT 26.250 420.619 Td /F1 9.8 Tf [(spread to densely populated cities, and enforced quarantine was imposed on several regions in the countries; this may indicate )] TJ ET BT 26.250 408.714 Td /F1 9.8 Tf [(that enforced quarantine may not be an effective control measure.)] TJ ET BT 26.250 389.310 Td /F1 9.8 Tf [(Conclusions)] TJ ET BT 26.250 377.405 Td /F1 9.8 Tf [(If effective control measures are not put in place, and the current rate of exponential rise of new cases continues, we predict )] TJ ET BT 26.250 365.500 Td /F1 9.8 Tf [(4400 new Ebola cases in West Africa during the last half of the month of September, with an upper 95% confidence level of )] TJ ET BT 26.250 353.595 Td /F1 9.8 Tf [(6800 new cases.)] TJ ET BT 26.250 316.993 Td /F4 12.0 Tf [(Funding Statement)] TJ ET BT 26.250 297.039 Td /F1 9.8 Tf [(This publication was made possible by grant number 1R01GM100471-01 from the National Institute of General Medical )] TJ ET BT 26.250 285.134 Td /F1 9.8 Tf [(Sciences \(NIGMS\) at the National Institutes of Health. Its contents are solely the responsibility of the authors and do not )] TJ ET BT 26.250 273.229 Td /F1 9.8 Tf [(necessarily represent the official views of NIGMS. OPL additionally gratefully acknowledges the support of NIH training grant )] TJ ET BT 26.250 261.324 Td /F1 9.8 Tf [(T32AI007358-26. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of )] TJ ET BT 26.250 249.420 Td /F1 9.8 Tf [(the manuscript.)] TJ ET BT 26.250 220.317 Td /F4 12.0 Tf [(Introduction)] TJ ET BT 26.250 200.363 Td /F1 9.8 Tf [(Ebola virus disease \(EVD\) is a severe, often fatal viral infection in humans, with a case fatality risk \(CFR\) of up to 90% in )] TJ ET BT 26.250 188.458 Td /F1 9.8 Tf [(previous outbreaks )] TJ ET 0.267 0.267 0.267 rg BT 111.329 189.965 Td /F4 8.7 Tf [(1)] TJ ET 0.271 0.267 0.267 rg BT 116.147 192.346 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 118.557 189.965 Td /F4 8.7 Tf [(2)] TJ ET 0.271 0.267 0.267 rg BT 123.375 192.346 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 125.785 189.965 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 130.603 192.346 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 133.013 189.965 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 142.650 192.346 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 145.059 189.965 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 154.697 188.458 Td /F1 9.8 Tf [(. There have been 13 recorded outbreaks since 2000, associated with at least two distinct strains )] TJ ET BT 26.250 176.553 Td /F1 9.8 Tf [(of the Ebola virus \(Ebola-Zaire and the Ebola-Sudan\) )] TJ ET 0.267 0.267 0.267 rg BT 258.193 178.061 Td /F4 8.7 Tf [(23)] TJ ET 0.271 0.267 0.267 rg BT 267.830 176.553 Td /F1 9.8 Tf [(, but the current West African outbreak has spread over the largest )] TJ ET BT 26.250 164.649 Td /F1 9.8 Tf [(geographic area and caused the greatest number of infections and deaths )] TJ ET 0.267 0.267 0.267 rg BT 348.185 166.156 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 353.004 168.537 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 355.413 166.156 Td /F4 8.7 Tf [(15)] TJ ET 0.271 0.267 0.267 rg BT 365.051 168.537 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 367.460 166.156 Td /F4 8.7 Tf [(16)] TJ ET 0.271 0.267 0.267 rg BT 377.097 168.537 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 379.507 166.156 Td /F4 8.7 Tf [(22)] TJ ET 0.271 0.267 0.267 rg BT 389.144 168.537 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 391.553 166.156 Td /F4 8.7 Tf [(23)] TJ ET 0.271 0.267 0.267 rg BT 401.191 164.649 Td /F1 9.8 Tf [(. Critically, unlike previous epidemics, )] TJ ET BT 26.250 152.744 Td /F1 9.8 Tf [(this outbreak has spread to densely populated areas, increasing the risk of international spread )] TJ ET 0.267 0.267 0.267 rg BT 438.665 154.251 Td /F4 8.7 Tf [(22)] TJ ET 0.271 0.267 0.267 rg BT 448.303 152.744 Td /F1 9.8 Tf [(; the problem is compounded )] TJ ET BT 26.250 140.839 Td /F1 9.8 Tf [(by lack of resources for effective quarantine and isolation in the under-developed countries that have been affected, and the )] TJ ET BT 26.250 128.934 Td /F1 9.8 Tf [(high mobility of the population in a region with porous borders.)] TJ ET BT 26.250 109.530 Td /F1 9.8 Tf [(The spread of EVD requires direct contact with infected blood, tissue, or body fluids of either the living ill or the recently )] TJ ET BT 26.250 97.625 Td /F1 9.8 Tf [(deceased, and the disease is particularly prone to transmission in unprotected homecare settings and during traditional burials )] TJ ET 0.267 0.267 0.267 rg BT 26.250 87.227 Td /F4 8.7 Tf [(24)] TJ ET 0.271 0.267 0.267 rg BT 35.887 89.608 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 38.297 87.227 Td /F4 8.7 Tf [(25)] TJ ET 0.271 0.267 0.267 rg BT 47.934 85.720 Td /F1 9.8 Tf [(. Symptoms typically appear after 221 days, and the disease quickly progresses and kills most infected patients within a )] TJ ET BT 26.250 73.815 Td /F1 9.8 Tf [(few days )] TJ ET 0.267 0.267 0.267 rg BT 67.434 75.323 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 77.071 77.704 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 79.481 75.323 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 89.118 73.815 Td /F1 9.8 Tf [(. No licensed vaccine or specific treatment is currently available )] TJ ET 0.267 0.267 0.267 rg BT 365.462 75.323 Td /F4 8.7 Tf [(26)] TJ ET 0.271 0.267 0.267 rg BT 375.100 73.815 Td /F1 9.8 Tf [(, leaving improved hygiene, quarantine, )] TJ ET BT 26.250 61.911 Td /F1 9.8 Tf [(isolation, and social distancing as the only potential interventions. In an attempt to quell the outbreak, on August 1st the )] TJ ET BT 26.250 50.006 Td /F1 9.8 Tf [(governments of Guinea, Liberia, and Sierra Leone announced plans to impose a military-enforced mass quarantine of entire )] TJ ET BT 26.250 38.101 Td /F1 9.8 Tf [(regions and villages \(referred to as )] TJ ET BT 179.062 38.101 Td /F5 9.8 Tf [(cordons sanitaire)] TJ ET BT 253.298 38.101 Td /F1 9.8 Tf [(\), in an attempt to prevent spread of the disease to other areas )] TJ ET 0.267 0.267 0.267 rg BT 525.908 39.608 Td /F4 8.7 Tf [(17)] TJ ET 0.271 0.267 0.267 rg BT 535.546 38.101 Td /F1 9.8 Tf [(. The )] TJ ET Q q 15.000 684.354 577.500 53.646 re W n 0.267 0.267 0.267 rg BT 15.000 718.042 Td /F2 21.0 Tf [(Temporal Variations in the Effective Reproduction Number of )] TJ ET BT 15.000 693.094 Td /F2 21.0 Tf [(the 2014 West Africa Ebola Outbreak)] TJ ET Q 0.271 0.267 0.267 rg BT 15.000 675.088 Td /F3 9.8 Tf [(September 18, 2014)] TJ ET BT 97.592 675.088 Td /F3 9.8 Tf [()] TJ ET 0.267 0.267 0.267 rg BT 102.467 675.088 Td /F3 9.8 Tf [(Research Article)] TJ ET BT 26.250 663.247 Td /F1 9.8 Tf [(Sherry Towers)] TJ ET 0.271 0.267 0.267 rg BT 89.635 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 95.056 663.247 Td /F1 9.8 Tf [(Oscar Patterson-Lomba)] TJ ET 0.271 0.267 0.267 rg BT 198.552 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 203.973 663.247 Td /F1 9.8 Tf [(Carlos Castillo-Chavez)] TJ ET 0.271 0.267 0.267 rg BT 26.250 651.342 Td /F1 9.8 Tf [(Towers S, Patterson-Lomba O, Castillo-Chavez C. Temporal Variations in the Effective Reproduction Number of the 2014 West )] TJ ET BT 26.250 639.438 Td /F1 9.8 Tf [(Africa Ebola Outbreak. PLOS Currents Outbreaks. 2014 Sep 18 . Edition 1. doi: )] TJ ET BT 26.250 627.533 Td /F1 9.8 Tf [(10.1371/currents.outbreaks.9e4c4294ec8ce1adad283172b16bc908.)] TJ ET q 15.000 23.815 577.500 601.337 re W n 0.271 0.267 0.267 rg BT 26.250 598.430 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 578.476 Td /F1 9.8 Tf [(Background)] TJ ET BT 26.250 566.571 Td /F1 9.8 Tf [(The rapidly evolving 2014 Ebola virus disease \(EVD\) outbreak in West Africa is the largest documented in history, both in terms )] TJ ET BT 26.250 554.667 Td /F1 9.8 Tf [(of the number of people infected and in the geographic spread. The high morbidity and mortality have inspired response )] TJ ET BT 26.250 542.762 Td /F1 9.8 Tf [(strategies to the outbreak at the individual, regional, and national levels. Methods to provide real-time assessment of changing )] TJ ET BT 26.250 530.857 Td /F1 9.8 Tf [(transmission dynamics are critical to the understanding of how these adaptive intervention measures have affected the spread )] TJ ET BT 26.250 518.952 Td /F1 9.8 Tf [(of the outbreak.)] TJ ET BT 26.250 499.548 Td /F1 9.8 Tf [(Methods)] TJ ET BT 26.250 487.643 Td /F1 9.8 Tf [(In this analysis, we use the time series of EVD cases in Guinea, Sierra Leone, and Liberia up to September 8, 2014, and )] TJ ET BT 26.250 475.738 Td /F1 9.8 Tf [(employ novel methodology to estimate how the rate of exponential rise of new cases has changed over the outbreak using )] TJ ET BT 26.250 463.833 Td /F1 9.8 Tf [(piecewise fits of exponential curves to the outbreak data.)] TJ ET BT 26.250 444.429 Td /F1 9.8 Tf [(Results)] TJ ET BT 26.250 432.524 Td /F1 9.8 Tf [(We find that for Liberia and Guinea, the effective reproduction number rose, rather than fell, around the time that the outbreak )] TJ ET BT 26.250 420.619 Td /F1 9.8 Tf [(spread to densely populated cities, and enforced quarantine was imposed on several regions in the countries; this may indicate )] TJ ET BT 26.250 408.714 Td /F1 9.8 Tf [(that enforced quarantine may not be an effective control measure.)] TJ ET BT 26.250 389.310 Td /F1 9.8 Tf [(Conclusions)] TJ ET BT 26.250 377.405 Td /F1 9.8 Tf [(If effective control measures are not put in place, and the current rate of exponential rise of new cases continues, we predict )] TJ ET BT 26.250 365.500 Td /F1 9.8 Tf [(4400 new Ebola cases in West Africa during the last half of the month of September, with an upper 95% confidence level of )] TJ ET BT 26.250 353.595 Td /F1 9.8 Tf [(6800 new cases.)] TJ ET BT 26.250 316.993 Td /F4 12.0 Tf [(Funding Statement)] TJ ET BT 26.250 297.039 Td /F1 9.8 Tf [(This publication was made possible by grant number 1R01GM100471-01 from the National Institute of General Medical )] TJ ET BT 26.250 285.134 Td /F1 9.8 Tf [(Sciences \(NIGMS\) at the National Institutes of Health. Its contents are solely the responsibility of the authors and do not )] TJ ET BT 26.250 273.229 Td /F1 9.8 Tf [(necessarily represent the official views of NIGMS. OPL additionally gratefully acknowledges the support of NIH training grant )] TJ ET BT 26.250 261.324 Td /F1 9.8 Tf [(T32AI007358-26. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of )] TJ ET BT 26.250 249.420 Td /F1 9.8 Tf [(the manuscript.)] TJ ET BT 26.250 220.317 Td /F4 12.0 Tf [(Introduction)] TJ ET BT 26.250 200.363 Td /F1 9.8 Tf [(Ebola virus disease \(EVD\) is a severe, often fatal viral infection in humans, with a case fatality risk \(CFR\) of up to 90% in )] TJ ET BT 26.250 188.458 Td /F1 9.8 Tf [(previous outbreaks )] TJ ET 0.267 0.267 0.267 rg BT 111.329 189.965 Td /F4 8.7 Tf [(1)] TJ ET 0.271 0.267 0.267 rg BT 116.147 192.346 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 118.557 189.965 Td /F4 8.7 Tf [(2)] TJ ET 0.271 0.267 0.267 rg BT 123.375 192.346 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 125.785 189.965 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 130.603 192.346 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 133.013 189.965 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 142.650 192.346 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 145.059 189.965 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 154.697 188.458 Td /F1 9.8 Tf [(. There have been 13 recorded outbreaks since 2000, associated with at least two distinct strains )] TJ ET BT 26.250 176.553 Td /F1 9.8 Tf [(of the Ebola virus \(Ebola-Zaire and the Ebola-Sudan\) )] TJ ET 0.267 0.267 0.267 rg BT 258.193 178.061 Td /F4 8.7 Tf [(23)] TJ ET 0.271 0.267 0.267 rg BT 267.830 176.553 Td /F1 9.8 Tf [(, but the current West African outbreak has spread over the largest )] TJ ET BT 26.250 164.649 Td /F1 9.8 Tf [(geographic area and caused the greatest number of infections and deaths )] TJ ET 0.267 0.267 0.267 rg BT 348.185 166.156 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 353.004 168.537 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 355.413 166.156 Td /F4 8.7 Tf [(15)] TJ ET 0.271 0.267 0.267 rg BT 365.051 168.537 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 367.460 166.156 Td /F4 8.7 Tf [(16)] TJ ET 0.271 0.267 0.267 rg BT 377.097 168.537 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 379.507 166.156 Td /F4 8.7 Tf [(22)] TJ ET 0.271 0.267 0.267 rg BT 389.144 168.537 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 391.553 166.156 Td /F4 8.7 Tf [(23)] TJ ET 0.271 0.267 0.267 rg BT 401.191 164.649 Td /F1 9.8 Tf [(. Critically, unlike previous epidemics, )] TJ ET BT 26.250 152.744 Td /F1 9.8 Tf [(this outbreak has spread to densely populated areas, increasing the risk of international spread )] TJ ET 0.267 0.267 0.267 rg BT 438.665 154.251 Td /F4 8.7 Tf [(22)] TJ ET 0.271 0.267 0.267 rg BT 448.303 152.744 Td /F1 9.8 Tf [(; the problem is compounded )] TJ ET BT 26.250 140.839 Td /F1 9.8 Tf [(by lack of resources for effective quarantine and isolation in the under-developed countries that have been affected, and the )] TJ ET BT 26.250 128.934 Td /F1 9.8 Tf [(high mobility of the population in a region with porous borders.)] TJ ET BT 26.250 109.530 Td /F1 9.8 Tf [(The spread of EVD requires direct contact with infected blood, tissue, or body fluids of either the living ill or the recently )] TJ ET BT 26.250 97.625 Td /F1 9.8 Tf [(deceased, and the disease is particularly prone to transmission in unprotected homecare settings and during traditional burials )] TJ ET 0.267 0.267 0.267 rg BT 26.250 87.227 Td /F4 8.7 Tf [(24)] TJ ET 0.271 0.267 0.267 rg BT 35.887 89.608 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 38.297 87.227 Td /F4 8.7 Tf [(25)] TJ ET 0.271 0.267 0.267 rg BT 47.934 85.720 Td /F1 9.8 Tf [(. Symptoms typically appear after 221 days, and the disease quickly progresses and kills most infected patients within a )] TJ ET BT 26.250 73.815 Td /F1 9.8 Tf [(few days )] TJ ET 0.267 0.267 0.267 rg BT 67.434 75.323 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 77.071 77.704 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 79.481 75.323 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 89.118 73.815 Td /F1 9.8 Tf [(. No licensed vaccine or specific treatment is currently available )] TJ ET 0.267 0.267 0.267 rg BT 365.462 75.323 Td /F4 8.7 Tf [(26)] TJ ET 0.271 0.267 0.267 rg BT 375.100 73.815 Td /F1 9.8 Tf [(, leaving improved hygiene, quarantine, )] TJ ET BT 26.250 61.911 Td /F1 9.8 Tf [(isolation, and social distancing as the only potential interventions. In an attempt to quell the outbreak, on August 1st the )] TJ ET BT 26.250 50.006 Td /F1 9.8 Tf [(governments of Guinea, Liberia, and Sierra Leone announced plans to impose a military-enforced mass quarantine of entire )] TJ ET BT 26.250 38.101 Td /F1 9.8 Tf [(regions and villages \(referred to as )] TJ ET BT 179.062 38.101 Td /F5 9.8 Tf [(cordons sanitaire)] TJ ET BT 253.298 38.101 Td /F1 9.8 Tf [(\), in an attempt to prevent spread of the disease to other areas )] TJ ET 0.267 0.267 0.267 rg BT 525.908 39.608 Td /F4 8.7 Tf [(17)] TJ ET 0.271 0.267 0.267 rg BT 535.546 38.101 Td /F1 9.8 Tf [(. The )] TJ ET Q q 15.000 684.354 577.500 53.646 re W n 0.267 0.267 0.267 rg BT 15.000 718.042 Td /F2 21.0 Tf [(Temporal Variations in the Effective Reproduction Number of )] TJ ET BT 15.000 693.094 Td /F2 21.0 Tf [(the 2014 West Africa Ebola Outbreak)] TJ ET Q 0.271 0.267 0.267 rg BT 15.000 675.088 Td /F3 9.8 Tf [(September 18, 2014)] TJ ET BT 97.592 675.088 Td /F3 9.8 Tf [()] TJ ET 0.267 0.267 0.267 rg BT 102.467 675.088 Td /F3 9.8 Tf [(Research Article)] TJ ET BT 26.250 663.247 Td /F1 9.8 Tf [(Sherry Towers)] TJ ET 0.271 0.267 0.267 rg BT 89.635 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 95.056 663.247 Td /F1 9.8 Tf [(Oscar Patterson-Lomba)] TJ ET 0.271 0.267 0.267 rg BT 198.552 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 203.973 663.247 Td /F1 9.8 Tf [(Carlos Castillo-Chavez)] TJ ET 0.271 0.267 0.267 rg BT 26.250 651.342 Td /F1 9.8 Tf [(Towers S, Patterson-Lomba O, Castillo-Chavez C. Temporal Variations in the Effective Reproduction Number of the 2014 West )] TJ ET BT 26.250 639.438 Td /F1 9.8 Tf [(Africa Ebola Outbreak. PLOS Currents Outbreaks. 2014 Sep 18 . Edition 1. doi: )] TJ ET BT 26.250 627.533 Td /F1 9.8 Tf [(10.1371/currents.outbreaks.9e4c4294ec8ce1adad283172b16bc908.)] TJ ET q 15.000 23.815 577.500 601.337 re W n 0.271 0.267 0.267 rg BT 26.250 598.430 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 578.476 Td /F1 9.8 Tf [(Background)] TJ ET BT 26.250 566.571 Td /F1 9.8 Tf [(The rapidly evolving 2014 Ebola virus disease \(EVD\) outbreak in West Africa is the largest documented in history, both in terms )] TJ ET BT 26.250 554.667 Td /F1 9.8 Tf [(of the number of people infected and in the geographic spread. The high morbidity and mortality have inspired response )] TJ ET BT 26.250 542.762 Td /F1 9.8 Tf [(strategies to the outbreak at the individual, regional, and national levels. Methods to provide real-time assessment of changing )] TJ ET BT 26.250 530.857 Td /F1 9.8 Tf [(transmission dynamics are critical to the understanding of how these adaptive intervention measures have affected the spread )] TJ ET BT 26.250 518.952 Td /F1 9.8 Tf [(of the outbreak.)] TJ ET BT 26.250 499.548 Td /F1 9.8 Tf [(Methods)] TJ ET BT 26.250 487.643 Td /F1 9.8 Tf [(In this analysis, we use the time series of EVD cases in Guinea, Sierra Leone, and Liberia up to September 8, 2014, and )] TJ ET BT 26.250 475.738 Td /F1 9.8 Tf [(employ novel methodology to estimate how the rate of exponential rise of new cases has changed over the outbreak using )] TJ ET BT 26.250 463.833 Td /F1 9.8 Tf [(piecewise fits of exponential curves to the outbreak data.)] TJ ET BT 26.250 444.429 Td /F1 9.8 Tf [(Results)] TJ ET BT 26.250 432.524 Td /F1 9.8 Tf [(We find that for Liberia and Guinea, the effective reproduction number rose, rather than fell, around the time that the outbreak )] TJ ET BT 26.250 420.619 Td /F1 9.8 Tf [(spread to densely populated cities, and enforced quarantine was imposed on several regions in the countries; this may indicate )] TJ ET BT 26.250 408.714 Td /F1 9.8 Tf [(that enforced quarantine may not be an effective control measure.)] TJ ET BT 26.250 389.310 Td /F1 9.8 Tf [(Conclusions)] TJ ET BT 26.250 377.405 Td /F1 9.8 Tf [(If effective control measures are not put in place, and the current rate of exponential rise of new cases continues, we predict )] TJ ET BT 26.250 365.500 Td /F1 9.8 Tf [(4400 new Ebola cases in West Africa during the last half of the month of September, with an upper 95% confidence level of )] TJ ET BT 26.250 353.595 Td /F1 9.8 Tf [(6800 new cases.)] TJ ET BT 26.250 316.993 Td /F4 12.0 Tf [(Funding Statement)] TJ ET BT 26.250 297.039 Td /F1 9.8 Tf [(This publication was made possible by grant number 1R01GM100471-01 from the National Institute of General Medical )] TJ ET BT 26.250 285.134 Td /F1 9.8 Tf [(Sciences \(NIGMS\) at the National Institutes of Health. Its contents are solely the responsibility of the authors and do not )] TJ ET BT 26.250 273.229 Td /F1 9.8 Tf [(necessarily represent the official views of NIGMS. OPL additionally gratefully acknowledges the support of NIH training grant )] TJ ET BT 26.250 261.324 Td /F1 9.8 Tf [(T32AI007358-26. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of )] TJ ET BT 26.250 249.420 Td /F1 9.8 Tf [(the manuscript.)] TJ ET BT 26.250 220.317 Td /F4 12.0 Tf [(Introduction)] TJ ET BT 26.250 200.363 Td /F1 9.8 Tf [(Ebola virus disease \(EVD\) is a severe, often fatal viral infection in humans, with a case fatality risk \(CFR\) of up to 90% in )] TJ ET BT 26.250 188.458 Td /F1 9.8 Tf [(previous outbreaks )] TJ ET 0.267 0.267 0.267 rg BT 111.329 189.965 Td /F4 8.7 Tf [(1)] TJ ET 0.271 0.267 0.267 rg BT 116.147 192.346 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 118.557 189.965 Td /F4 8.7 Tf [(2)] TJ ET 0.271 0.267 0.267 rg BT 123.375 192.346 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 125.785 189.965 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 130.603 192.346 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 133.013 189.965 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 142.650 192.346 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 145.059 189.965 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 154.697 188.458 Td /F1 9.8 Tf [(. There have been 13 recorded outbreaks since 2000, associated with at least two distinct strains )] TJ ET BT 26.250 176.553 Td /F1 9.8 Tf [(of the Ebola virus \(Ebola-Zaire and the Ebola-Sudan\) )] TJ ET 0.267 0.267 0.267 rg BT 258.193 178.061 Td /F4 8.7 Tf [(23)] TJ ET 0.271 0.267 0.267 rg BT 267.830 176.553 Td /F1 9.8 Tf [(, but the current West African outbreak has spread over the largest )] TJ ET BT 26.250 164.649 Td /F1 9.8 Tf [(geographic area and caused the greatest number of infections and deaths )] TJ ET 0.267 0.267 0.267 rg BT 348.185 166.156 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 353.004 168.537 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 355.413 166.156 Td /F4 8.7 Tf [(15)] TJ ET 0.271 0.267 0.267 rg BT 365.051 168.537 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 367.460 166.156 Td /F4 8.7 Tf [(16)] TJ ET 0.271 0.267 0.267 rg BT 377.097 168.537 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 379.507 166.156 Td /F4 8.7 Tf [(22)] TJ ET 0.271 0.267 0.267 rg BT 389.144 168.537 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 391.553 166.156 Td /F4 8.7 Tf [(23)] TJ ET 0.271 0.267 0.267 rg BT 401.191 164.649 Td /F1 9.8 Tf [(. Critically, unlike previous epidemics, )] TJ ET BT 26.250 152.744 Td /F1 9.8 Tf [(this outbreak has spread to densely populated areas, increasing the risk of international spread )] TJ ET 0.267 0.267 0.267 rg BT 438.665 154.251 Td /F4 8.7 Tf [(22)] TJ ET 0.271 0.267 0.267 rg BT 448.303 152.744 Td /F1 9.8 Tf [(; the problem is compounded )] TJ ET BT 26.250 140.839 Td /F1 9.8 Tf [(by lack of resources for effective quarantine and isolation in the under-developed countries that have been affected, and the )] TJ ET BT 26.250 128.934 Td /F1 9.8 Tf [(high mobility of the population in a region with porous borders.)] TJ ET BT 26.250 109.530 Td /F1 9.8 Tf [(The spread of EVD requires direct contact with infected blood, tissue, or body fluids of either the living ill or the recently )] TJ ET BT 26.250 97.625 Td /F1 9.8 Tf [(deceased, and the disease is particularly prone to transmission in unprotected homecare settings and during traditional burials )] TJ ET 0.267 0.267 0.267 rg BT 26.250 87.227 Td /F4 8.7 Tf [(24)] TJ ET 0.271 0.267 0.267 rg BT 35.887 89.608 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 38.297 87.227 Td /F4 8.7 Tf [(25)] TJ ET 0.271 0.267 0.267 rg BT 47.934 85.720 Td /F1 9.8 Tf [(. Symptoms typically appear after 221 days, and the disease quickly progresses and kills most infected patients within a )] TJ ET BT 26.250 73.815 Td /F1 9.8 Tf [(few days )] TJ ET 0.267 0.267 0.267 rg BT 67.434 75.323 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 77.071 77.704 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 79.481 75.323 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 89.118 73.815 Td /F1 9.8 Tf [(. No licensed vaccine or specific treatment is currently available )] TJ ET 0.267 0.267 0.267 rg BT 365.462 75.323 Td /F4 8.7 Tf [(26)] TJ ET 0.271 0.267 0.267 rg BT 375.100 73.815 Td /F1 9.8 Tf [(, leaving improved hygiene, quarantine, )] TJ ET BT 26.250 61.911 Td /F1 9.8 Tf [(isolation, and social distancing as the only potential interventions. In an attempt to quell the outbreak, on August 1st the )] TJ ET BT 26.250 50.006 Td /F1 9.8 Tf [(governments of Guinea, Liberia, and Sierra Leone announced plans to impose a military-enforced mass quarantine of entire )] TJ ET BT 26.250 38.101 Td /F1 9.8 Tf [(regions and villages \(referred to as )] TJ ET BT 179.062 38.101 Td /F5 9.8 Tf [(cordons sanitaire)] TJ ET BT 253.298 38.101 Td /F1 9.8 Tf [(\), in an attempt to prevent spread of the disease to other areas )] TJ ET 0.267 0.267 0.267 rg BT 525.908 39.608 Td /F4 8.7 Tf [(17)] TJ ET 0.271 0.267 0.267 rg BT 535.546 38.101 Td /F1 9.8 Tf [(. 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They have )] TJ ET BT 26.250 521.753 Td /F1 9.8 Tf [(made the compilation publicly available online at )] TJ ET 0.267 0.267 0.267 rg BT 237.591 521.753 Td /F1 9.8 Tf [(www.healthmap.org/ebola)] TJ ET 0.271 0.267 0.267 rg BT 350.301 521.753 Td /F1 9.8 Tf [( . The HealthMap data do not include separate )] TJ ET BT 26.250 509.848 Td /F1 9.8 Tf [(information regarding the confirmed and probable cases. For this analysis, the time series of EVD cumulative confirmed and )] TJ ET BT 26.250 497.943 Td /F1 9.8 Tf [(probable cases and deaths in Guinea, Sierra Leone, and Liberia were obtained from HealthMap up to September 4, 2014, and )] TJ ET BT 26.250 486.039 Td /F1 9.8 Tf [(supplemented with more recent data from the WHO website.)] TJ ET BT 26.250 466.634 Td /F1 9.8 Tf [(The estimated daily average of the new case incidence data for the three countries are shown in Figure 1. Updates to the WHO )] TJ ET BT 26.250 454.729 Td /F1 9.8 Tf [(case counts occur irregularly in time \(situation updates have occurred every 2 to 9 days since July 1st \), thus to estimate the )] TJ ET BT 26.250 442.824 Td /F1 9.8 Tf [(daily average incidence data between two updates, we take the new incidence accumulated between updates, and divide by the )] TJ ET BT 26.250 430.920 Td /F1 9.8 Tf [(time between updates.)] TJ ET BT 26.250 411.515 Td /F4 9.8 Tf [(Statistical Methods)] TJ ET BT 26.250 392.110 Td /F1 9.8 Tf [(Cumulative incidence data are highly inter-correlated from point to point, and thus are inappropriate for fitting with standard least )] TJ ET BT 26.250 380.205 Td /F1 9.8 Tf [(squares or likelihood fitting methods, which have as an underlying assumption that the observations are independent )] TJ ET 0.267 0.267 0.267 rg BT 531.875 381.713 Td /F4 8.7 Tf [(5)] TJ ET 0.271 0.267 0.267 rg BT 536.694 384.094 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 539.103 381.713 Td /F4 8.7 Tf [(6)] TJ ET 0.271 0.267 0.267 rg BT 543.922 380.205 Td /F1 9.8 Tf [(. Fitting )] TJ ET BT 26.250 368.301 Td /F1 9.8 Tf [(to cumulative incidence data, instead of the time series of number of new cases, can thus lead to dramatically under-estimated )] TJ ET BT 26.250 356.396 Td /F1 9.8 Tf [(confidence intervals on the model parameters, and also potential biases in the fit central values, since points further along the )] TJ ET BT 26.250 344.491 Td /F1 9.8 Tf [(time series \(which are nearly 100% correlated\) are given too much weight in the fit. In this analysis we thus fit to the time series )] TJ ET BT 26.250 332.586 Td /F1 9.8 Tf [(of newly identified cases for each country.)] TJ ET BT 26.250 313.182 Td /F1 9.8 Tf [(Using a Negative Binomial likelihood fit to account for over-dispersion in the data )] TJ ET 0.267 0.267 0.267 rg BT 376.314 314.689 Td /F4 8.7 Tf [(7)] TJ ET 0.271 0.267 0.267 rg BT 381.133 313.182 Td /F1 9.8 Tf [(, for each country we fit piecewise )] TJ ET BT 26.250 301.277 Td /F1 9.8 Tf [(exponential curves along the incidence time series, in which ten contiguous points are fit at a time, and the local exponential )] TJ ET BT 26.250 288.096 Td /F1 9.8 Tf [(rate of rise, )] TJ ET q 24.000 0 0 9.000 77.730 289.896 cm /I4 Do Q BT 101.730 288.096 Td /F1 9.8 Tf [( , is estimated for each. If we have M incidence data points )] TJ ET q 21.000 0 0 13.500 357.521 285.396 cm /I6 Do Q BT 378.521 288.096 Td /F1 9.8 Tf [(, recorded between times )] TJ ET q 19.500 0 0 13.500 490.695 285.396 cm /I8 Do Q BT 510.195 288.096 Td /F1 9.8 Tf [( to )] TJ ET q 21.000 0 0 12.000 523.747 286.896 cm /I10 Do Q BT 544.747 288.096 Td /F1 9.8 Tf [(, where )] TJ ET BT 26.250 275.872 Td /F1 9.8 Tf [(i=1,,M, then the predicted incidence for each point under an exponential rise hypothesis with some rate, )] TJ ET q 24.000 0 0 9.000 484.997 276.396 cm /I12 Do Q BT 508.997 275.872 Td /F1 9.8 Tf [(, is )] TJ ET 0.267 0.267 0.267 rg BT 524.168 277.379 Td /F4 8.7 Tf [(8)] TJ ET 0.271 0.267 0.267 rg BT 528.987 275.872 Td /F1 9.8 Tf [(:)] TJ ET q 160.500 0 0 24.750 26.250 241.241 cm /I14 Do Q BT 26.250 224.217 Td /F1 9.8 Tf [(which simplifies to)] TJ ET q 270.750 0 0 19.500 26.250 194.837 cm /I16 Do Q BT 26.250 175.337 Td /F1 9.8 Tf [(where the )] TJ ET q 25.500 0 0 15.000 71.773 172.337 cm /I18 Do Q BT 97.273 175.337 Td /F1 9.8 Tf [( are normalized such that )] TJ ET q 95.250 0 0 15.000 209.447 172.337 cm /I20 Do Q BT 304.697 175.337 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 155.313 Td /F1 9.8 Tf [(Because of the irregular updates in the data, the time spanned by ten contiguous points ranges from 21 to 34 days. Sensitivity )] TJ ET BT 26.250 143.408 Td /F1 9.8 Tf [(analyses indicate the conclusions of this analysis do not depend on the exact number of contiguous points used for the fits.)] TJ ET BT 26.250 124.003 Td /F1 9.8 Tf [(We also fit an exponential curve to the entire time series for each country, from July 1st onwards \(after July 1st the WHO EVD )] TJ ET BT 26.250 112.098 Td /F1 9.8 Tf [(case count updates for each country became more regular, occurring on average every three days\).)] TJ ET BT 26.250 92.694 Td /F4 9.8 Tf [(Estimation of the effective reproduction number from the local rates of exponential rise)] TJ ET BT 26.250 73.289 Td /F1 9.8 Tf [(The basic reproduction number, )] TJ ET q 14.250 0 0 9.750 166.601 73.063 cm /I22 Do Q BT 180.851 73.289 Td /F1 9.8 Tf [(, of an infectious disease is the average number of secondary cases a case generates )] TJ ET BT 26.250 61.384 Td /F1 9.8 Tf [(during the course of its infectious period, in a completely susceptible population. The basic reproduction number is affected not )] TJ ET BT 26.250 49.479 Td /F1 9.8 Tf [(only by the ease at which an infection is transmitted upon contact between two hosts, but also by the contact rate between )] TJ ET BT 26.250 37.575 Td /F1 9.8 Tf [(members of the population. Because of heterogeneity in susceptibility, infectiousness, and differing social dynamics, the )] TJ ET Q q 15.000 23.289 577.500 753.711 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(spread of disease within the isolated areas has typically been allowed to run its course )] TJ ET 0.267 0.267 0.267 rg BT 401.255 768.983 Td /F4 8.7 Tf [(19)] TJ ET 0.271 0.267 0.267 rg BT 410.892 771.364 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 413.301 768.983 Td /F4 8.7 Tf [(20)] TJ ET 0.271 0.267 0.267 rg BT 422.939 767.476 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 748.071 Td /F1 9.8 Tf [(Assessing the net positive or negative impact of such attempted intervention measures involves assessment of a complex )] TJ ET BT 26.250 736.167 Td /F1 9.8 Tf [(adaptive system, where the system dynamics are intimately connected to the impact of multiple feedback mechanisms that )] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(evolve over time )] TJ ET 0.267 0.267 0.267 rg BT 99.941 725.769 Td /F4 8.7 Tf [(9)] TJ ET 0.271 0.267 0.267 rg BT 104.759 724.262 Td /F1 9.8 Tf [(. Because the situation in West Africa is rapidly evolving in time, and attempts at intervention measures are )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(far ranging and also rapidly evolving, understanding how best to control the outbreak, and/or assessing whether or not current )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(attempts to contain the spread are working, poses unique challenges.)] TJ ET BT 26.250 681.048 Td /F1 9.8 Tf [(In this analysis, we examine current outbreak incidence data for Guinea, Sierra Leone, and Liberia up to September 8, 2014, as )] TJ ET BT 26.250 669.143 Td /F1 9.8 Tf [(estimated by the World Health Organization \(WHO\) )] TJ ET 0.267 0.267 0.267 rg BT 250.568 670.650 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 255.387 673.031 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 257.796 670.650 Td /F4 8.7 Tf [(4)] TJ ET 0.271 0.267 0.267 rg BT 262.615 669.143 Td /F1 9.8 Tf [(. Using novel methodology, we assess the impact of adaptive response )] TJ ET BT 26.250 657.238 Td /F1 9.8 Tf [(measures by fitting piecewise exponential curves along the data time series to estimate the evolving rate of exponential rise \(or )] TJ ET BT 26.250 645.333 Td /F1 9.8 Tf [(decline\) in cases. We then use a Susceptible, Exposed, Infected, Recovered \(SEIR\) model to estimate the temporal patterns of )] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(the effective reproduction number for the outbreak in each country. In the following sections, we describe our sources of data, )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(and the statistical and modeling methods used to estimate the effective reproduction number.)] TJ ET BT 26.250 584.921 Td /F4 12.0 Tf [(Methods and Materials)] TJ ET BT 26.250 564.967 Td /F4 9.8 Tf [(Data)] TJ ET BT 26.250 545.562 Td /F1 9.8 Tf [(As part of the HealthMap project )] TJ ET 0.267 0.267 0.267 rg BT 168.775 547.070 Td /F4 8.7 Tf [(4)] TJ ET 0.271 0.267 0.267 rg BT 173.594 545.562 Td /F1 9.8 Tf [(, epidemiologists and researchers at the Boston Childrens Hospital have compiled from WHO )] TJ ET BT 26.250 533.658 Td /F1 9.8 Tf [(reports of the time series of confirmed and probable EVD case counts during the 2014 West African outbreak )] TJ ET 0.267 0.267 0.267 rg BT 498.803 535.165 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 503.622 533.658 Td /F1 9.8 Tf [(. They have )] TJ ET BT 26.250 521.753 Td /F1 9.8 Tf [(made the compilation publicly available online at )] TJ ET 0.267 0.267 0.267 rg BT 237.591 521.753 Td /F1 9.8 Tf [(www.healthmap.org/ebola)] TJ ET 0.271 0.267 0.267 rg BT 350.301 521.753 Td /F1 9.8 Tf [( . The HealthMap data do not include separate )] TJ ET BT 26.250 509.848 Td /F1 9.8 Tf [(information regarding the confirmed and probable cases. For this analysis, the time series of EVD cumulative confirmed and )] TJ ET BT 26.250 497.943 Td /F1 9.8 Tf [(probable cases and deaths in Guinea, Sierra Leone, and Liberia were obtained from HealthMap up to September 4, 2014, and )] TJ ET BT 26.250 486.039 Td /F1 9.8 Tf [(supplemented with more recent data from the WHO website.)] TJ ET BT 26.250 466.634 Td /F1 9.8 Tf [(The estimated daily average of the new case incidence data for the three countries are shown in Figure 1. Updates to the WHO )] TJ ET BT 26.250 454.729 Td /F1 9.8 Tf [(case counts occur irregularly in time \(situation updates have occurred every 2 to 9 days since July 1st \), thus to estimate the )] TJ ET BT 26.250 442.824 Td /F1 9.8 Tf [(daily average incidence data between two updates, we take the new incidence accumulated between updates, and divide by the )] TJ ET BT 26.250 430.920 Td /F1 9.8 Tf [(time between updates.)] TJ ET BT 26.250 411.515 Td /F4 9.8 Tf [(Statistical Methods)] TJ ET BT 26.250 392.110 Td /F1 9.8 Tf [(Cumulative incidence data are highly inter-correlated from point to point, and thus are inappropriate for fitting with standard least )] TJ ET BT 26.250 380.205 Td /F1 9.8 Tf [(squares or likelihood fitting methods, which have as an underlying assumption that the observations are independent )] TJ ET 0.267 0.267 0.267 rg BT 531.875 381.713 Td /F4 8.7 Tf [(5)] TJ ET 0.271 0.267 0.267 rg BT 536.694 384.094 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 539.103 381.713 Td /F4 8.7 Tf [(6)] TJ ET 0.271 0.267 0.267 rg BT 543.922 380.205 Td /F1 9.8 Tf [(. Fitting )] TJ ET BT 26.250 368.301 Td /F1 9.8 Tf [(to cumulative incidence data, instead of the time series of number of new cases, can thus lead to dramatically under-estimated )] TJ ET BT 26.250 356.396 Td /F1 9.8 Tf [(confidence intervals on the model parameters, and also potential biases in the fit central values, since points further along the )] TJ ET BT 26.250 344.491 Td /F1 9.8 Tf [(time series \(which are nearly 100% correlated\) are given too much weight in the fit. In this analysis we thus fit to the time series )] TJ ET BT 26.250 332.586 Td /F1 9.8 Tf [(of newly identified cases for each country.)] TJ ET BT 26.250 313.182 Td /F1 9.8 Tf [(Using a Negative Binomial likelihood fit to account for over-dispersion in the data )] TJ ET 0.267 0.267 0.267 rg BT 376.314 314.689 Td /F4 8.7 Tf [(7)] TJ ET 0.271 0.267 0.267 rg BT 381.133 313.182 Td /F1 9.8 Tf [(, for each country we fit piecewise )] TJ ET BT 26.250 301.277 Td /F1 9.8 Tf [(exponential curves along the incidence time series, in which ten contiguous points are fit at a time, and the local exponential )] TJ ET BT 26.250 288.096 Td /F1 9.8 Tf [(rate of rise, )] TJ ET q 24.000 0 0 9.000 77.730 289.896 cm /I24 Do Q BT 101.730 288.096 Td /F1 9.8 Tf [( , is estimated for each. If we have M incidence data points )] TJ ET q 21.000 0 0 13.500 357.521 285.396 cm /I26 Do Q BT 378.521 288.096 Td /F1 9.8 Tf [(, recorded between times )] TJ ET q 19.500 0 0 13.500 490.695 285.396 cm /I28 Do Q BT 510.195 288.096 Td /F1 9.8 Tf [( to )] TJ ET q 21.000 0 0 12.000 523.747 286.896 cm /I30 Do Q BT 544.747 288.096 Td /F1 9.8 Tf [(, where )] TJ ET BT 26.250 275.872 Td /F1 9.8 Tf [(i=1,,M, then the predicted incidence for each point under an exponential rise hypothesis with some rate, )] TJ ET q 24.000 0 0 9.000 484.997 276.396 cm /I32 Do Q BT 508.997 275.872 Td /F1 9.8 Tf [(, is )] TJ ET 0.267 0.267 0.267 rg BT 524.168 277.379 Td /F4 8.7 Tf [(8)] TJ ET 0.271 0.267 0.267 rg BT 528.987 275.872 Td /F1 9.8 Tf [(:)] TJ ET q 160.500 0 0 24.750 26.250 241.241 cm /I34 Do Q BT 26.250 224.217 Td /F1 9.8 Tf [(which simplifies to)] TJ ET q 270.750 0 0 19.500 26.250 194.837 cm /I36 Do Q BT 26.250 175.337 Td /F1 9.8 Tf [(where the )] TJ ET q 25.500 0 0 15.000 71.773 172.337 cm /I38 Do Q BT 97.273 175.337 Td /F1 9.8 Tf [( are normalized such that )] TJ ET q 95.250 0 0 15.000 209.447 172.337 cm /I40 Do Q BT 304.697 175.337 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 155.313 Td /F1 9.8 Tf [(Because of the irregular updates in the data, the time spanned by ten contiguous points ranges from 21 to 34 days. Sensitivity )] TJ ET BT 26.250 143.408 Td /F1 9.8 Tf [(analyses indicate the conclusions of this analysis do not depend on the exact number of contiguous points used for the fits.)] TJ ET BT 26.250 124.003 Td /F1 9.8 Tf [(We also fit an exponential curve to the entire time series for each country, from July 1st onwards \(after July 1st the WHO EVD )] TJ ET BT 26.250 112.098 Td /F1 9.8 Tf [(case count updates for each country became more regular, occurring on average every three days\).)] TJ ET BT 26.250 92.694 Td /F4 9.8 Tf [(Estimation of the effective reproduction number from the local rates of exponential rise)] TJ ET BT 26.250 73.289 Td /F1 9.8 Tf [(The basic reproduction number, )] TJ ET q 14.250 0 0 9.750 166.601 73.063 cm /I42 Do Q BT 180.851 73.289 Td /F1 9.8 Tf [(, of an infectious disease is the average number of secondary cases a case generates )] TJ ET BT 26.250 61.384 Td /F1 9.8 Tf [(during the course of its infectious period, in a completely susceptible population. The basic reproduction number is affected not )] TJ ET BT 26.250 49.479 Td /F1 9.8 Tf [(only by the ease at which an infection is transmitted upon contact between two hosts, but also by the contact rate between )] TJ ET BT 26.250 37.575 Td /F1 9.8 Tf [(members of the population. Because of heterogeneity in susceptibility, infectiousness, and differing social dynamics, the )] TJ ET Q q 15.000 23.289 577.500 753.711 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(spread of disease within the isolated areas has typically been allowed to run its course )] TJ ET 0.267 0.267 0.267 rg BT 401.255 768.983 Td /F4 8.7 Tf [(19)] TJ ET 0.271 0.267 0.267 rg BT 410.892 771.364 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 413.301 768.983 Td /F4 8.7 Tf [(20)] TJ ET 0.271 0.267 0.267 rg BT 422.939 767.476 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 748.071 Td /F1 9.8 Tf [(Assessing the net positive or negative impact of such attempted intervention measures involves assessment of a complex )] TJ ET BT 26.250 736.167 Td /F1 9.8 Tf [(adaptive system, where the system dynamics are intimately connected to the impact of multiple feedback mechanisms that )] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(evolve over time )] TJ ET 0.267 0.267 0.267 rg BT 99.941 725.769 Td /F4 8.7 Tf [(9)] TJ ET 0.271 0.267 0.267 rg BT 104.759 724.262 Td /F1 9.8 Tf [(. Because the situation in West Africa is rapidly evolving in time, and attempts at intervention measures are )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(far ranging and also rapidly evolving, understanding how best to control the outbreak, and/or assessing whether or not current )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(attempts to contain the spread are working, poses unique challenges.)] TJ ET BT 26.250 681.048 Td /F1 9.8 Tf [(In this analysis, we examine current outbreak incidence data for Guinea, Sierra Leone, and Liberia up to September 8, 2014, as )] TJ ET BT 26.250 669.143 Td /F1 9.8 Tf [(estimated by the World Health Organization \(WHO\) )] TJ ET 0.267 0.267 0.267 rg BT 250.568 670.650 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 255.387 673.031 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 257.796 670.650 Td /F4 8.7 Tf [(4)] TJ ET 0.271 0.267 0.267 rg BT 262.615 669.143 Td /F1 9.8 Tf [(. Using novel methodology, we assess the impact of adaptive response )] TJ ET BT 26.250 657.238 Td /F1 9.8 Tf [(measures by fitting piecewise exponential curves along the data time series to estimate the evolving rate of exponential rise \(or )] TJ ET BT 26.250 645.333 Td /F1 9.8 Tf [(decline\) in cases. We then use a Susceptible, Exposed, Infected, Recovered \(SEIR\) model to estimate the temporal patterns of )] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(the effective reproduction number for the outbreak in each country. In the following sections, we describe our sources of data, )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(and the statistical and modeling methods used to estimate the effective reproduction number.)] TJ ET BT 26.250 584.921 Td /F4 12.0 Tf [(Methods and Materials)] TJ ET BT 26.250 564.967 Td /F4 9.8 Tf [(Data)] TJ ET BT 26.250 545.562 Td /F1 9.8 Tf [(As part of the HealthMap project )] TJ ET 0.267 0.267 0.267 rg BT 168.775 547.070 Td /F4 8.7 Tf [(4)] TJ ET 0.271 0.267 0.267 rg BT 173.594 545.562 Td /F1 9.8 Tf [(, epidemiologists and researchers at the Boston Childrens Hospital have compiled from WHO )] TJ ET BT 26.250 533.658 Td /F1 9.8 Tf [(reports of the time series of confirmed and probable EVD case counts during the 2014 West African outbreak )] TJ ET 0.267 0.267 0.267 rg BT 498.803 535.165 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 503.622 533.658 Td /F1 9.8 Tf [(. They have )] TJ ET BT 26.250 521.753 Td /F1 9.8 Tf [(made the compilation publicly available online at )] TJ ET 0.267 0.267 0.267 rg BT 237.591 521.753 Td /F1 9.8 Tf [(www.healthmap.org/ebola)] TJ ET 0.271 0.267 0.267 rg BT 350.301 521.753 Td /F1 9.8 Tf [( . The HealthMap data do not include separate )] TJ ET BT 26.250 509.848 Td /F1 9.8 Tf [(information regarding the confirmed and probable cases. For this analysis, the time series of EVD cumulative confirmed and )] TJ ET BT 26.250 497.943 Td /F1 9.8 Tf [(probable cases and deaths in Guinea, Sierra Leone, and Liberia were obtained from HealthMap up to September 4, 2014, and )] TJ ET BT 26.250 486.039 Td /F1 9.8 Tf [(supplemented with more recent data from the WHO website.)] TJ ET BT 26.250 466.634 Td /F1 9.8 Tf [(The estimated daily average of the new case incidence data for the three countries are shown in Figure 1. Updates to the WHO )] TJ ET BT 26.250 454.729 Td /F1 9.8 Tf [(case counts occur irregularly in time \(situation updates have occurred every 2 to 9 days since July 1st \), thus to estimate the )] TJ ET BT 26.250 442.824 Td /F1 9.8 Tf [(daily average incidence data between two updates, we take the new incidence accumulated between updates, and divide by the )] TJ ET BT 26.250 430.920 Td /F1 9.8 Tf [(time between updates.)] TJ ET BT 26.250 411.515 Td /F4 9.8 Tf [(Statistical Methods)] TJ ET BT 26.250 392.110 Td /F1 9.8 Tf [(Cumulative incidence data are highly inter-correlated from point to point, and thus are inappropriate for fitting with standard least )] TJ ET BT 26.250 380.205 Td /F1 9.8 Tf [(squares or likelihood fitting methods, which have as an underlying assumption that the observations are independent )] TJ ET 0.267 0.267 0.267 rg BT 531.875 381.713 Td /F4 8.7 Tf [(5)] TJ ET 0.271 0.267 0.267 rg BT 536.694 384.094 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 539.103 381.713 Td /F4 8.7 Tf [(6)] TJ ET 0.271 0.267 0.267 rg BT 543.922 380.205 Td /F1 9.8 Tf [(. Fitting )] TJ ET BT 26.250 368.301 Td /F1 9.8 Tf [(to cumulative incidence data, instead of the time series of number of new cases, can thus lead to dramatically under-estimated )] TJ ET BT 26.250 356.396 Td /F1 9.8 Tf [(confidence intervals on the model parameters, and also potential biases in the fit central values, since points further along the )] TJ ET BT 26.250 344.491 Td /F1 9.8 Tf [(time series \(which are nearly 100% correlated\) are given too much weight in the fit. In this analysis we thus fit to the time series )] TJ ET BT 26.250 332.586 Td /F1 9.8 Tf [(of newly identified cases for each country.)] TJ ET BT 26.250 313.182 Td /F1 9.8 Tf [(Using a Negative Binomial likelihood fit to account for over-dispersion in the data )] TJ ET 0.267 0.267 0.267 rg BT 376.314 314.689 Td /F4 8.7 Tf [(7)] TJ ET 0.271 0.267 0.267 rg BT 381.133 313.182 Td /F1 9.8 Tf [(, for each country we fit piecewise )] TJ ET BT 26.250 301.277 Td /F1 9.8 Tf [(exponential curves along the incidence time series, in which ten contiguous points are fit at a time, and the local exponential )] TJ ET BT 26.250 288.096 Td /F1 9.8 Tf [(rate of rise, )] TJ ET q 24.000 0 0 9.000 77.730 289.896 cm /I44 Do Q BT 101.730 288.096 Td /F1 9.8 Tf [( , is estimated for each. If we have M incidence data points )] TJ ET q 21.000 0 0 13.500 357.521 285.396 cm /I46 Do Q BT 378.521 288.096 Td /F1 9.8 Tf [(, recorded between times )] TJ ET q 19.500 0 0 13.500 490.695 285.396 cm /I48 Do Q BT 510.195 288.096 Td /F1 9.8 Tf [( to )] TJ ET q 21.000 0 0 12.000 523.747 286.896 cm /I50 Do Q BT 544.747 288.096 Td /F1 9.8 Tf [(, where )] TJ ET BT 26.250 275.872 Td /F1 9.8 Tf [(i=1,,M, then the predicted incidence for each point under an exponential rise hypothesis with some rate, )] TJ ET q 24.000 0 0 9.000 484.997 276.396 cm /I52 Do Q BT 508.997 275.872 Td /F1 9.8 Tf [(, is )] TJ ET 0.267 0.267 0.267 rg BT 524.168 277.379 Td /F4 8.7 Tf [(8)] TJ ET 0.271 0.267 0.267 rg BT 528.987 275.872 Td /F1 9.8 Tf [(:)] TJ ET q 160.500 0 0 24.750 26.250 241.241 cm /I54 Do Q BT 26.250 224.217 Td /F1 9.8 Tf [(which simplifies to)] TJ ET q 270.750 0 0 19.500 26.250 194.837 cm /I56 Do Q BT 26.250 175.337 Td /F1 9.8 Tf [(where the )] TJ ET q 25.500 0 0 15.000 71.773 172.337 cm /I58 Do Q BT 97.273 175.337 Td /F1 9.8 Tf [( are normalized such that )] TJ ET q 95.250 0 0 15.000 209.447 172.337 cm /I60 Do Q BT 304.697 175.337 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 155.313 Td /F1 9.8 Tf [(Because of the irregular updates in the data, the time spanned by ten contiguous points ranges from 21 to 34 days. Sensitivity )] TJ ET BT 26.250 143.408 Td /F1 9.8 Tf [(analyses indicate the conclusions of this analysis do not depend on the exact number of contiguous points used for the fits.)] TJ ET BT 26.250 124.003 Td /F1 9.8 Tf [(We also fit an exponential curve to the entire time series for each country, from July 1st onwards \(after July 1st the WHO EVD )] TJ ET BT 26.250 112.098 Td /F1 9.8 Tf [(case count updates for each country became more regular, occurring on average every three days\).)] TJ ET BT 26.250 92.694 Td /F4 9.8 Tf [(Estimation of the effective reproduction number from the local rates of exponential rise)] TJ ET BT 26.250 73.289 Td /F1 9.8 Tf [(The basic reproduction number, )] TJ ET q 14.250 0 0 9.750 166.601 73.063 cm /I62 Do Q BT 180.851 73.289 Td /F1 9.8 Tf [(, of an infectious disease is the average number of secondary cases a case generates )] TJ ET BT 26.250 61.384 Td /F1 9.8 Tf [(during the course of its infectious period, in a completely susceptible population. The basic reproduction number is affected not )] TJ ET BT 26.250 49.479 Td /F1 9.8 Tf [(only by the ease at which an infection is transmitted upon contact between two hosts, but also by the contact rate between )] TJ ET BT 26.250 37.575 Td /F1 9.8 Tf [(members of the population. 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"! (k.)X, s!Ni&)QL1@6tr3t+C endstream endobj 292 0 obj << /Type /XObject /Subtype /Image /Width 19 /Height 13 /SMask 291 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 19 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 15>> stream (c``$ endstream endobj 293 0 obj << /Type /Page /Parent 3 0 R /Annots [ 297 0 R 301 0 R 321 0 R 337 0 R 342 0 R 346 0 R 366 0 R 382 0 R 386 0 R 390 0 R 410 0 R 426 0 R ] /Contents 294 0 R >> endobj 294 0 obj << /Length 23933 >> stream 0.271 0.267 0.267 rg q 15.000 -250.568 577.500 1027.568 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(estimates of )] TJ ET q 14.250 0 0 9.750 81.523 767.250 cm /I64 Do Q BT 95.773 767.476 Td /F1 9.8 Tf [( for an infectious disease tend to be different across populations. For example, rural and densely populated )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(urban areas are likely to have substantial differences in contact rates )] TJ ET 0.267 0.267 0.267 rg BT 325.390 757.079 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 335.027 755.571 Td /F1 9.8 Tf [(. Traditionally )] TJ ET q 14.250 0 0 9.750 395.711 755.345 cm /I66 Do Q BT 409.961 755.571 Td /F1 9.8 Tf [( has been computed under simplifying )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(assumptions, like the existence of a constant contact structure, or under the assumption that interventions like quarantine and )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(isolation are uniformly applied from the very beginning of the epidemic. However, particularly in the case of a disease with high )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(morbidity and mortality, it has been shown that human behaviors adapt to limit spread of the disease )] TJ ET 0.267 0.267 0.267 rg BT 461.412 721.364 Td /F4 8.7 Tf [(9)] TJ ET 0.271 0.267 0.267 rg BT 466.231 719.857 Td /F1 9.8 Tf [(, thus limiting the )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(usefulness of )] TJ ET q 14.250 0 0 9.750 86.407 707.726 cm /I68 Do Q BT 100.657 707.952 Td /F1 9.8 Tf [( as a means to assess the efficacy of evolving intervention strategies, and to forecast the future progression of )] TJ ET BT 26.250 696.048 Td /F1 9.8 Tf [(the outbreak.)] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(Given these limitations of )] TJ ET q 14.250 0 0 9.750 137.878 676.417 cm /I70 Do Q BT 152.128 676.643 Td /F1 9.8 Tf [(, in this analysis we thus instead assess the time evolution of the effective reproduction number, )] TJ ET q 21.750 0 0 9.750 26.250 664.512 cm /I72 Do Q BT 48.000 664.738 Td /F1 9.8 Tf [(, which is a dynamic estimate of the average number of secondary cases per infectious case in a population composed of )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(both susceptible and non-susceptible individuals during the course of an outbreak. The effective reproduction number is a )] TJ ET BT 26.250 640.929 Td /F1 9.8 Tf [(function of, among other things, the probability of transmission upon contact of the disease, the contact rate within the )] TJ ET BT 26.250 629.024 Td /F1 9.8 Tf [(population, and the number of susceptible individuals in the population, all of which may be time dependent.)] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(In an epidemic, given a short enough period of time, the value of )] TJ ET q 21.750 0 0 9.750 306.445 609.393 cm /I74 Do Q BT 328.195 609.619 Td /F1 9.8 Tf [( during that time period can be considered to be )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(approximately constant. Given a mathematical model for the spread of infectious disease, such as a classic Susceptible, )] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(Exposed, Infected, Recovered \(SEIR\) model, the equations of the mathematical model can be linearized about this temporary )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(equilibrium, to determine the predicted local rate of exponential rise of the epidemic curve, )] TJ ET q 24.000 0 0 9.000 423.455 574.429 cm /I76 Do Q BT 447.455 573.905 Td /F1 9.8 Tf [(. For the SEIR model, this is )] TJ ET BT 26.250 562.000 Td /F1 9.8 Tf [(related to )] TJ ET q 21.750 0 0 9.750 69.608 561.774 cm /I78 Do Q BT 91.358 562.000 Td /F1 9.8 Tf [( by)] TJ ET q 235.500 0 0 16.500 26.250 535.619 cm /I80 Do Q BT 26.250 518.519 Td /F1 9.8 Tf [(where )] TJ ET q 16.500 0 0 12.000 55.510 516.119 cm /I82 Do Q BT 72.010 518.519 Td /F1 9.8 Tf [( and )] TJ ET q 17.250 0 0 12.000 93.694 516.119 cm /I84 Do Q BT 110.944 518.519 Td /F1 9.8 Tf [( are the average incubation and infectious periods of the disease, respectively )] TJ ET 0.267 0.267 0.267 rg BT 449.659 520.103 Td /F4 8.7 Tf [(12)] TJ ET 0.271 0.267 0.267 rg BT 459.296 518.519 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 499.095 Td /F1 9.8 Tf [(With estimates of )] TJ ET q 24.000 0 0 9.000 103.733 499.619 cm /I86 Do Q BT 127.733 499.095 Td /F1 9.8 Tf [( from piecewise exponential rise fits to the incidence data from an outbreak \(along with estimates of the )] TJ ET BT 26.250 487.191 Td /F1 9.8 Tf [(incubation and infectious periods of the disease\), we can thus use Equation 2 to obtain estimates of the temporal behavior of )] TJ ET q 21.750 0 0 9.750 26.250 475.060 cm /I88 Do Q BT 48.000 475.286 Td /F1 9.8 Tf [(, in essence approximating the temporal behavior with a piecewise step-function.)] TJ ET BT 26.250 455.881 Td /F1 9.8 Tf [(Typically, if the transmissibility and contact rates in the population remain constant, one expects to see the effective )] TJ ET BT 26.250 443.976 Td /F1 9.8 Tf [(reproduction number decrease in time as the fraction of susceptible individuals in the population decreases. However, if )] TJ ET q 21.750 0 0 9.750 543.770 443.750 cm /I90 Do Q BT 26.250 432.072 Td /F1 9.8 Tf [(increases, it can signal that, for instance, contact rates within the population have increased, the virus has become more )] TJ ET BT 26.250 420.167 Td /F1 9.8 Tf [(transmissible, and/or that attempted intervention strategies are actually making the outbreak worse.)] TJ ET BT 26.250 400.762 Td /F1 9.8 Tf [(While we use an SEIR model and Equation 2 in this analysis to estimate )] TJ ET q 21.750 0 0 9.750 340.015 400.536 cm /I92 Do Q BT 361.765 400.762 Td /F1 9.8 Tf [(, it needs to be stressed that our methodology for )] TJ ET BT 26.250 388.857 Td /F1 9.8 Tf [(estimating the temporal variation in the effective reproduction number from the local rates of exponential rise in incidence can )] TJ ET BT 26.250 376.953 Td /F1 9.8 Tf [(be applied with any mathematical model appropriate to simulate the spread of a particular disease.)] TJ ET BT 26.250 340.350 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 320.396 Td /F1 9.8 Tf [(In Figure 1 we show the time series of the recorded daily average incidence data for Guinea, Sierra Leone, and Liberia. )] TJ ET BT 26.250 308.491 Td /F1 9.8 Tf [(Overlaid in green, we show a selection of the piecewise exponential fits along the incidence time series, in which ten contiguous )] TJ ET BT 26.250 296.586 Td /F1 9.8 Tf [(points are fit at a time, and the local exponential rate of rise, )] TJ ET q 24.000 0 0 9.000 286.926 297.110 cm /I94 Do Q BT 310.926 296.586 Td /F1 9.8 Tf [(, is estimated. For clarity of presentation, we only show every )] TJ ET BT 26.250 284.682 Td /F1 9.8 Tf [(third fit. The fit of an exponential to the time series from July 1st onwards is shown overlaid with a red dotted line.)] TJ ET BT 26.250 265.277 Td /F1 9.8 Tf [(In Figure 2 we show the time series of the estimates of the local exponential rise )] TJ ET q 24.000 0 0 9.000 374.695 265.801 cm /I96 Do Q BT 398.695 265.277 Td /F1 9.8 Tf [( \(along with the 95% confidence intervals )] TJ ET BT 26.250 253.372 Td /F1 9.8 Tf [(obtained from the Negative Binomial likelihood fit\) for each of the piecewise exponential fits for each country. We also indicate )] TJ ET BT 26.250 241.467 Td /F1 9.8 Tf [(the estimate of the the exponential rise from a fit to the time series from July 1st onwards for each country.)] TJ ET BT 26.250 222.063 Td /F1 9.8 Tf [(Note that the rates of )] TJ ET q 24.000 0 0 9.000 120.016 222.587 cm /I98 Do Q BT 144.016 222.063 Td /F1 9.8 Tf [( are significantly correlated from point to point.)] TJ ET 0.965 0.965 0.965 rg 26.250 -250.568 555.000 462.750 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 212.182 m 581.250 212.182 l 581.250 211.432 l 26.250 211.432 l f q 450.000 0 0 447.000 35.250 -244.568 cm /I99 Do Q q 35.250 -250.568 537.000 0.000 re W n Q Q q 15.000 -250.568 577.500 1027.568 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(estimates of )] TJ ET q 14.250 0 0 9.750 81.523 767.250 cm /I101 Do Q BT 95.773 767.476 Td /F1 9.8 Tf [( for an infectious disease tend to be different across populations. For example, rural and densely populated )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(urban areas are likely to have substantial differences in contact rates )] TJ ET 0.267 0.267 0.267 rg BT 325.390 757.079 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 335.027 755.571 Td /F1 9.8 Tf [(. Traditionally )] TJ ET q 14.250 0 0 9.750 395.711 755.345 cm /I103 Do Q BT 409.961 755.571 Td /F1 9.8 Tf [( has been computed under simplifying )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(assumptions, like the existence of a constant contact structure, or under the assumption that interventions like quarantine and )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(isolation are uniformly applied from the very beginning of the epidemic. However, particularly in the case of a disease with high )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(morbidity and mortality, it has been shown that human behaviors adapt to limit spread of the disease )] TJ ET 0.267 0.267 0.267 rg BT 461.412 721.364 Td /F4 8.7 Tf [(9)] TJ ET 0.271 0.267 0.267 rg BT 466.231 719.857 Td /F1 9.8 Tf [(, thus limiting the )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(usefulness of )] TJ ET q 14.250 0 0 9.750 86.407 707.726 cm /I105 Do Q BT 100.657 707.952 Td /F1 9.8 Tf [( as a means to assess the efficacy of evolving intervention strategies, and to forecast the future progression of )] TJ ET BT 26.250 696.048 Td /F1 9.8 Tf [(the outbreak.)] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(Given these limitations of )] TJ ET q 14.250 0 0 9.750 137.878 676.417 cm /I107 Do Q BT 152.128 676.643 Td /F1 9.8 Tf [(, in this analysis we thus instead assess the time evolution of the effective reproduction number, )] TJ ET q 21.750 0 0 9.750 26.250 664.512 cm /I109 Do Q BT 48.000 664.738 Td /F1 9.8 Tf [(, which is a dynamic estimate of the average number of secondary cases per infectious case in a population composed of )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(both susceptible and non-susceptible individuals during the course of an outbreak. The effective reproduction number is a )] TJ ET BT 26.250 640.929 Td /F1 9.8 Tf [(function of, among other things, the probability of transmission upon contact of the disease, the contact rate within the )] TJ ET BT 26.250 629.024 Td /F1 9.8 Tf [(population, and the number of susceptible individuals in the population, all of which may be time dependent.)] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(In an epidemic, given a short enough period of time, the value of )] TJ ET q 21.750 0 0 9.750 306.445 609.393 cm /I111 Do Q BT 328.195 609.619 Td /F1 9.8 Tf [( during that time period can be considered to be )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(approximately constant. Given a mathematical model for the spread of infectious disease, such as a classic Susceptible, )] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(Exposed, Infected, Recovered \(SEIR\) model, the equations of the mathematical model can be linearized about this temporary )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(equilibrium, to determine the predicted local rate of exponential rise of the epidemic curve, )] TJ ET q 24.000 0 0 9.000 423.455 574.429 cm /I113 Do Q BT 447.455 573.905 Td /F1 9.8 Tf [(. For the SEIR model, this is )] TJ ET BT 26.250 562.000 Td /F1 9.8 Tf [(related to )] TJ ET q 21.750 0 0 9.750 69.608 561.774 cm /I115 Do Q BT 91.358 562.000 Td /F1 9.8 Tf [( by)] TJ ET q 235.500 0 0 16.500 26.250 535.619 cm /I117 Do Q BT 26.250 518.519 Td /F1 9.8 Tf [(where )] TJ ET q 16.500 0 0 12.000 55.510 516.119 cm /I119 Do Q BT 72.010 518.519 Td /F1 9.8 Tf [( and )] TJ ET q 17.250 0 0 12.000 93.694 516.119 cm /I121 Do Q BT 110.944 518.519 Td /F1 9.8 Tf [( are the average incubation and infectious periods of the disease, respectively )] TJ ET 0.267 0.267 0.267 rg BT 449.659 520.103 Td /F4 8.7 Tf [(12)] TJ ET 0.271 0.267 0.267 rg BT 459.296 518.519 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 499.095 Td /F1 9.8 Tf [(With estimates of )] TJ ET q 24.000 0 0 9.000 103.733 499.619 cm /I123 Do Q BT 127.733 499.095 Td /F1 9.8 Tf [( from piecewise exponential rise fits to the incidence data from an outbreak \(along with estimates of the )] TJ ET BT 26.250 487.191 Td /F1 9.8 Tf [(incubation and infectious periods of the disease\), we can thus use Equation 2 to obtain estimates of the temporal behavior of )] TJ ET q 21.750 0 0 9.750 26.250 475.060 cm /I125 Do Q BT 48.000 475.286 Td /F1 9.8 Tf [(, in essence approximating the temporal behavior with a piecewise step-function.)] TJ ET BT 26.250 455.881 Td /F1 9.8 Tf [(Typically, if the transmissibility and contact rates in the population remain constant, one expects to see the effective )] TJ ET BT 26.250 443.976 Td /F1 9.8 Tf [(reproduction number decrease in time as the fraction of susceptible individuals in the population decreases. However, if )] TJ ET q 21.750 0 0 9.750 543.770 443.750 cm /I127 Do Q BT 26.250 432.072 Td /F1 9.8 Tf [(increases, it can signal that, for instance, contact rates within the population have increased, the virus has become more )] TJ ET BT 26.250 420.167 Td /F1 9.8 Tf [(transmissible, and/or that attempted intervention strategies are actually making the outbreak worse.)] TJ ET BT 26.250 400.762 Td /F1 9.8 Tf [(While we use an SEIR model and Equation 2 in this analysis to estimate )] TJ ET q 21.750 0 0 9.750 340.015 400.536 cm /I129 Do Q BT 361.765 400.762 Td /F1 9.8 Tf [(, it needs to be stressed that our methodology for )] TJ ET BT 26.250 388.857 Td /F1 9.8 Tf [(estimating the temporal variation in the effective reproduction number from the local rates of exponential rise in incidence can )] TJ ET BT 26.250 376.953 Td /F1 9.8 Tf [(be applied with any mathematical model appropriate to simulate the spread of a particular disease.)] TJ ET BT 26.250 340.350 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 320.396 Td /F1 9.8 Tf [(In Figure 1 we show the time series of the recorded daily average incidence data for Guinea, Sierra Leone, and Liberia. )] TJ ET BT 26.250 308.491 Td /F1 9.8 Tf [(Overlaid in green, we show a selection of the piecewise exponential fits along the incidence time series, in which ten contiguous )] TJ ET BT 26.250 296.586 Td /F1 9.8 Tf [(points are fit at a time, and the local exponential rate of rise, )] TJ ET q 24.000 0 0 9.000 286.926 297.110 cm /I131 Do Q BT 310.926 296.586 Td /F1 9.8 Tf [(, is estimated. For clarity of presentation, we only show every )] TJ ET BT 26.250 284.682 Td /F1 9.8 Tf [(third fit. The fit of an exponential to the time series from July 1st onwards is shown overlaid with a red dotted line.)] TJ ET BT 26.250 265.277 Td /F1 9.8 Tf [(In Figure 2 we show the time series of the estimates of the local exponential rise )] TJ ET q 24.000 0 0 9.000 374.695 265.801 cm /I133 Do Q BT 398.695 265.277 Td /F1 9.8 Tf [( \(along with the 95% confidence intervals )] TJ ET BT 26.250 253.372 Td /F1 9.8 Tf [(obtained from the Negative Binomial likelihood fit\) for each of the piecewise exponential fits for each country. We also indicate )] TJ ET BT 26.250 241.467 Td /F1 9.8 Tf [(the estimate of the the exponential rise from a fit to the time series from July 1st onwards for each country.)] TJ ET BT 26.250 222.063 Td /F1 9.8 Tf [(Note that the rates of )] TJ ET q 24.000 0 0 9.000 120.016 222.587 cm /I135 Do Q BT 144.016 222.063 Td /F1 9.8 Tf [( are significantly correlated from point to point.)] TJ ET 0.965 0.965 0.965 rg 26.250 -250.568 555.000 462.750 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 212.182 m 581.250 212.182 l 581.250 211.432 l 26.250 211.432 l f q 450.000 0 0 447.000 35.250 -244.568 cm /I99 Do Q q 35.250 -250.568 537.000 0.000 re W n Q Q q 15.000 -250.568 577.500 1027.568 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(estimates of )] TJ ET q 14.250 0 0 9.750 81.523 767.250 cm /I137 Do Q BT 95.773 767.476 Td /F1 9.8 Tf [( for an infectious disease tend to be different across populations. For example, rural and densely populated )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(urban areas are likely to have substantial differences in contact rates )] TJ ET 0.267 0.267 0.267 rg BT 325.390 757.079 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 335.027 755.571 Td /F1 9.8 Tf [(. Traditionally )] TJ ET q 14.250 0 0 9.750 395.711 755.345 cm /I139 Do Q BT 409.961 755.571 Td /F1 9.8 Tf [( has been computed under simplifying )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(assumptions, like the existence of a constant contact structure, or under the assumption that interventions like quarantine and )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(isolation are uniformly applied from the very beginning of the epidemic. However, particularly in the case of a disease with high )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(morbidity and mortality, it has been shown that human behaviors adapt to limit spread of the disease )] TJ ET 0.267 0.267 0.267 rg BT 461.412 721.364 Td /F4 8.7 Tf [(9)] TJ ET 0.271 0.267 0.267 rg BT 466.231 719.857 Td /F1 9.8 Tf [(, thus limiting the )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(usefulness of )] TJ ET q 14.250 0 0 9.750 86.407 707.726 cm /I141 Do Q BT 100.657 707.952 Td /F1 9.8 Tf [( as a means to assess the efficacy of evolving intervention strategies, and to forecast the future progression of )] TJ ET BT 26.250 696.048 Td /F1 9.8 Tf [(the outbreak.)] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(Given these limitations of )] TJ ET q 14.250 0 0 9.750 137.878 676.417 cm /I143 Do Q BT 152.128 676.643 Td /F1 9.8 Tf [(, in this analysis we thus instead assess the time evolution of the effective reproduction number, )] TJ ET q 21.750 0 0 9.750 26.250 664.512 cm /I145 Do Q BT 48.000 664.738 Td /F1 9.8 Tf [(, which is a dynamic estimate of the average number of secondary cases per infectious case in a population composed of )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(both susceptible and non-susceptible individuals during the course of an outbreak. The effective reproduction number is a )] TJ ET BT 26.250 640.929 Td /F1 9.8 Tf [(function of, among other things, the probability of transmission upon contact of the disease, the contact rate within the )] TJ ET BT 26.250 629.024 Td /F1 9.8 Tf [(population, and the number of susceptible individuals in the population, all of which may be time dependent.)] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(In an epidemic, given a short enough period of time, the value of )] TJ ET q 21.750 0 0 9.750 306.445 609.393 cm /I147 Do Q BT 328.195 609.619 Td /F1 9.8 Tf [( during that time period can be considered to be )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(approximately constant. Given a mathematical model for the spread of infectious disease, such as a classic Susceptible, )] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(Exposed, Infected, Recovered \(SEIR\) model, the equations of the mathematical model can be linearized about this temporary )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(equilibrium, to determine the predicted local rate of exponential rise of the epidemic curve, )] TJ ET q 24.000 0 0 9.000 423.455 574.429 cm /I149 Do Q BT 447.455 573.905 Td /F1 9.8 Tf [(. For the SEIR model, this is )] TJ ET BT 26.250 562.000 Td /F1 9.8 Tf [(related to )] TJ ET q 21.750 0 0 9.750 69.608 561.774 cm /I151 Do Q BT 91.358 562.000 Td /F1 9.8 Tf [( by)] TJ ET q 235.500 0 0 16.500 26.250 535.619 cm /I153 Do Q BT 26.250 518.519 Td /F1 9.8 Tf [(where )] TJ ET q 16.500 0 0 12.000 55.510 516.119 cm /I155 Do Q BT 72.010 518.519 Td /F1 9.8 Tf [( and )] TJ ET q 17.250 0 0 12.000 93.694 516.119 cm /I157 Do Q BT 110.944 518.519 Td /F1 9.8 Tf [( are the average incubation and infectious periods of the disease, respectively )] TJ ET 0.267 0.267 0.267 rg BT 449.659 520.103 Td /F4 8.7 Tf [(12)] TJ ET 0.271 0.267 0.267 rg BT 459.296 518.519 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 499.095 Td /F1 9.8 Tf [(With estimates of )] TJ ET q 24.000 0 0 9.000 103.733 499.619 cm /I159 Do Q BT 127.733 499.095 Td /F1 9.8 Tf [( from piecewise exponential rise fits to the incidence data from an outbreak \(along with estimates of the )] TJ ET BT 26.250 487.191 Td /F1 9.8 Tf [(incubation and infectious periods of the disease\), we can thus use Equation 2 to obtain estimates of the temporal behavior of )] TJ ET q 21.750 0 0 9.750 26.250 475.060 cm /I161 Do Q BT 48.000 475.286 Td /F1 9.8 Tf [(, in essence approximating the temporal behavior with a piecewise step-function.)] TJ ET BT 26.250 455.881 Td /F1 9.8 Tf [(Typically, if the transmissibility and contact rates in the population remain constant, one expects to see the effective )] TJ ET BT 26.250 443.976 Td /F1 9.8 Tf [(reproduction number decrease in time as the fraction of susceptible individuals in the population decreases. However, if )] TJ ET q 21.750 0 0 9.750 543.770 443.750 cm /I163 Do Q BT 26.250 432.072 Td /F1 9.8 Tf [(increases, it can signal that, for instance, contact rates within the population have increased, the virus has become more )] TJ ET BT 26.250 420.167 Td /F1 9.8 Tf [(transmissible, and/or that attempted intervention strategies are actually making the outbreak worse.)] TJ ET BT 26.250 400.762 Td /F1 9.8 Tf [(While we use an SEIR model and Equation 2 in this analysis to estimate )] TJ ET q 21.750 0 0 9.750 340.015 400.536 cm /I165 Do Q BT 361.765 400.762 Td /F1 9.8 Tf [(, it needs to be stressed that our methodology for )] TJ ET BT 26.250 388.857 Td /F1 9.8 Tf [(estimating the temporal variation in the effective reproduction number from the local rates of exponential rise in incidence can )] TJ ET BT 26.250 376.953 Td /F1 9.8 Tf [(be applied with any mathematical model appropriate to simulate the spread of a particular disease.)] TJ ET BT 26.250 340.350 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 320.396 Td /F1 9.8 Tf [(In Figure 1 we show the time series of the recorded daily average incidence data for Guinea, Sierra Leone, and Liberia. )] TJ ET BT 26.250 308.491 Td /F1 9.8 Tf [(Overlaid in green, we show a selection of the piecewise exponential fits along the incidence time series, in which ten contiguous )] TJ ET BT 26.250 296.586 Td /F1 9.8 Tf [(points are fit at a time, and the local exponential rate of rise, )] TJ ET q 24.000 0 0 9.000 286.926 297.110 cm /I167 Do Q BT 310.926 296.586 Td /F1 9.8 Tf [(, is estimated. For clarity of presentation, we only show every )] TJ ET BT 26.250 284.682 Td /F1 9.8 Tf [(third fit. The fit of an exponential to the time series from July 1st onwards is shown overlaid with a red dotted line.)] TJ ET BT 26.250 265.277 Td /F1 9.8 Tf [(In Figure 2 we show the time series of the estimates of the local exponential rise )] TJ ET q 24.000 0 0 9.000 374.695 265.801 cm /I169 Do Q BT 398.695 265.277 Td /F1 9.8 Tf [( \(along with the 95% confidence intervals )] TJ ET BT 26.250 253.372 Td /F1 9.8 Tf [(obtained from the Negative Binomial likelihood fit\) for each of the piecewise exponential fits for each country. We also indicate )] TJ ET BT 26.250 241.467 Td /F1 9.8 Tf [(the estimate of the the exponential rise from a fit to the time series from July 1st onwards for each country.)] TJ ET BT 26.250 222.063 Td /F1 9.8 Tf [(Note that the rates of )] TJ ET q 24.000 0 0 9.000 120.016 222.587 cm /I171 Do Q BT 144.016 222.063 Td /F1 9.8 Tf [( are significantly correlated from point to point.)] TJ ET 0.965 0.965 0.965 rg 26.250 -250.568 555.000 462.750 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 212.182 m 581.250 212.182 l 581.250 211.432 l 26.250 211.432 l f q 450.000 0 0 447.000 35.250 -244.568 cm /I99 Do Q q 35.250 -250.568 537.000 0.000 re W n Q Q q 450.000 0 0 447.000 35.250 -244.568 cm /I99 Do Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(3)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Outbreaks)] TJ ET Q endstream endobj 295 0 obj << /Type /XObject /Subtype /Image /Width 19 /Height 13 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 19 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 168>> stream c`. `b@nsڲؾPU ۤ  |0! &m@16 3e R`2IW0-e8 ,! 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y ̀ 16i@.B@LKY12Z°I,` Pa ȸm B``cP 9 @>;%R0r[rtՓ³!braH U÷*-fM@ToqÜLl, x7 endstream endobj 425 0 obj << /Type /XObject /Subtype /Image /Width 32 /Height 12 /SMask 424 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 32 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 18>> stream 8c`` endstream endobj 426 0 obj << /Type /Annot /Subtype /Link /A 427 0 R /Border [0 0 0] /H /I /Rect [ 35.2500 -244.5682 485.2500 202.4318 ] >> endobj 427 0 obj << /Type /Action /S /URI /URI (http://currents.plos.org/outbreaks/files/2014/09/country_fitsb.jpg) >> endobj 428 0 obj << /Type /Page /Parent 3 0 R /Annots [ 430 0 R 433 0 R 435 0 R ] /Contents 429 0 R >> endobj 429 0 obj << /Length 7988 >> stream q 15.000 30.190 577.500 746.810 re W n 0.965 0.965 0.965 rg 26.250 671.664 555.000 105.336 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 671.664 m 581.250 671.664 l 581.250 672.414 l 26.250 672.414 l f q 35.250 682.914 537.000 94.086 re W n 0.271 0.267 0.267 rg BT 35.250 767.476 Td /F4 9.8 Tf [(Fig. 1: Time series of iIncidence of EVD cases in West Africa)] TJ ET BT 35.250 748.106 Td /F1 9.8 Tf [(Time series of recorded average number of new EVD cases per day during the initial phase of the 2014 West African )] TJ ET BT 35.250 734.370 Td /F1 9.8 Tf [(outbreak, for Guinea, Sierra Leone, and Liberia \(dots\). The green lines show a selection of the piecewise exponential fits to )] TJ ET BT 35.250 720.634 Td /F1 9.8 Tf [(the data \(not all fits are shown to clarify the presentation\); a moving window of groups of 10 contiguous points are taken at a )] TJ ET BT 35.250 706.897 Td /F1 9.8 Tf [(time, and the rate of exponential rise estimated for those 10 points. The results for the estimations of the exponential rise for )] TJ ET BT 35.250 693.161 Td /F1 9.8 Tf [(the full set of piecewise fits are shown in Figure 2. Shown in red is the fitted exponential rise from July 1st onwards.)] TJ ET Q 0.965 0.965 0.965 rg 26.250 74.842 555.000 589.322 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 664.164 m 581.250 664.164 l 581.250 663.414 l 26.250 663.414 l f 26.250 74.842 m 581.250 74.842 l 581.250 75.592 l 26.250 75.592 l f q 450.000 0 0 454.500 35.250 199.914 cm /I172 Do Q q 35.250 86.092 537.000 107.822 re W n 0.271 0.267 0.267 rg BT 35.250 184.390 Td /F4 9.8 Tf [(Fig. 2: Estimated rates of exponential rise from piecewise exponential fits)] TJ ET BT 35.250 165.020 Td /F1 9.8 Tf [(Estimated rates of exponential rise from piecewise exponential fits to the average daily EVD incidence data, as shown in )] TJ ET BT 35.250 151.284 Td /F1 9.8 Tf [(Figure 1; a moving window of groups of 10 contiguous incidence data time series points are taken at a time, and the rate of )] TJ ET BT 35.250 137.548 Td /F1 9.8 Tf [(exponential rise estimated for those 10 points. The dates shown on the x axis are last date in each contiguous set of 10 )] TJ ET BT 35.250 123.811 Td /F1 9.8 Tf [(points, and the vertical error bars denote the 95% confidence interval. The horizontal black line shows the estimated rate of )] TJ ET BT 35.250 110.075 Td /F1 9.8 Tf [(rise of an exponential fit to the incidence time series from July 1st to Sep 8th, with the black dotted lines indicating the 95% )] TJ ET BT 35.250 96.339 Td /F1 9.8 Tf [(confidence interval.)] TJ ET Q Q q 15.000 30.190 577.500 746.810 re W n 0.965 0.965 0.965 rg 26.250 671.664 555.000 105.336 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 671.664 m 581.250 671.664 l 581.250 672.414 l 26.250 672.414 l f q 35.250 682.914 537.000 94.086 re W n 0.271 0.267 0.267 rg BT 35.250 767.476 Td /F4 9.8 Tf [(Fig. 1: Time series of iIncidence of EVD cases in West Africa)] TJ ET BT 35.250 748.106 Td /F1 9.8 Tf [(Time series of recorded average number of new EVD cases per day during the initial phase of the 2014 West African )] TJ ET BT 35.250 734.370 Td /F1 9.8 Tf [(outbreak, for Guinea, Sierra Leone, and Liberia \(dots\). The green lines show a selection of the piecewise exponential fits to )] TJ ET BT 35.250 720.634 Td /F1 9.8 Tf [(the data \(not all fits are shown to clarify the presentation\); a moving window of groups of 10 contiguous points are taken at a )] TJ ET BT 35.250 706.897 Td /F1 9.8 Tf [(time, and the rate of exponential rise estimated for those 10 points. The results for the estimations of the exponential rise for )] TJ ET BT 35.250 693.161 Td /F1 9.8 Tf [(the full set of piecewise fits are shown in Figure 2. Shown in red is the fitted exponential rise from July 1st onwards.)] TJ ET Q 0.965 0.965 0.965 rg 26.250 74.842 555.000 589.322 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 664.164 m 581.250 664.164 l 581.250 663.414 l 26.250 663.414 l f 26.250 74.842 m 581.250 74.842 l 581.250 75.592 l 26.250 75.592 l f q 450.000 0 0 454.500 35.250 199.914 cm /I172 Do Q q 35.250 86.092 537.000 107.822 re W n 0.271 0.267 0.267 rg BT 35.250 184.390 Td /F4 9.8 Tf [(Fig. 2: Estimated rates of exponential rise from piecewise exponential fits)] TJ ET BT 35.250 165.020 Td /F1 9.8 Tf [(Estimated rates of exponential rise from piecewise exponential fits to the average daily EVD incidence data, as shown in )] TJ ET BT 35.250 151.284 Td /F1 9.8 Tf [(Figure 1; a moving window of groups of 10 contiguous incidence data time series points are taken at a time, and the rate of )] TJ ET BT 35.250 137.548 Td /F1 9.8 Tf [(exponential rise estimated for those 10 points. The dates shown on the x axis are last date in each contiguous set of 10 )] TJ ET BT 35.250 123.811 Td /F1 9.8 Tf [(points, and the vertical error bars denote the 95% confidence interval. The horizontal black line shows the estimated rate of )] TJ ET BT 35.250 110.075 Td /F1 9.8 Tf [(rise of an exponential fit to the incidence time series from July 1st to Sep 8th, with the black dotted lines indicating the 95% )] TJ ET BT 35.250 96.339 Td /F1 9.8 Tf [(confidence interval.)] TJ ET Q Q q 15.000 30.190 577.500 746.810 re W n 0.965 0.965 0.965 rg 26.250 671.664 555.000 105.336 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 671.664 m 581.250 671.664 l 581.250 672.414 l 26.250 672.414 l f q 35.250 682.914 537.000 94.086 re W n 0.271 0.267 0.267 rg BT 35.250 767.476 Td /F4 9.8 Tf [(Fig. 1: Time series of iIncidence of EVD cases in West Africa)] TJ ET BT 35.250 748.106 Td /F1 9.8 Tf [(Time series of recorded average number of new EVD cases per day during the initial phase of the 2014 West African )] TJ ET BT 35.250 734.370 Td /F1 9.8 Tf [(outbreak, for Guinea, Sierra Leone, and Liberia \(dots\). The green lines show a selection of the piecewise exponential fits to )] TJ ET BT 35.250 720.634 Td /F1 9.8 Tf [(the data \(not all fits are shown to clarify the presentation\); a moving window of groups of 10 contiguous points are taken at a )] TJ ET BT 35.250 706.897 Td /F1 9.8 Tf [(time, and the rate of exponential rise estimated for those 10 points. The results for the estimations of the exponential rise for )] TJ ET BT 35.250 693.161 Td /F1 9.8 Tf [(the full set of piecewise fits are shown in Figure 2. Shown in red is the fitted exponential rise from July 1st onwards.)] TJ ET Q 0.965 0.965 0.965 rg 26.250 74.842 555.000 589.322 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 664.164 m 581.250 664.164 l 581.250 663.414 l 26.250 663.414 l f 26.250 74.842 m 581.250 74.842 l 581.250 75.592 l 26.250 75.592 l f q 450.000 0 0 454.500 35.250 199.914 cm /I172 Do Q q 35.250 86.092 537.000 107.822 re W n 0.271 0.267 0.267 rg BT 35.250 184.390 Td /F4 9.8 Tf [(Fig. 2: Estimated rates of exponential rise from piecewise exponential fits)] TJ ET BT 35.250 165.020 Td /F1 9.8 Tf [(Estimated rates of exponential rise from piecewise exponential fits to the average daily EVD incidence data, as shown in )] TJ ET BT 35.250 151.284 Td /F1 9.8 Tf [(Figure 1; a moving window of groups of 10 contiguous incidence data time series points are taken at a time, and the rate of )] TJ ET BT 35.250 137.548 Td /F1 9.8 Tf [(exponential rise estimated for those 10 points. The dates shown on the x axis are last date in each contiguous set of 10 )] TJ ET BT 35.250 123.811 Td /F1 9.8 Tf [(points, and the vertical error bars denote the 95% confidence interval. 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: Z2H\FF-18?yzb9/O )|9h`ީ {Or$~!K U@Ec'oOs7ז>(-:OoO{'_}A3mNwLwX^]QlO]'ַN)H>qWX'+v޳j^xw-#H ) /_#.?>ڌPEQ/G!Wq om3O꺅kmgy[3q ۏOAA 9[dmOQbRm =JZBh*>2/_#.?>QBh*>6/_#.?>ڒ<++2/_#.?>@_EGF\}q hxǾ_^o  9 -7;mǝ?w=_T /3?_#:P`X*$[P _EGF\}_T| e'׻Q@_EGF\}_T| e'׻bBh*>23_#.?>ړ>{?EhYpc)lggOᄟ~#|4b5"Tsυ%ٻ8ߌg+imxSӖA ^Zn$#!K\O ¿N/'t[-.K@)Z#[oxEZxZu  I!nu (t?j^,4 jz׈4oG,> 6&]\F #ͿeZğ'u?^ դDŽ&)Q~Cx >@ǜfKvKEèмSj'][]}92˼_OjoٶDž<9~] Cq.`6х =̌5+LQW{%u7Iy=7cjhJM|cS!Zkӧ?ekw1Vc?7c8+g'}e8..:k(cRZ\LdsA4~_T< e'_ECF\}{( /_#.?>C?h*2h /_#.?>Bh*2h}~4{exF>EϘGN+>si_ECF\}w_O;a? 뭫c:+}7{)__T< e'_ECF\}{h¿ xˏO+Z(¿ ˏO/^u7"O^7;] \0I+n+Nwvv_T| e'uo7sA;}6HxMLIwy5 /_#.?>Bh*2h /_#.?>Bh*>2h /qoO-3"m'׻:RƯ xxZwŢRy<1==z>#.Mk~!k/fMӚV[4v ;7 >x_W==*U$ #w]({IE-PEPEPECҼ?O̭skOhU6|UmpL6Y RvVIe^~]wd`]Y] )y3]zMm^JIkX]gHܻe%@` o~2xW%.16'\#O4jb(N kŸ-|[iG$څۭ}iח36i0vH rk6>%5F-䍱D&Rw[?A@QE ({~,_i lniaeC+x&=6Sy3,Ȼ2{p7>$X$񕮵6Echc6l%K'R7l\gk&Nj)3FJF ;%Ľ7ٺ]XO~5jf"~qZCgj@8YYĚVȳOqma.נETw7A$8ԻP2I+~ƾuw&ۗ+$5OwI[7fO#0p1ۂz[]~麔:ٗeZmib0Kc,@zּ97$ri{0@C{mz(+,|b u]Ni).ҭu!ǔ&3yXs}2 w~ ![i) Y! 1#,:1ao揩1ۖYIdQ&/.mwًv b3FTq\$?OcG,x,%ID xA8b(0k_gCyC]k֙4ha&،cE.7Ā3}I "R=iZmJyQFy`]]d>G5F9dyuiTlmB@/{Z((Eu3@J((4P(/f_hgohwQO7%w*) g2xW!D.F@gn`VE8i#X(Nk?fK1m|WXCwcbݚcYF|d;0|q]O5 KS%}s{9@ s@4?|ChJ}y/.^.<֔ 0`_(+N uuŗzCsse Dq,RJ&fV3Ń^]MM7v~Pg|]El7v;g5W __Z_˯jVVHm Η`6"w)(|7 A@tb n_Cg4)ǖr5|3y4J{qXecn!l ;/f|A_^I{?Mdb}̥0tPXקk^e7Z%La٭怆mZAEt 9 Ƒ$3iSOcKA2Ti8s4sZZOi-l@Wz 3^b߳/{KM/ቢ“F2HW!fPƩBGR!˒Km.xɸ{e84Ȋd*##O[_ º nu?.;{Wk[mI&e>Ys&CA֧y&Vյ[p]Ne@lm\:֍<iw10"<7%'A@h Z3Eyſ)#I"-f vqɉp؛~mUlh EiRkfF@@nV%hdbUuIo\xK-z@Ijt)Uʤd 4b&Dw2KYL󨹖/ >^yGB| w U:v{w5Y&ӮmaX%+l- DGMtJm m̗\2xXycޣ\ԯtO>D o'#޽ÐZQׄ5항qV .Hn[?z4QEQA(Ph)h3EPEPEP( 3EQEf((3EPFh JZN(=(@(@((@Q4Phh(hu4PEEQGQE~4(1E.('NJbъNR@ endstream endobj 433 0 obj << /Type /Annot /Subtype /Link /A 434 0 R /Border [0 0 0] /H /I /Rect [ 35.2500 199.9140 485.2500 654.4140 ] >> endobj 434 0 obj << /Type /Action /S /URI /URI (http://currents.plos.org/outbreaks/files/2014/09/rho.jpg) >> endobj 435 0 obj << /Type /Annot /Subtype /Link /A 436 0 R /Border [0 0 0] /H /I /Rect [ 35.2500 199.9140 485.2500 654.4140 ] >> endobj 436 0 obj << /Type /Action /S /URI /URI (http://currents.plos.org/outbreaks/files/2014/09/rho.jpg) >> endobj 437 0 obj << /Type /Page /Parent 3 0 R /Annots [ 441 0 R 443 0 R 445 0 R 447 0 R 449 0 R 451 0 R 453 0 R 463 0 R 465 0 R 467 0 R 469 0 R 471 0 R 473 0 R 475 0 R 485 0 R 487 0 R 489 0 R 491 0 R 493 0 R 495 0 R 497 0 R ] /Contents 438 0 R >> endobj 438 0 obj << /Length 51958 >> stream 0.271 0.267 0.267 rg q 15.000 25.197 577.500 751.803 re W n 0.271 0.267 0.267 rg BT 26.250 750.278 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 730.324 Td /F1 9.8 Tf [(For each country in Figure 2 the solid and dotted black lines denote the central value and 95% CI, respectively, of the rate of )] TJ ET BT 26.250 718.419 Td /F1 9.8 Tf [(exponential rise of case incidence data between July 1st and September 8th . The estimates of the rates of exponential rise )] TJ ET BT 26.250 706.515 Td /F1 9.8 Tf [(between July 1st and September 8th are ?=0. 052 0. 008, ?=0. 015 0. 008, and ?=0. 046 0. 005 for Guinea, Sierra Leone, )] TJ ET BT 26.250 694.610 Td /F1 9.8 Tf [(and Liberia, respectively. The value estimated from the combined data samples is ?=0. 037 0. 006. The values are statistically )] TJ ET BT 26.250 682.705 Td /F1 9.8 Tf [(consistent for the Guinea and Liberia data \(one-sided Z test p = 0. 28\). However, the estimate for the Sierra Leone data is )] TJ ET BT 26.250 670.800 Td /F1 9.8 Tf [(significantly lower than the estimates obtained from the Guinea and Liberia data \(one-sided Z test p = 0. 0005, and p = 0. 0003, )] TJ ET BT 26.250 658.896 Td /F1 9.8 Tf [(respectively\). In Table 1 we show the values of the effective reproduction number, )] TJ ET q 21.750 0 0 9.750 381.745 658.669 cm /I174 Do Q BT 403.495 658.896 Td /F1 9.8 Tf [( , as estimated from Equation 2 under )] TJ ET BT 26.250 646.991 Td /F1 9.8 Tf [(several hypotheses for the incubation and infectious periods \(the incubation and infectious periods for this outbreak are poorly )] TJ ET BT 26.250 635.086 Td /F1 9.8 Tf [(known, and have shown wide apparent variation in previous outbreaks )] TJ ET 0.267 0.267 0.267 rg BT 332.439 636.593 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 342.076 638.974 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 344.486 636.593 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 354.123 635.086 Td /F1 9.8 Tf [(\). The reproduction numbers estimated by this )] TJ ET BT 26.250 623.181 Td /F1 9.8 Tf [(analysis are in broad agreement with the reproduction numbers estimated from this and previous outbreaks, which range from )] TJ ET BT 26.250 611.277 Td /F1 9.8 Tf [(approximately 1.3 to 2.7 )] TJ ET 0.267 0.267 0.267 rg BT 133.012 612.784 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 142.650 615.165 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 145.059 612.784 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 154.697 615.165 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 157.106 612.784 Td /F4 8.7 Tf [(22)] TJ ET 0.271 0.267 0.267 rg BT 166.743 611.277 Td /F1 9.8 Tf [(.)] TJ ET q 26.250 587.659 555.000 13.736 re W n 0.271 0.267 0.267 rg BT 26.250 590.407 Td /F1 9.8 Tf [(Table 1: Estimates of the effective reproduction number between July 1 to present)] TJ ET Q 0.965 0.965 0.965 rg 26.250 520.122 555.000 60.037 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 580.159 m 581.250 580.159 l 580.500 579.409 l 27.000 579.409 l f 581.250 580.159 m 581.250 520.122 l 580.500 520.122 l 580.500 579.409 l f 26.250 580.159 m 26.250 520.122 l 27.000 520.122 l 27.000 579.409 l f 0.271 0.267 0.267 rg BT 33.000 566.083 Td /F1 9.0 Tf [(Estimates of the effective reproduction number for the 2014 West African EBV outbreak data, for an SEIR model as obtained from )] TJ ET BT 33.000 556.926 Td /F1 9.0 Tf [(Equation 2 under several hypotheses for the incubation and infectious periods. The estimates and the 95% confidence intervals are )] TJ ET BT 33.000 547.768 Td /F1 9.0 Tf [(derived from the rate of rise of an exponential fit to the new case incidence data for the various countries between July 1st and )] TJ ET BT 33.000 538.611 Td /F1 9.0 Tf [(September 8th \(the beginning of July is when the World Health Organization began frequent updates of the new case information for all )] TJ ET BT 33.000 529.453 Td /F1 9.0 Tf [(three countries\).)] TJ ET 1.000 1.000 1.000 rg 26.250 339.601 555.000 180.521 re f 0.965 0.965 0.965 rg 27.000 483.283 171.966 36.089 re f 0.267 0.267 0.267 rg 26.625 518.997 172.341 0.750 re f 26.625 482.908 0.750 36.839 re f 0.271 0.267 0.267 rg BT 31.500 509.848 Td /F4 9.8 Tf [(Hypothesized incubation)] TJ ET BT 31.500 497.943 Td /F4 9.8 Tf [(and infectious periods,)] TJ ET BT 31.500 486.039 Td /F4 9.8 Tf [(respectively \(days\))] TJ ET 0.965 0.965 0.965 rg 198.966 483.283 94.019 36.089 re f 0.267 0.267 0.267 rg 198.966 518.997 94.019 0.750 re f 0.271 0.267 0.267 rg BT 203.466 509.848 Td /F4 9.8 Tf [(Guinea)] TJ ET 0.965 0.965 0.965 rg 292.985 483.283 94.019 36.089 re f 0.267 0.267 0.267 rg 292.985 518.997 94.019 0.750 re f 0.271 0.267 0.267 rg BT 297.485 509.848 Td /F4 9.8 Tf [(Liberia)] TJ ET 0.965 0.965 0.965 rg 387.005 483.283 99.476 36.089 re f 0.267 0.267 0.267 rg 387.005 518.997 99.476 0.750 re f 0.271 0.267 0.267 rg BT 391.505 509.848 Td /F4 9.8 Tf [(Sierra Leone)] TJ ET 0.965 0.965 0.965 rg 486.481 483.283 94.019 36.089 re f 0.267 0.267 0.267 rg 486.481 518.997 94.394 0.750 re f 580.125 482.908 0.750 36.839 re f 0.271 0.267 0.267 rg BT 490.981 509.848 Td /F4 9.8 Tf [(All)] TJ ET 0.267 0.267 0.267 rg 26.625 482.908 172.716 0.750 re f 26.625 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 473.053 Td /F1 9.8 Tf [(5 and 5)] TJ ET 0.267 0.267 0.267 rg 198.591 482.908 94.769 0.750 re f 198.591 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 473.053 Td /F1 9.8 Tf [(1.6 [1.4,1.8])] TJ ET 0.267 0.267 0.267 rg 292.610 482.908 94.769 0.750 re f 292.610 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 473.053 Td /F1 9.8 Tf [(1.5 [1.4,1.6])] TJ ET 0.267 0.267 0.267 rg 386.630 482.908 100.226 0.750 re f 386.630 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 473.053 Td /F1 9.8 Tf [(1.2 [1.0,1.3])] TJ ET 0.267 0.267 0.267 rg 486.106 482.908 94.769 0.750 re f 486.106 467.026 0.750 16.631 re f 580.125 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 473.053 Td /F1 9.8 Tf [(1.4 [1.3,1.5])] TJ ET 0.267 0.267 0.267 rg 26.625 467.026 172.716 0.750 re f 26.625 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 457.171 Td /F1 9.8 Tf [(7 and 5)] TJ ET 0.267 0.267 0.267 rg 198.591 467.026 94.769 0.750 re f 198.591 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 457.171 Td /F1 9.8 Tf [(1.7 [1.5,2.0])] TJ ET 0.267 0.267 0.267 rg 292.610 467.026 94.769 0.750 re f 292.610 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 457.171 Td /F1 9.8 Tf [(1.6 [1.5,1.8])] TJ ET 0.267 0.267 0.267 rg 386.630 467.026 100.226 0.750 re f 386.630 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 457.171 Td /F1 9.8 Tf [(1.2 [1.0,1.4])] TJ ET 0.267 0.267 0.267 rg 486.106 467.026 94.769 0.750 re f 486.106 451.145 0.750 16.631 re f 580.125 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 457.171 Td /F1 9.8 Tf [(1.5 [1.3,1.7])] TJ ET 0.267 0.267 0.267 rg 26.625 451.145 172.716 0.750 re f 26.625 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 441.290 Td /F1 9.8 Tf [(10 and 5)] TJ ET 0.267 0.267 0.267 rg 198.591 451.145 94.769 0.750 re f 198.591 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 441.290 Td /F1 9.8 Tf [(1.9 [1.6,2.3])] TJ ET 0.267 0.267 0.267 rg 292.610 451.145 94.769 0.750 re f 292.610 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 441.290 Td /F1 9.8 Tf [(1.8 [1.6,2.0])] TJ ET 0.267 0.267 0.267 rg 386.630 451.145 100.226 0.750 re f 386.630 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 441.290 Td /F1 9.8 Tf [(1.2 [1.0,1.5])] TJ ET 0.267 0.267 0.267 rg 486.106 451.145 94.769 0.750 re f 486.106 435.264 0.750 16.631 re f 580.125 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 441.290 Td /F1 9.8 Tf [(1.6 [1.4,1.8])] TJ ET 0.267 0.267 0.267 rg 26.625 435.264 172.716 0.750 re f 26.625 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 425.409 Td /F1 9.8 Tf [(5 and 7)] TJ ET 0.267 0.267 0.267 rg 198.591 435.264 94.769 0.750 re f 198.591 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 425.409 Td /F1 9.8 Tf [(1.7 [1.5,2.0])] TJ ET 0.267 0.267 0.267 rg 292.610 435.264 94.769 0.750 re f 292.610 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 425.409 Td /F1 9.8 Tf [(1.6 [1.5,1.8])] TJ ET 0.267 0.267 0.267 rg 386.630 435.264 100.226 0.750 re f 386.630 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 425.409 Td /F1 9.8 Tf [(1.2 [1.0,1.4])] TJ ET 0.267 0.267 0.267 rg 486.106 435.264 94.769 0.750 re f 486.106 419.383 0.750 16.631 re f 580.125 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 425.409 Td /F1 9.8 Tf [(1.5 [1.3,1.7])] TJ ET 0.267 0.267 0.267 rg 26.625 419.383 172.716 0.750 re f 26.625 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 409.528 Td /F1 9.8 Tf [(7 and 7)] TJ ET 0.267 0.267 0.267 rg 198.591 419.383 94.769 0.750 re f 198.591 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 409.528 Td /F1 9.8 Tf [(1.9 [1.6,2.2])] TJ ET 0.267 0.267 0.267 rg 292.610 419.383 94.769 0.750 re f 292.610 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 409.528 Td /F1 9.8 Tf [(1.8 [1.6,1.9])] TJ ET 0.267 0.267 0.267 rg 386.630 419.383 100.226 0.750 re f 386.630 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 409.528 Td /F1 9.8 Tf [(1.2 [1.0,1.5])] TJ ET 0.267 0.267 0.267 rg 486.106 419.383 94.769 0.750 re f 486.106 403.501 0.750 16.631 re f 580.125 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 409.528 Td /F1 9.8 Tf [(1.6 [1.4,1.8])] TJ ET 0.267 0.267 0.267 rg 26.625 403.501 172.716 0.750 re f 26.625 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 393.646 Td /F1 9.8 Tf [(10 and 7)] TJ ET 0.267 0.267 0.267 rg 198.591 403.501 94.769 0.750 re f 198.591 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 393.646 Td /F1 9.8 Tf [(2.1 [1.7,2.5])] TJ ET 0.267 0.267 0.267 rg 292.610 403.501 94.769 0.750 re f 292.610 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 393.646 Td /F1 9.8 Tf [(1.9 [1.7,2.2])] TJ ET 0.267 0.267 0.267 rg 386.630 403.501 100.226 0.750 re f 386.630 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 393.646 Td /F1 9.8 Tf [(1.3 [1.0,1.6])] TJ ET 0.267 0.267 0.267 rg 486.106 403.501 94.769 0.750 re f 486.106 387.620 0.750 16.631 re f 580.125 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 393.646 Td /F1 9.8 Tf [(1.7 [1.5,2.0])] TJ ET 0.267 0.267 0.267 rg 26.625 387.620 172.716 0.750 re f 26.625 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 377.765 Td /F1 9.8 Tf [(5 and 10)] TJ ET 0.267 0.267 0.267 rg 198.591 387.620 94.769 0.750 re f 198.591 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 377.765 Td /F1 9.8 Tf [(1.9 [1.6,2.3])] TJ ET 0.267 0.267 0.267 rg 292.610 387.620 94.769 0.750 re f 292.610 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 377.765 Td /F1 9.8 Tf [(1.8 [1.6,2.0])] TJ ET 0.267 0.267 0.267 rg 386.630 387.620 100.226 0.750 re f 386.630 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 377.765 Td /F1 9.8 Tf [(1.2 [1.0,1.5])] TJ ET 0.267 0.267 0.267 rg 486.106 387.620 94.769 0.750 re f 486.106 371.739 0.750 16.631 re f 580.125 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 377.765 Td /F1 9.8 Tf [(1.6 [1.4,1.8])] TJ ET 0.267 0.267 0.267 rg 26.625 371.739 172.716 0.750 re f 26.625 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 361.884 Td /F1 9.8 Tf [(7 and 10)] TJ ET 0.267 0.267 0.267 rg 198.591 371.739 94.769 0.750 re f 198.591 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 361.884 Td /F1 9.8 Tf [(2.1 [1.7,2.5])] TJ ET 0.267 0.267 0.267 rg 292.610 371.739 94.769 0.750 re f 292.610 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 361.884 Td /F1 9.8 Tf [(1.9 [1.7,2.2])] TJ ET 0.267 0.267 0.267 rg 386.630 371.739 100.226 0.750 re f 386.630 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 361.884 Td /F1 9.8 Tf [(1.3 [1.0,1.6])] TJ ET 0.267 0.267 0.267 rg 486.106 371.739 94.769 0.750 re f 486.106 355.858 0.750 16.631 re f 580.125 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 361.884 Td /F1 9.8 Tf [(1.7 [1.5,2.0])] TJ ET 0.267 0.267 0.267 rg 26.625 355.858 172.716 0.750 re f 26.625 339.976 172.716 0.750 re f 26.625 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 346.003 Td /F1 9.8 Tf [(10 and 10)] TJ ET 0.267 0.267 0.267 rg 198.591 355.858 94.769 0.750 re f 198.591 339.976 94.769 0.750 re f 198.591 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 346.003 Td /F1 9.8 Tf [(2.3 [1.8,2.8])] TJ ET 0.267 0.267 0.267 rg 292.610 355.858 94.769 0.750 re f 292.610 339.976 94.769 0.750 re f 292.610 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 346.003 Td /F1 9.8 Tf [(2.1 [1.9,2.4])] TJ ET 0.267 0.267 0.267 rg 386.630 355.858 100.226 0.750 re f 386.630 339.976 100.226 0.750 re f 386.630 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 346.003 Td /F1 9.8 Tf [(1.3 [1.0,1.7])] TJ ET 0.267 0.267 0.267 rg 486.106 355.858 94.769 0.750 re f 486.106 339.976 94.769 0.750 re f 486.106 339.976 0.750 16.631 re f 580.125 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 346.003 Td /F1 9.8 Tf [(1.9 [1.6,2.2])] TJ ET BT 26.250 285.078 Td /F1 9.8 Tf [(Two recent papers have attempted to estimate the effect of control measures on the spread of EBV during the West African )] TJ ET BT 26.250 273.173 Td /F1 9.8 Tf [(outbreak. The first \(Althaus, 2014\) employs a Poisson likelihood fit to the cumulative incidence under the assumption of an SEIR )] TJ ET BT 26.250 261.268 Td /F1 9.8 Tf [(model with control that begins the day the first case appears in the population, and causes the transmission rate to )] TJ ET BT 26.250 249.363 Td /F1 9.8 Tf [(exponentially decay )] TJ ET 0.267 0.267 0.267 rg BT 114.585 250.871 Td /F4 8.7 Tf [(15)] TJ ET 0.271 0.267 0.267 rg BT 124.222 249.363 Td /F1 9.8 Tf [(. A second recent paper \(Fisman )] TJ ET BT 268.366 249.363 Td /F5 9.8 Tf [(et a)] TJ ET BT 284.629 249.363 Td /F1 9.8 Tf [(l , 2014\) also fits to the cumulative incidence curve, with a model )] TJ ET BT 26.250 237.459 Td /F1 9.8 Tf [(that assumes that the incidence over time is a function of the basic reproduction number, and a control parameter that causes )] TJ ET BT 26.250 225.554 Td /F1 9.8 Tf [(the incidence to decay )] TJ ET 0.267 0.267 0.267 rg BT 125.973 227.061 Td /F4 8.7 Tf [(16)] TJ ET 0.271 0.267 0.267 rg BT 135.610 225.554 Td /F1 9.8 Tf [(. The Althaus and Fisman )] TJ ET BT 249.412 225.554 Td /F5 9.8 Tf [(et al)] TJ ET BT 267.840 225.554 Td /F1 9.8 Tf [( estimates of the reproduction number for the Guinea and Liberia )] TJ ET BT 26.250 213.649 Td /F1 9.8 Tf [(outbreaks are within our corresponding 95% confidence intervals under the same hypotheses for the incubation and infectious )] TJ ET BT 26.250 201.744 Td /F1 9.8 Tf [(periods. However, both analyses predict significantly higher reproduction numbers for the Sierra Leone outbreak. The )] TJ ET BT 26.250 189.840 Td /F1 9.8 Tf [(discrepancy is likely due to the fact that both analyses employ models that assume that control measures are immediately )] TJ ET BT 26.250 177.935 Td /F1 9.8 Tf [(employed and effective; the results thus inherently attribute the low effective reproduction number to a high basic reproduction )] TJ ET BT 26.250 166.030 Td /F1 9.8 Tf [(number being modulated by highly effective control measures. Neither analysis provides a comparison of the model fit results to )] TJ ET BT 26.250 154.125 Td /F1 9.8 Tf [(those of a reduced model where control is excluded, so it is unknown what the estimates for the reproduction number would be )] TJ ET BT 26.250 142.221 Td /F1 9.8 Tf [(if control was not inherently assumed.)] TJ ET BT 26.250 122.816 Td /F1 9.8 Tf [(We stress again that our analysis makes no assumptions about whether or not control measures have been employed, and/or )] TJ ET BT 26.250 110.911 Td /F1 9.8 Tf [(when they were employed. We simply examine the local rates of exponential rise to estimate how the effective reproduction )] TJ ET BT 26.250 99.006 Td /F1 9.8 Tf [(number appears to be changing in time. We note that up until mid-August, the values of )] TJ ET q 24.000 0 0 9.000 405.613 99.530 cm /I176 Do Q BT 429.613 99.006 Td /F1 9.8 Tf [(for Guinea are significantly below )] TJ ET BT 26.250 87.102 Td /F1 9.8 Tf [(the average central value obtained from the fit the the data from July 1st onwards, and were rising \(unless otherwise noted, all )] TJ ET BT 26.250 75.197 Td /F1 9.8 Tf [(subsequent statistical tests are Bonferroni corrected one-sided Z tests, with rejection of the null hypothesis occurring when p < )] TJ ET BT 26.250 63.292 Td /F1 9.8 Tf [(0.05/k, where k is the number of values being compared\). The dip in the two recent Guinea data points compared to the central )] TJ ET BT 26.250 51.387 Td /F1 9.8 Tf [(value is not significant. In addition, the dip in the two recent estimates of )] TJ ET q 24.000 0 0 9.000 338.952 51.911 cm /I178 Do Q BT 362.952 51.387 Td /F1 9.8 Tf [( from the Liberia data are also not significant. )] TJ ET BT 26.250 39.483 Td /F1 9.8 Tf [(However, the estimates of )] TJ ET q 24.000 0 0 9.000 141.671 40.006 cm /I180 Do Q BT 165.671 39.483 Td /F1 9.8 Tf [( for the three earliest points in the Liberia local time series are significantly lower than the )] TJ ET Q q 15.000 25.197 577.500 751.803 re W n 0.271 0.267 0.267 rg BT 26.250 750.278 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 730.324 Td /F1 9.8 Tf [(For each country in Figure 2 the solid and dotted black lines denote the central value and 95% CI, respectively, of the rate of )] TJ ET BT 26.250 718.419 Td /F1 9.8 Tf [(exponential rise of case incidence data between July 1st and September 8th . The estimates of the rates of exponential rise )] TJ ET BT 26.250 706.515 Td /F1 9.8 Tf [(between July 1st and September 8th are ?=0. 052 0. 008, ?=0. 015 0. 008, and ?=0. 046 0. 005 for Guinea, Sierra Leone, )] TJ ET BT 26.250 694.610 Td /F1 9.8 Tf [(and Liberia, respectively. The value estimated from the combined data samples is ?=0. 037 0. 006. The values are statistically )] TJ ET BT 26.250 682.705 Td /F1 9.8 Tf [(consistent for the Guinea and Liberia data \(one-sided Z test p = 0. 28\). However, the estimate for the Sierra Leone data is )] TJ ET BT 26.250 670.800 Td /F1 9.8 Tf [(significantly lower than the estimates obtained from the Guinea and Liberia data \(one-sided Z test p = 0. 0005, and p = 0. 0003, )] TJ ET BT 26.250 658.896 Td /F1 9.8 Tf [(respectively\). In Table 1 we show the values of the effective reproduction number, )] TJ ET q 21.750 0 0 9.750 381.745 658.669 cm /I182 Do Q BT 403.495 658.896 Td /F1 9.8 Tf [( , as estimated from Equation 2 under )] TJ ET BT 26.250 646.991 Td /F1 9.8 Tf [(several hypotheses for the incubation and infectious periods \(the incubation and infectious periods for this outbreak are poorly )] TJ ET BT 26.250 635.086 Td /F1 9.8 Tf [(known, and have shown wide apparent variation in previous outbreaks )] TJ ET 0.267 0.267 0.267 rg BT 332.439 636.593 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 342.076 638.974 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 344.486 636.593 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 354.123 635.086 Td /F1 9.8 Tf [(\). The reproduction numbers estimated by this )] TJ ET BT 26.250 623.181 Td /F1 9.8 Tf [(analysis are in broad agreement with the reproduction numbers estimated from this and previous outbreaks, which range from )] TJ ET BT 26.250 611.277 Td /F1 9.8 Tf [(approximately 1.3 to 2.7 )] TJ ET 0.267 0.267 0.267 rg BT 133.012 612.784 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 142.650 615.165 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 145.059 612.784 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 154.697 615.165 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 157.106 612.784 Td /F4 8.7 Tf [(22)] TJ ET 0.271 0.267 0.267 rg BT 166.743 611.277 Td /F1 9.8 Tf [(.)] TJ ET q 26.250 587.659 555.000 13.736 re W n 0.271 0.267 0.267 rg BT 26.250 590.407 Td /F1 9.8 Tf [(Table 1: Estimates of the effective reproduction number between July 1 to present)] TJ ET Q 0.965 0.965 0.965 rg 26.250 520.122 555.000 60.037 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 580.159 m 581.250 580.159 l 580.500 579.409 l 27.000 579.409 l f 581.250 580.159 m 581.250 520.122 l 580.500 520.122 l 580.500 579.409 l f 26.250 580.159 m 26.250 520.122 l 27.000 520.122 l 27.000 579.409 l f 0.271 0.267 0.267 rg BT 33.000 566.083 Td /F1 9.0 Tf [(Estimates of the effective reproduction number for the 2014 West African EBV outbreak data, for an SEIR model as obtained from )] TJ ET BT 33.000 556.926 Td /F1 9.0 Tf [(Equation 2 under several hypotheses for the incubation and infectious periods. The estimates and the 95% confidence intervals are )] TJ ET BT 33.000 547.768 Td /F1 9.0 Tf [(derived from the rate of rise of an exponential fit to the new case incidence data for the various countries between July 1st and )] TJ ET BT 33.000 538.611 Td /F1 9.0 Tf [(September 8th \(the beginning of July is when the World Health Organization began frequent updates of the new case information for all )] TJ ET BT 33.000 529.453 Td /F1 9.0 Tf [(three countries\).)] TJ ET 1.000 1.000 1.000 rg 26.250 339.601 555.000 180.521 re f 0.965 0.965 0.965 rg 27.000 483.283 171.966 36.089 re f 0.267 0.267 0.267 rg 26.625 518.997 172.341 0.750 re f 26.625 482.908 0.750 36.839 re f 0.271 0.267 0.267 rg BT 31.500 509.848 Td /F4 9.8 Tf [(Hypothesized incubation)] TJ ET BT 31.500 497.943 Td /F4 9.8 Tf [(and infectious periods,)] TJ ET BT 31.500 486.039 Td /F4 9.8 Tf [(respectively \(days\))] TJ ET 0.965 0.965 0.965 rg 198.966 483.283 94.019 36.089 re f 0.267 0.267 0.267 rg 198.966 518.997 94.019 0.750 re f 0.271 0.267 0.267 rg BT 203.466 509.848 Td /F4 9.8 Tf [(Guinea)] TJ ET 0.965 0.965 0.965 rg 292.985 483.283 94.019 36.089 re f 0.267 0.267 0.267 rg 292.985 518.997 94.019 0.750 re f 0.271 0.267 0.267 rg BT 297.485 509.848 Td /F4 9.8 Tf [(Liberia)] TJ ET 0.965 0.965 0.965 rg 387.005 483.283 99.476 36.089 re f 0.267 0.267 0.267 rg 387.005 518.997 99.476 0.750 re f 0.271 0.267 0.267 rg BT 391.505 509.848 Td /F4 9.8 Tf [(Sierra Leone)] TJ ET 0.965 0.965 0.965 rg 486.481 483.283 94.019 36.089 re f 0.267 0.267 0.267 rg 486.481 518.997 94.394 0.750 re f 580.125 482.908 0.750 36.839 re f 0.271 0.267 0.267 rg BT 490.981 509.848 Td /F4 9.8 Tf [(All)] TJ ET 0.267 0.267 0.267 rg 26.625 482.908 172.716 0.750 re f 26.625 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 473.053 Td /F1 9.8 Tf [(5 and 5)] TJ ET 0.267 0.267 0.267 rg 198.591 482.908 94.769 0.750 re f 198.591 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 473.053 Td /F1 9.8 Tf [(1.6 [1.4,1.8])] TJ ET 0.267 0.267 0.267 rg 292.610 482.908 94.769 0.750 re f 292.610 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 473.053 Td /F1 9.8 Tf [(1.5 [1.4,1.6])] TJ ET 0.267 0.267 0.267 rg 386.630 482.908 100.226 0.750 re f 386.630 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 473.053 Td /F1 9.8 Tf [(1.2 [1.0,1.3])] TJ ET 0.267 0.267 0.267 rg 486.106 482.908 94.769 0.750 re f 486.106 467.026 0.750 16.631 re f 580.125 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 473.053 Td /F1 9.8 Tf [(1.4 [1.3,1.5])] TJ ET 0.267 0.267 0.267 rg 26.625 467.026 172.716 0.750 re f 26.625 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 457.171 Td /F1 9.8 Tf [(7 and 5)] TJ ET 0.267 0.267 0.267 rg 198.591 467.026 94.769 0.750 re f 198.591 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 457.171 Td /F1 9.8 Tf [(1.7 [1.5,2.0])] TJ ET 0.267 0.267 0.267 rg 292.610 467.026 94.769 0.750 re f 292.610 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 457.171 Td /F1 9.8 Tf [(1.6 [1.5,1.8])] TJ ET 0.267 0.267 0.267 rg 386.630 467.026 100.226 0.750 re f 386.630 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 457.171 Td /F1 9.8 Tf [(1.2 [1.0,1.4])] TJ ET 0.267 0.267 0.267 rg 486.106 467.026 94.769 0.750 re f 486.106 451.145 0.750 16.631 re f 580.125 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 457.171 Td /F1 9.8 Tf [(1.5 [1.3,1.7])] TJ ET 0.267 0.267 0.267 rg 26.625 451.145 172.716 0.750 re f 26.625 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 441.290 Td /F1 9.8 Tf [(10 and 5)] TJ ET 0.267 0.267 0.267 rg 198.591 451.145 94.769 0.750 re f 198.591 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 441.290 Td /F1 9.8 Tf [(1.9 [1.6,2.3])] TJ ET 0.267 0.267 0.267 rg 292.610 451.145 94.769 0.750 re f 292.610 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 441.290 Td /F1 9.8 Tf [(1.8 [1.6,2.0])] TJ ET 0.267 0.267 0.267 rg 386.630 451.145 100.226 0.750 re f 386.630 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 441.290 Td /F1 9.8 Tf [(1.2 [1.0,1.5])] TJ ET 0.267 0.267 0.267 rg 486.106 451.145 94.769 0.750 re f 486.106 435.264 0.750 16.631 re f 580.125 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 441.290 Td /F1 9.8 Tf [(1.6 [1.4,1.8])] TJ ET 0.267 0.267 0.267 rg 26.625 435.264 172.716 0.750 re f 26.625 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 425.409 Td /F1 9.8 Tf [(5 and 7)] TJ ET 0.267 0.267 0.267 rg 198.591 435.264 94.769 0.750 re f 198.591 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 425.409 Td /F1 9.8 Tf [(1.7 [1.5,2.0])] TJ ET 0.267 0.267 0.267 rg 292.610 435.264 94.769 0.750 re f 292.610 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 425.409 Td /F1 9.8 Tf [(1.6 [1.5,1.8])] TJ ET 0.267 0.267 0.267 rg 386.630 435.264 100.226 0.750 re f 386.630 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 425.409 Td /F1 9.8 Tf [(1.2 [1.0,1.4])] TJ ET 0.267 0.267 0.267 rg 486.106 435.264 94.769 0.750 re f 486.106 419.383 0.750 16.631 re f 580.125 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 425.409 Td /F1 9.8 Tf [(1.5 [1.3,1.7])] TJ ET 0.267 0.267 0.267 rg 26.625 419.383 172.716 0.750 re f 26.625 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 409.528 Td /F1 9.8 Tf [(7 and 7)] TJ ET 0.267 0.267 0.267 rg 198.591 419.383 94.769 0.750 re f 198.591 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 409.528 Td /F1 9.8 Tf [(1.9 [1.6,2.2])] TJ ET 0.267 0.267 0.267 rg 292.610 419.383 94.769 0.750 re f 292.610 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 409.528 Td /F1 9.8 Tf [(1.8 [1.6,1.9])] TJ ET 0.267 0.267 0.267 rg 386.630 419.383 100.226 0.750 re f 386.630 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 409.528 Td /F1 9.8 Tf [(1.2 [1.0,1.5])] TJ ET 0.267 0.267 0.267 rg 486.106 419.383 94.769 0.750 re f 486.106 403.501 0.750 16.631 re f 580.125 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 409.528 Td /F1 9.8 Tf [(1.6 [1.4,1.8])] TJ ET 0.267 0.267 0.267 rg 26.625 403.501 172.716 0.750 re f 26.625 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 393.646 Td /F1 9.8 Tf [(10 and 7)] TJ ET 0.267 0.267 0.267 rg 198.591 403.501 94.769 0.750 re f 198.591 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 393.646 Td /F1 9.8 Tf [(2.1 [1.7,2.5])] TJ ET 0.267 0.267 0.267 rg 292.610 403.501 94.769 0.750 re f 292.610 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 393.646 Td /F1 9.8 Tf [(1.9 [1.7,2.2])] TJ ET 0.267 0.267 0.267 rg 386.630 403.501 100.226 0.750 re f 386.630 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 393.646 Td /F1 9.8 Tf [(1.3 [1.0,1.6])] TJ ET 0.267 0.267 0.267 rg 486.106 403.501 94.769 0.750 re f 486.106 387.620 0.750 16.631 re f 580.125 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 393.646 Td /F1 9.8 Tf [(1.7 [1.5,2.0])] TJ ET 0.267 0.267 0.267 rg 26.625 387.620 172.716 0.750 re f 26.625 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 377.765 Td /F1 9.8 Tf [(5 and 10)] TJ ET 0.267 0.267 0.267 rg 198.591 387.620 94.769 0.750 re f 198.591 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 377.765 Td /F1 9.8 Tf [(1.9 [1.6,2.3])] TJ ET 0.267 0.267 0.267 rg 292.610 387.620 94.769 0.750 re f 292.610 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 377.765 Td /F1 9.8 Tf [(1.8 [1.6,2.0])] TJ ET 0.267 0.267 0.267 rg 386.630 387.620 100.226 0.750 re f 386.630 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 377.765 Td /F1 9.8 Tf [(1.2 [1.0,1.5])] TJ ET 0.267 0.267 0.267 rg 486.106 387.620 94.769 0.750 re f 486.106 371.739 0.750 16.631 re f 580.125 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 377.765 Td /F1 9.8 Tf [(1.6 [1.4,1.8])] TJ ET 0.267 0.267 0.267 rg 26.625 371.739 172.716 0.750 re f 26.625 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 361.884 Td /F1 9.8 Tf [(7 and 10)] TJ ET 0.267 0.267 0.267 rg 198.591 371.739 94.769 0.750 re f 198.591 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 361.884 Td /F1 9.8 Tf [(2.1 [1.7,2.5])] TJ ET 0.267 0.267 0.267 rg 292.610 371.739 94.769 0.750 re f 292.610 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 361.884 Td /F1 9.8 Tf [(1.9 [1.7,2.2])] TJ ET 0.267 0.267 0.267 rg 386.630 371.739 100.226 0.750 re f 386.630 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 361.884 Td /F1 9.8 Tf [(1.3 [1.0,1.6])] TJ ET 0.267 0.267 0.267 rg 486.106 371.739 94.769 0.750 re f 486.106 355.858 0.750 16.631 re f 580.125 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 361.884 Td /F1 9.8 Tf [(1.7 [1.5,2.0])] TJ ET 0.267 0.267 0.267 rg 26.625 355.858 172.716 0.750 re f 26.625 339.976 172.716 0.750 re f 26.625 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 346.003 Td /F1 9.8 Tf [(10 and 10)] TJ ET 0.267 0.267 0.267 rg 198.591 355.858 94.769 0.750 re f 198.591 339.976 94.769 0.750 re f 198.591 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 346.003 Td /F1 9.8 Tf [(2.3 [1.8,2.8])] TJ ET 0.267 0.267 0.267 rg 292.610 355.858 94.769 0.750 re f 292.610 339.976 94.769 0.750 re f 292.610 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 346.003 Td /F1 9.8 Tf [(2.1 [1.9,2.4])] TJ ET 0.267 0.267 0.267 rg 386.630 355.858 100.226 0.750 re f 386.630 339.976 100.226 0.750 re f 386.630 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 346.003 Td /F1 9.8 Tf [(1.3 [1.0,1.7])] TJ ET 0.267 0.267 0.267 rg 486.106 355.858 94.769 0.750 re f 486.106 339.976 94.769 0.750 re f 486.106 339.976 0.750 16.631 re f 580.125 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 346.003 Td /F1 9.8 Tf [(1.9 [1.6,2.2])] TJ ET BT 26.250 285.078 Td /F1 9.8 Tf [(Two recent papers have attempted to estimate the effect of control measures on the spread of EBV during the West African )] TJ ET BT 26.250 273.173 Td /F1 9.8 Tf [(outbreak. The first \(Althaus, 2014\) employs a Poisson likelihood fit to the cumulative incidence under the assumption of an SEIR )] TJ ET BT 26.250 261.268 Td /F1 9.8 Tf [(model with control that begins the day the first case appears in the population, and causes the transmission rate to )] TJ ET BT 26.250 249.363 Td /F1 9.8 Tf [(exponentially decay )] TJ ET 0.267 0.267 0.267 rg BT 114.585 250.871 Td /F4 8.7 Tf [(15)] TJ ET 0.271 0.267 0.267 rg BT 124.222 249.363 Td /F1 9.8 Tf [(. A second recent paper \(Fisman )] TJ ET BT 268.366 249.363 Td /F5 9.8 Tf [(et a)] TJ ET BT 284.629 249.363 Td /F1 9.8 Tf [(l , 2014\) also fits to the cumulative incidence curve, with a model )] TJ ET BT 26.250 237.459 Td /F1 9.8 Tf [(that assumes that the incidence over time is a function of the basic reproduction number, and a control parameter that causes )] TJ ET BT 26.250 225.554 Td /F1 9.8 Tf [(the incidence to decay )] TJ ET 0.267 0.267 0.267 rg BT 125.973 227.061 Td /F4 8.7 Tf [(16)] TJ ET 0.271 0.267 0.267 rg BT 135.610 225.554 Td /F1 9.8 Tf [(. The Althaus and Fisman )] TJ ET BT 249.412 225.554 Td /F5 9.8 Tf [(et al)] TJ ET BT 267.840 225.554 Td /F1 9.8 Tf [( estimates of the reproduction number for the Guinea and Liberia )] TJ ET BT 26.250 213.649 Td /F1 9.8 Tf [(outbreaks are within our corresponding 95% confidence intervals under the same hypotheses for the incubation and infectious )] TJ ET BT 26.250 201.744 Td /F1 9.8 Tf [(periods. However, both analyses predict significantly higher reproduction numbers for the Sierra Leone outbreak. The )] TJ ET BT 26.250 189.840 Td /F1 9.8 Tf [(discrepancy is likely due to the fact that both analyses employ models that assume that control measures are immediately )] TJ ET BT 26.250 177.935 Td /F1 9.8 Tf [(employed and effective; the results thus inherently attribute the low effective reproduction number to a high basic reproduction )] TJ ET BT 26.250 166.030 Td /F1 9.8 Tf [(number being modulated by highly effective control measures. Neither analysis provides a comparison of the model fit results to )] TJ ET BT 26.250 154.125 Td /F1 9.8 Tf [(those of a reduced model where control is excluded, so it is unknown what the estimates for the reproduction number would be )] TJ ET BT 26.250 142.221 Td /F1 9.8 Tf [(if control was not inherently assumed.)] TJ ET BT 26.250 122.816 Td /F1 9.8 Tf [(We stress again that our analysis makes no assumptions about whether or not control measures have been employed, and/or )] TJ ET BT 26.250 110.911 Td /F1 9.8 Tf [(when they were employed. We simply examine the local rates of exponential rise to estimate how the effective reproduction )] TJ ET BT 26.250 99.006 Td /F1 9.8 Tf [(number appears to be changing in time. We note that up until mid-August, the values of )] TJ ET q 24.000 0 0 9.000 405.613 99.530 cm /I184 Do Q BT 429.613 99.006 Td /F1 9.8 Tf [(for Guinea are significantly below )] TJ ET BT 26.250 87.102 Td /F1 9.8 Tf [(the average central value obtained from the fit the the data from July 1st onwards, and were rising \(unless otherwise noted, all )] TJ ET BT 26.250 75.197 Td /F1 9.8 Tf [(subsequent statistical tests are Bonferroni corrected one-sided Z tests, with rejection of the null hypothesis occurring when p < )] TJ ET BT 26.250 63.292 Td /F1 9.8 Tf [(0.05/k, where k is the number of values being compared\). The dip in the two recent Guinea data points compared to the central )] TJ ET BT 26.250 51.387 Td /F1 9.8 Tf [(value is not significant. In addition, the dip in the two recent estimates of )] TJ ET q 24.000 0 0 9.000 338.952 51.911 cm /I186 Do Q BT 362.952 51.387 Td /F1 9.8 Tf [( from the Liberia data are also not significant. )] TJ ET BT 26.250 39.483 Td /F1 9.8 Tf [(However, the estimates of )] TJ ET q 24.000 0 0 9.000 141.671 40.006 cm /I188 Do Q BT 165.671 39.483 Td /F1 9.8 Tf [( for the three earliest points in the Liberia local time series are significantly lower than the )] TJ ET Q q 15.000 25.197 577.500 751.803 re W n 0.271 0.267 0.267 rg BT 26.250 750.278 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 730.324 Td /F1 9.8 Tf [(For each country in Figure 2 the solid and dotted black lines denote the central value and 95% CI, respectively, of the rate of )] TJ ET BT 26.250 718.419 Td /F1 9.8 Tf [(exponential rise of case incidence data between July 1st and September 8th . The estimates of the rates of exponential rise )] TJ ET BT 26.250 706.515 Td /F1 9.8 Tf [(between July 1st and September 8th are ?=0. 052 0. 008, ?=0. 015 0. 008, and ?=0. 046 0. 005 for Guinea, Sierra Leone, )] TJ ET BT 26.250 694.610 Td /F1 9.8 Tf [(and Liberia, respectively. The value estimated from the combined data samples is ?=0. 037 0. 006. The values are statistically )] TJ ET BT 26.250 682.705 Td /F1 9.8 Tf [(consistent for the Guinea and Liberia data \(one-sided Z test p = 0. 28\). However, the estimate for the Sierra Leone data is )] TJ ET BT 26.250 670.800 Td /F1 9.8 Tf [(significantly lower than the estimates obtained from the Guinea and Liberia data \(one-sided Z test p = 0. 0005, and p = 0. 0003, )] TJ ET BT 26.250 658.896 Td /F1 9.8 Tf [(respectively\). In Table 1 we show the values of the effective reproduction number, )] TJ ET q 21.750 0 0 9.750 381.745 658.669 cm /I190 Do Q BT 403.495 658.896 Td /F1 9.8 Tf [( , as estimated from Equation 2 under )] TJ ET BT 26.250 646.991 Td /F1 9.8 Tf [(several hypotheses for the incubation and infectious periods \(the incubation and infectious periods for this outbreak are poorly )] TJ ET BT 26.250 635.086 Td /F1 9.8 Tf [(known, and have shown wide apparent variation in previous outbreaks )] TJ ET 0.267 0.267 0.267 rg BT 332.439 636.593 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 342.076 638.974 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 344.486 636.593 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 354.123 635.086 Td /F1 9.8 Tf [(\). The reproduction numbers estimated by this )] TJ ET BT 26.250 623.181 Td /F1 9.8 Tf [(analysis are in broad agreement with the reproduction numbers estimated from this and previous outbreaks, which range from )] TJ ET BT 26.250 611.277 Td /F1 9.8 Tf [(approximately 1.3 to 2.7 )] TJ ET 0.267 0.267 0.267 rg BT 133.012 612.784 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 142.650 615.165 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 145.059 612.784 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 154.697 615.165 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 157.106 612.784 Td /F4 8.7 Tf [(22)] TJ ET 0.271 0.267 0.267 rg BT 166.743 611.277 Td /F1 9.8 Tf [(.)] TJ ET q 26.250 587.659 555.000 13.736 re W n 0.271 0.267 0.267 rg BT 26.250 590.407 Td /F1 9.8 Tf [(Table 1: Estimates of the effective reproduction number between July 1 to present)] TJ ET Q 0.965 0.965 0.965 rg 26.250 520.122 555.000 60.037 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 580.159 m 581.250 580.159 l 580.500 579.409 l 27.000 579.409 l f 581.250 580.159 m 581.250 520.122 l 580.500 520.122 l 580.500 579.409 l f 26.250 580.159 m 26.250 520.122 l 27.000 520.122 l 27.000 579.409 l f 0.271 0.267 0.267 rg BT 33.000 566.083 Td /F1 9.0 Tf [(Estimates of the effective reproduction number for the 2014 West African EBV outbreak data, for an SEIR model as obtained from )] TJ ET BT 33.000 556.926 Td /F1 9.0 Tf [(Equation 2 under several hypotheses for the incubation and infectious periods. The estimates and the 95% confidence intervals are )] TJ ET BT 33.000 547.768 Td /F1 9.0 Tf [(derived from the rate of rise of an exponential fit to the new case incidence data for the various countries between July 1st and )] TJ ET BT 33.000 538.611 Td /F1 9.0 Tf [(September 8th \(the beginning of July is when the World Health Organization began frequent updates of the new case information for all )] TJ ET BT 33.000 529.453 Td /F1 9.0 Tf [(three countries\).)] TJ ET 1.000 1.000 1.000 rg 26.250 339.601 555.000 180.521 re f 0.965 0.965 0.965 rg 27.000 483.283 171.966 36.089 re f 0.267 0.267 0.267 rg 26.625 518.997 172.341 0.750 re f 26.625 482.908 0.750 36.839 re f 0.271 0.267 0.267 rg BT 31.500 509.848 Td /F4 9.8 Tf [(Hypothesized incubation)] TJ ET BT 31.500 497.943 Td /F4 9.8 Tf [(and infectious periods,)] TJ ET BT 31.500 486.039 Td /F4 9.8 Tf [(respectively \(days\))] TJ ET 0.965 0.965 0.965 rg 198.966 483.283 94.019 36.089 re f 0.267 0.267 0.267 rg 198.966 518.997 94.019 0.750 re f 0.271 0.267 0.267 rg BT 203.466 509.848 Td /F4 9.8 Tf [(Guinea)] TJ ET 0.965 0.965 0.965 rg 292.985 483.283 94.019 36.089 re f 0.267 0.267 0.267 rg 292.985 518.997 94.019 0.750 re f 0.271 0.267 0.267 rg BT 297.485 509.848 Td /F4 9.8 Tf [(Liberia)] TJ ET 0.965 0.965 0.965 rg 387.005 483.283 99.476 36.089 re f 0.267 0.267 0.267 rg 387.005 518.997 99.476 0.750 re f 0.271 0.267 0.267 rg BT 391.505 509.848 Td /F4 9.8 Tf [(Sierra Leone)] TJ ET 0.965 0.965 0.965 rg 486.481 483.283 94.019 36.089 re f 0.267 0.267 0.267 rg 486.481 518.997 94.394 0.750 re f 580.125 482.908 0.750 36.839 re f 0.271 0.267 0.267 rg BT 490.981 509.848 Td /F4 9.8 Tf [(All)] TJ ET 0.267 0.267 0.267 rg 26.625 482.908 172.716 0.750 re f 26.625 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 473.053 Td /F1 9.8 Tf [(5 and 5)] TJ ET 0.267 0.267 0.267 rg 198.591 482.908 94.769 0.750 re f 198.591 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 473.053 Td /F1 9.8 Tf [(1.6 [1.4,1.8])] TJ ET 0.267 0.267 0.267 rg 292.610 482.908 94.769 0.750 re f 292.610 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 473.053 Td /F1 9.8 Tf [(1.5 [1.4,1.6])] TJ ET 0.267 0.267 0.267 rg 386.630 482.908 100.226 0.750 re f 386.630 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 473.053 Td /F1 9.8 Tf [(1.2 [1.0,1.3])] TJ ET 0.267 0.267 0.267 rg 486.106 482.908 94.769 0.750 re f 486.106 467.026 0.750 16.631 re f 580.125 467.026 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 473.053 Td /F1 9.8 Tf [(1.4 [1.3,1.5])] TJ ET 0.267 0.267 0.267 rg 26.625 467.026 172.716 0.750 re f 26.625 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 457.171 Td /F1 9.8 Tf [(7 and 5)] TJ ET 0.267 0.267 0.267 rg 198.591 467.026 94.769 0.750 re f 198.591 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 457.171 Td /F1 9.8 Tf [(1.7 [1.5,2.0])] TJ ET 0.267 0.267 0.267 rg 292.610 467.026 94.769 0.750 re f 292.610 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 457.171 Td /F1 9.8 Tf [(1.6 [1.5,1.8])] TJ ET 0.267 0.267 0.267 rg 386.630 467.026 100.226 0.750 re f 386.630 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 457.171 Td /F1 9.8 Tf [(1.2 [1.0,1.4])] TJ ET 0.267 0.267 0.267 rg 486.106 467.026 94.769 0.750 re f 486.106 451.145 0.750 16.631 re f 580.125 451.145 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 457.171 Td /F1 9.8 Tf [(1.5 [1.3,1.7])] TJ ET 0.267 0.267 0.267 rg 26.625 451.145 172.716 0.750 re f 26.625 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 441.290 Td /F1 9.8 Tf [(10 and 5)] TJ ET 0.267 0.267 0.267 rg 198.591 451.145 94.769 0.750 re f 198.591 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 441.290 Td /F1 9.8 Tf [(1.9 [1.6,2.3])] TJ ET 0.267 0.267 0.267 rg 292.610 451.145 94.769 0.750 re f 292.610 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 441.290 Td /F1 9.8 Tf [(1.8 [1.6,2.0])] TJ ET 0.267 0.267 0.267 rg 386.630 451.145 100.226 0.750 re f 386.630 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 441.290 Td /F1 9.8 Tf [(1.2 [1.0,1.5])] TJ ET 0.267 0.267 0.267 rg 486.106 451.145 94.769 0.750 re f 486.106 435.264 0.750 16.631 re f 580.125 435.264 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 441.290 Td /F1 9.8 Tf [(1.6 [1.4,1.8])] TJ ET 0.267 0.267 0.267 rg 26.625 435.264 172.716 0.750 re f 26.625 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 425.409 Td /F1 9.8 Tf [(5 and 7)] TJ ET 0.267 0.267 0.267 rg 198.591 435.264 94.769 0.750 re f 198.591 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 425.409 Td /F1 9.8 Tf [(1.7 [1.5,2.0])] TJ ET 0.267 0.267 0.267 rg 292.610 435.264 94.769 0.750 re f 292.610 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 425.409 Td /F1 9.8 Tf [(1.6 [1.5,1.8])] TJ ET 0.267 0.267 0.267 rg 386.630 435.264 100.226 0.750 re f 386.630 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 425.409 Td /F1 9.8 Tf [(1.2 [1.0,1.4])] TJ ET 0.267 0.267 0.267 rg 486.106 435.264 94.769 0.750 re f 486.106 419.383 0.750 16.631 re f 580.125 419.383 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 425.409 Td /F1 9.8 Tf [(1.5 [1.3,1.7])] TJ ET 0.267 0.267 0.267 rg 26.625 419.383 172.716 0.750 re f 26.625 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 409.528 Td /F1 9.8 Tf [(7 and 7)] TJ ET 0.267 0.267 0.267 rg 198.591 419.383 94.769 0.750 re f 198.591 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 409.528 Td /F1 9.8 Tf [(1.9 [1.6,2.2])] TJ ET 0.267 0.267 0.267 rg 292.610 419.383 94.769 0.750 re f 292.610 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 409.528 Td /F1 9.8 Tf [(1.8 [1.6,1.9])] TJ ET 0.267 0.267 0.267 rg 386.630 419.383 100.226 0.750 re f 386.630 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 409.528 Td /F1 9.8 Tf [(1.2 [1.0,1.5])] TJ ET 0.267 0.267 0.267 rg 486.106 419.383 94.769 0.750 re f 486.106 403.501 0.750 16.631 re f 580.125 403.501 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 409.528 Td /F1 9.8 Tf [(1.6 [1.4,1.8])] TJ ET 0.267 0.267 0.267 rg 26.625 403.501 172.716 0.750 re f 26.625 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 393.646 Td /F1 9.8 Tf [(10 and 7)] TJ ET 0.267 0.267 0.267 rg 198.591 403.501 94.769 0.750 re f 198.591 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 393.646 Td /F1 9.8 Tf [(2.1 [1.7,2.5])] TJ ET 0.267 0.267 0.267 rg 292.610 403.501 94.769 0.750 re f 292.610 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 393.646 Td /F1 9.8 Tf [(1.9 [1.7,2.2])] TJ ET 0.267 0.267 0.267 rg 386.630 403.501 100.226 0.750 re f 386.630 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 393.646 Td /F1 9.8 Tf [(1.3 [1.0,1.6])] TJ ET 0.267 0.267 0.267 rg 486.106 403.501 94.769 0.750 re f 486.106 387.620 0.750 16.631 re f 580.125 387.620 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 393.646 Td /F1 9.8 Tf [(1.7 [1.5,2.0])] TJ ET 0.267 0.267 0.267 rg 26.625 387.620 172.716 0.750 re f 26.625 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 377.765 Td /F1 9.8 Tf [(5 and 10)] TJ ET 0.267 0.267 0.267 rg 198.591 387.620 94.769 0.750 re f 198.591 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 377.765 Td /F1 9.8 Tf [(1.9 [1.6,2.3])] TJ ET 0.267 0.267 0.267 rg 292.610 387.620 94.769 0.750 re f 292.610 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 377.765 Td /F1 9.8 Tf [(1.8 [1.6,2.0])] TJ ET 0.267 0.267 0.267 rg 386.630 387.620 100.226 0.750 re f 386.630 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 377.765 Td /F1 9.8 Tf [(1.2 [1.0,1.5])] TJ ET 0.267 0.267 0.267 rg 486.106 387.620 94.769 0.750 re f 486.106 371.739 0.750 16.631 re f 580.125 371.739 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 377.765 Td /F1 9.8 Tf [(1.6 [1.4,1.8])] TJ ET 0.267 0.267 0.267 rg 26.625 371.739 172.716 0.750 re f 26.625 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 361.884 Td /F1 9.8 Tf [(7 and 10)] TJ ET 0.267 0.267 0.267 rg 198.591 371.739 94.769 0.750 re f 198.591 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 361.884 Td /F1 9.8 Tf [(2.1 [1.7,2.5])] TJ ET 0.267 0.267 0.267 rg 292.610 371.739 94.769 0.750 re f 292.610 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 361.884 Td /F1 9.8 Tf [(1.9 [1.7,2.2])] TJ ET 0.267 0.267 0.267 rg 386.630 371.739 100.226 0.750 re f 386.630 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 361.884 Td /F1 9.8 Tf [(1.3 [1.0,1.6])] TJ ET 0.267 0.267 0.267 rg 486.106 371.739 94.769 0.750 re f 486.106 355.858 0.750 16.631 re f 580.125 355.858 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 361.884 Td /F1 9.8 Tf [(1.7 [1.5,2.0])] TJ ET 0.267 0.267 0.267 rg 26.625 355.858 172.716 0.750 re f 26.625 339.976 172.716 0.750 re f 26.625 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 31.875 346.003 Td /F1 9.8 Tf [(10 and 10)] TJ ET 0.267 0.267 0.267 rg 198.591 355.858 94.769 0.750 re f 198.591 339.976 94.769 0.750 re f 198.591 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 203.841 346.003 Td /F1 9.8 Tf [(2.3 [1.8,2.8])] TJ ET 0.267 0.267 0.267 rg 292.610 355.858 94.769 0.750 re f 292.610 339.976 94.769 0.750 re f 292.610 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 297.860 346.003 Td /F1 9.8 Tf [(2.1 [1.9,2.4])] TJ ET 0.267 0.267 0.267 rg 386.630 355.858 100.226 0.750 re f 386.630 339.976 100.226 0.750 re f 386.630 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 391.880 346.003 Td /F1 9.8 Tf [(1.3 [1.0,1.7])] TJ ET 0.267 0.267 0.267 rg 486.106 355.858 94.769 0.750 re f 486.106 339.976 94.769 0.750 re f 486.106 339.976 0.750 16.631 re f 580.125 339.976 0.750 16.631 re f 0.271 0.267 0.267 rg BT 491.356 346.003 Td /F1 9.8 Tf [(1.9 [1.6,2.2])] TJ ET BT 26.250 285.078 Td /F1 9.8 Tf [(Two recent papers have attempted to estimate the effect of control measures on the spread of EBV during the West African )] TJ ET BT 26.250 273.173 Td /F1 9.8 Tf [(outbreak. The first \(Althaus, 2014\) employs a Poisson likelihood fit to the cumulative incidence under the assumption of an SEIR )] TJ ET BT 26.250 261.268 Td /F1 9.8 Tf [(model with control that begins the day the first case appears in the population, and causes the transmission rate to )] TJ ET BT 26.250 249.363 Td /F1 9.8 Tf [(exponentially decay )] TJ ET 0.267 0.267 0.267 rg BT 114.585 250.871 Td /F4 8.7 Tf [(15)] TJ ET 0.271 0.267 0.267 rg BT 124.222 249.363 Td /F1 9.8 Tf [(. A second recent paper \(Fisman )] TJ ET BT 268.366 249.363 Td /F5 9.8 Tf [(et a)] TJ ET BT 284.629 249.363 Td /F1 9.8 Tf [(l , 2014\) also fits to the cumulative incidence curve, with a model )] TJ ET BT 26.250 237.459 Td /F1 9.8 Tf [(that assumes that the incidence over time is a function of the basic reproduction number, and a control parameter that causes )] TJ ET BT 26.250 225.554 Td /F1 9.8 Tf [(the incidence to decay )] TJ ET 0.267 0.267 0.267 rg BT 125.973 227.061 Td /F4 8.7 Tf [(16)] TJ ET 0.271 0.267 0.267 rg BT 135.610 225.554 Td /F1 9.8 Tf [(. The Althaus and Fisman )] TJ ET BT 249.412 225.554 Td /F5 9.8 Tf [(et al)] TJ ET BT 267.840 225.554 Td /F1 9.8 Tf [( estimates of the reproduction number for the Guinea and Liberia )] TJ ET BT 26.250 213.649 Td /F1 9.8 Tf [(outbreaks are within our corresponding 95% confidence intervals under the same hypotheses for the incubation and infectious )] TJ ET BT 26.250 201.744 Td /F1 9.8 Tf [(periods. However, both analyses predict significantly higher reproduction numbers for the Sierra Leone outbreak. The )] TJ ET BT 26.250 189.840 Td /F1 9.8 Tf [(discrepancy is likely due to the fact that both analyses employ models that assume that control measures are immediately )] TJ ET BT 26.250 177.935 Td /F1 9.8 Tf [(employed and effective; the results thus inherently attribute the low effective reproduction number to a high basic reproduction )] TJ ET BT 26.250 166.030 Td /F1 9.8 Tf [(number being modulated by highly effective control measures. Neither analysis provides a comparison of the model fit results to )] TJ ET BT 26.250 154.125 Td /F1 9.8 Tf [(those of a reduced model where control is excluded, so it is unknown what the estimates for the reproduction number would be )] TJ ET BT 26.250 142.221 Td /F1 9.8 Tf [(if control was not inherently assumed.)] TJ ET BT 26.250 122.816 Td /F1 9.8 Tf [(We stress again that our analysis makes no assumptions about whether or not control measures have been employed, and/or )] TJ ET BT 26.250 110.911 Td /F1 9.8 Tf [(when they were employed. We simply examine the local rates of exponential rise to estimate how the effective reproduction )] TJ ET BT 26.250 99.006 Td /F1 9.8 Tf [(number appears to be changing in time. We note that up until mid-August, the values of )] TJ ET q 24.000 0 0 9.000 405.613 99.530 cm /I192 Do Q BT 429.613 99.006 Td /F1 9.8 Tf [(for Guinea are significantly below )] TJ ET BT 26.250 87.102 Td /F1 9.8 Tf [(the average central value obtained from the fit the the data from July 1st onwards, and were rising \(unless otherwise noted, all )] TJ ET BT 26.250 75.197 Td /F1 9.8 Tf [(subsequent statistical tests are Bonferroni corrected one-sided Z tests, with rejection of the null hypothesis occurring when p < )] TJ ET BT 26.250 63.292 Td /F1 9.8 Tf [(0.05/k, where k is the number of values being compared\). The dip in the two recent Guinea data points compared to the central )] TJ ET BT 26.250 51.387 Td /F1 9.8 Tf [(value is not significant. In addition, the dip in the two recent estimates of )] TJ ET q 24.000 0 0 9.000 338.952 51.911 cm /I194 Do Q BT 362.952 51.387 Td /F1 9.8 Tf [( from the Liberia data are also not significant. )] TJ ET BT 26.250 39.483 Td /F1 9.8 Tf [(However, the estimates of )] TJ ET q 24.000 0 0 9.000 141.671 40.006 cm /I196 Do Q BT 165.671 39.483 Td /F1 9.8 Tf [( for the three earliest points in the Liberia local time series are significantly lower than the )] 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 Outbreaks)] TJ ET Q endstream endobj 439 0 obj << /Type /XObject /Subtype /Image /Width 29 /Height 13 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 29 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 224>> stream c`. `b 9e˱}9$b&U00]Ô`bdcd10؎ L+41L``2IǷ DZ5603!+M,ρ1Њ( V`u} v]K G]\ L;R|¶1 H\S # U6d%ӤmEl @[ &%Xĭ``Xǂ8> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 18>> stream 8c``x endstream endobj 441 0 obj << /Type /Annot /Subtype /Link /A 442 0 R /Border [0 0 0] /H /I /Rect [ 332.4390 635.7917 342.0763 644.6100 ] >> endobj 442 0 obj << /Type /Action >> endobj 443 0 obj << /Type /Annot /Subtype /Link /A 444 0 R /Border [0 0 0] /H /I /Rect [ 344.4857 635.7917 354.1230 644.6100 ] >> endobj 444 0 obj << /Type /Action >> endobj 445 0 obj << /Type /Annot /Subtype /Link /A 446 0 R /Border [0 0 0] /H /I /Rect [ 133.0125 611.9822 142.6498 620.8005 ] >> endobj 446 0 obj << /Type /Action >> endobj 447 0 obj << /Type /Annot /Subtype /Link /A 448 0 R /Border [0 0 0] /H /I /Rect [ 145.0592 611.9822 154.6965 620.8005 ] >> endobj 448 0 obj << /Type /Action >> endobj 449 0 obj << /Type /Annot /Subtype /Link /A 450 0 R /Border [0 0 0] /H /I /Rect [ 157.1058 611.9822 166.7432 620.8005 ] >> endobj 450 0 obj << /Type /Action >> endobj 451 0 obj << /Type /Annot /Subtype /Link /A 452 0 R /Border [0 0 0] /H /I /Rect [ 114.5850 250.0689 124.2223 258.8872 ] >> endobj 452 0 obj << /Type /Action >> endobj 453 0 obj << /Type /Annot /Subtype /Link /A 454 0 R /Border [0 0 0] /H /I /Rect [ 125.9730 226.2594 135.6103 235.0777 ] >> endobj 454 0 obj << /Type /Action >> endobj 455 0 obj << /Type /XObject /Subtype /Image /Width 32 /Height 12 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 32 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 230>> stream c`&@!!mxTLb`9 ֆ*A6,z=& # 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None of the estimates of )] TJ ET q 24.000 0 0 9.000 243.022 768.000 cm /I198 Do Q BT 267.022 767.476 Td /F1 9.8 Tf [( from the Sierra Leone data and combined data for all countries are )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(significantly different than the central value.)] TJ ET BT 26.250 736.167 Td /F1 9.8 Tf [(It is unclear why the transmission rate of the disease apparently rose for both Guinea and Liberia between mid July to mid )] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(August, and why the transmission rate in Sierra Leone is systematically lower, although is important to note that the WHO data )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(are obtained from rudimentary surveillance systems in under-developed countries, under the stress of a rapidly evolving )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(outbreak situation. The temporal patterns we observe may thus partly be due to variations in surveillance during the outbreak, )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(under-reporting, and/or reporting delays. In addition, serial passage of the disease as the outbreak progresses may be leading )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(to increased pathogenicity, and a subsequent increasingly larger rate of increase in case counts . However, it also must be )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(considered that otherwise well intentioned attempts at intervention may in fact be making the situation worse, at least in some )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(regions; in a joint meeting of officials from Guinea, Liberia, and Sierra Leone on Aug 1st , it was announced that )] TJ ET BT 509.665 652.833 Td /F5 9.8 Tf [(cordons )] TJ ET BT 26.250 640.929 Td /F5 9.8 Tf [(sanitaire)] TJ ET BT 63.095 640.929 Td /F1 9.8 Tf [( would be implemented, to seal off the villages and regions worst hit by the outbreak, in an attempt to limit its spread )] TJ ET BT 26.250 629.024 Td /F1 9.8 Tf [(outside those areas )] TJ ET 0.267 0.267 0.267 rg BT 114.049 630.531 Td /F4 8.7 Tf [(17)] TJ ET 0.271 0.267 0.267 rg BT 123.686 629.024 Td /F1 9.8 Tf [(. In addition, at that time Liberia closed all schools and non-essential government offices )] TJ ET 0.267 0.267 0.267 rg BT 506.286 630.531 Td /F4 8.7 Tf [(18)] TJ ET 0.271 0.267 0.267 rg BT 515.923 629.024 Td /F1 9.8 Tf [(, and two )] TJ ET BT 26.250 617.119 Td /F1 9.8 Tf [(weeks later imposed a military-enforced )] TJ ET BT 200.716 617.119 Td /F5 9.8 Tf [(cordon sanitaire)] TJ ET BT 270.078 617.119 Td /F1 9.8 Tf [( on the West Point slum of Monrovia, sparking riots )] TJ ET 0.267 0.267 0.267 rg BT 492.788 618.626 Td /F4 8.7 Tf [(19)] TJ ET 0.271 0.267 0.267 rg BT 502.425 617.119 Td /F1 9.8 Tf [(. It must be )] TJ ET BT 26.250 605.214 Td /F1 9.8 Tf [(stressed that )] TJ ET BT 84.779 605.214 Td /F5 9.8 Tf [(cordons sanitaire)] TJ ET BT 159.016 605.214 Td /F1 9.8 Tf [( do not generally attempt to limit disease spread within the quarantined areas, and the )] TJ ET BT 26.250 593.310 Td /F1 9.8 Tf [(implementation of these measures in West Africa has received criticism due to the fact that the quarantined areas are at risk for )] TJ ET BT 26.250 581.405 Td /F1 9.8 Tf [(crowding, lack of medical and basic services, and poor sanitation, potentially increasing the spread of disease within those )] TJ ET BT 26.250 569.500 Td /F1 9.8 Tf [(areas )] TJ ET 0.267 0.267 0.267 rg BT 53.345 571.007 Td /F4 8.7 Tf [(20)] TJ ET 0.271 0.267 0.267 rg BT 62.983 569.500 Td /F1 9.8 Tf [(. It was around the period of time that the )] TJ ET BT 242.919 569.500 Td /F5 9.8 Tf [(cordons sanitaire)] TJ ET BT 317.155 569.500 Td /F1 9.8 Tf [( were first imposed, and when the outbreak moved to the )] TJ ET BT 26.250 557.595 Td /F1 9.8 Tf [(densely populated cities of Conakry and Monrovia, that the exponential rise in new cases in Guinea and Liberia increased, )] TJ ET BT 26.250 545.691 Td /F1 9.8 Tf [(rather than went down. Again, it is unclear why the rate of exponential rise in Sierra Leone was apparently unaffected by these )] TJ ET BT 26.250 533.786 Td /F1 9.8 Tf [(events.)] TJ ET BT 26.250 514.381 Td /F1 9.8 Tf [(Based on our estimates of the exponential rise in cases between July 1st to the beginning of September, if this rise is to )] TJ ET BT 26.250 502.476 Td /F1 9.8 Tf [(continue unabated, there will be approximately 4400 new EVD cases in West Africa during the last half of the month of )] TJ ET BT 26.250 490.572 Td /F1 9.8 Tf [(September \(95% CI [3000, 6800]\), 500, 900, and 3000 of which will be in Sierra Leone, Guinea, and Liberia, respectively.)] TJ ET BT 26.250 453.969 Td /F4 12.0 Tf [(Summary)] TJ ET BT 26.250 434.015 Td /F1 9.8 Tf [(We have presented an analysis where piecewise exponential fits are employed to estimate the local rate of exponential rise in )] TJ ET BT 26.250 422.110 Td /F1 9.8 Tf [(cases in the 2014 West Africa Ebola outbreak. We have shown that these local rates of exponential rise can be used in )] TJ ET BT 26.250 410.205 Td /F1 9.8 Tf [(conjunction with a mathematical model to estimate the temporal changes in the effective reproduction number \(in the case of )] TJ ET BT 26.250 398.301 Td /F1 9.8 Tf [(this analysis, we employed an SEIR model\). Our analysis indicates that the spread of the disease to densely populated cities, )] TJ ET BT 26.250 386.396 Td /F1 9.8 Tf [(and/or the imposition of )] TJ ET BT 130.302 386.396 Td /F5 9.8 Tf [(cordons sanitaire )] TJ ET BT 207.249 386.396 Td /F1 9.8 Tf [( in West Africa may have accelerated the spread of the disease in some regions. Our )] TJ ET BT 26.250 374.491 Td /F1 9.8 Tf [(methodology is novel, and is applicable to any outbreak, and any mathematical disease model.)] TJ ET BT 26.250 337.889 Td /F4 12.0 Tf [(Competing Interests)] TJ ET BT 26.250 317.934 Td /F1 9.8 Tf [(The authors have declared that no competing interests exist.)] TJ ET BT 26.250 281.332 Td /F4 12.0 Tf [(Acknowledgements)] TJ ET BT 26.250 261.378 Td /F1 9.8 Tf [(The authors wish to acknowledge useful discussions with Gerardo Chowell regarding these studies.)] TJ ET BT 26.250 232.275 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 204.821 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 204.821 Td /F1 9.8 Tf [(Sanchez, Anthony. Ebola Viruses. John Wiley & Sons, Ltd, 2001.)] TJ ET BT 26.250 185.416 Td /F1 9.8 Tf [(2.)] TJ ET BT 38.132 185.416 Td /F1 9.8 Tf [(WHO. Ebola Virus Disease in Guinea, Mar 23 2014.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 176.930 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 158.380 Td /F1 9.8 Tf [(3.)] TJ ET BT 38.132 158.380 Td /F1 9.8 Tf [(World Health Organization. Global Alert and Response situation reports: Ebola response roadmap.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 149.894 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 131.344 Td /F1 9.8 Tf [(4.)] TJ ET BT 38.132 131.344 Td /F1 9.8 Tf [(Brownstein, John S., et al. "Surveillance Sans Frontieres: Internet-based emerging infectious disease intelligence and the )] TJ ET BT 26.250 119.439 Td /F1 9.8 Tf [(HealthMap project." PLoS medicine 5.7 \(2008\): e151.)] TJ ET BT 26.250 100.035 Td /F1 9.8 Tf [(5.)] TJ ET BT 38.132 100.035 Td /F1 9.8 Tf [(Hamilton, James Douglas. Time series analysis. Vol. 2. Princeton: Princeton university press, 1994.)] TJ ET BT 26.250 80.630 Td /F1 9.8 Tf [(6.)] TJ ET BT 38.132 80.630 Td /F1 9.8 Tf [(Casella, George, and Roger L. Berger. Statistical inference. Vol. 2. Pacific Grove, CA: Duxbury, 2002.)] TJ ET BT 26.250 61.225 Td /F1 9.8 Tf [(7.)] TJ ET BT 38.132 61.225 Td /F1 9.8 Tf [(Lloyd-Smith, James O. "Maximum likelihood estimation of the negative binomial dispersion parameter for highly )] TJ ET BT 26.250 49.320 Td /F1 9.8 Tf [(overdispersed data, with applications to infectious diseases." PloS one 2.2 \(2007\): e180.)] TJ ET Q q 15.000 39.439 577.500 737.561 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(central value, and rising. None of the estimates of )] TJ ET q 24.000 0 0 9.000 243.022 768.000 cm /I200 Do Q BT 267.022 767.476 Td /F1 9.8 Tf [( from the Sierra Leone data and combined data for all countries are )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(significantly different than the central value.)] TJ ET BT 26.250 736.167 Td /F1 9.8 Tf [(It is unclear why the transmission rate of the disease apparently rose for both Guinea and Liberia between mid July to mid )] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(August, and why the transmission rate in Sierra Leone is systematically lower, although is important to note that the WHO data )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(are obtained from rudimentary surveillance systems in under-developed countries, under the stress of a rapidly evolving )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(outbreak situation. The temporal patterns we observe may thus partly be due to variations in surveillance during the outbreak, )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(under-reporting, and/or reporting delays. In addition, serial passage of the disease as the outbreak progresses may be leading )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(to increased pathogenicity, and a subsequent increasingly larger rate of increase in case counts . However, it also must be )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(considered that otherwise well intentioned attempts at intervention may in fact be making the situation worse, at least in some )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(regions; in a joint meeting of officials from Guinea, Liberia, and Sierra Leone on Aug 1st , it was announced that )] TJ ET BT 509.665 652.833 Td /F5 9.8 Tf [(cordons )] TJ ET BT 26.250 640.929 Td /F5 9.8 Tf [(sanitaire)] TJ ET BT 63.095 640.929 Td /F1 9.8 Tf [( would be implemented, to seal off the villages and regions worst hit by the outbreak, in an attempt to limit its spread )] TJ ET BT 26.250 629.024 Td /F1 9.8 Tf [(outside those areas )] TJ ET 0.267 0.267 0.267 rg BT 114.049 630.531 Td /F4 8.7 Tf [(17)] TJ ET 0.271 0.267 0.267 rg BT 123.686 629.024 Td /F1 9.8 Tf [(. In addition, at that time Liberia closed all schools and non-essential government offices )] TJ ET 0.267 0.267 0.267 rg BT 506.286 630.531 Td /F4 8.7 Tf [(18)] TJ ET 0.271 0.267 0.267 rg BT 515.923 629.024 Td /F1 9.8 Tf [(, and two )] TJ ET BT 26.250 617.119 Td /F1 9.8 Tf [(weeks later imposed a military-enforced )] TJ ET BT 200.716 617.119 Td /F5 9.8 Tf [(cordon sanitaire)] TJ ET BT 270.078 617.119 Td /F1 9.8 Tf [( on the West Point slum of Monrovia, sparking riots )] TJ ET 0.267 0.267 0.267 rg BT 492.788 618.626 Td /F4 8.7 Tf [(19)] TJ ET 0.271 0.267 0.267 rg BT 502.425 617.119 Td /F1 9.8 Tf [(. It must be )] TJ ET BT 26.250 605.214 Td /F1 9.8 Tf [(stressed that )] TJ ET BT 84.779 605.214 Td /F5 9.8 Tf [(cordons sanitaire)] TJ ET BT 159.016 605.214 Td /F1 9.8 Tf [( do not generally attempt to limit disease spread within the quarantined areas, and the )] TJ ET BT 26.250 593.310 Td /F1 9.8 Tf [(implementation of these measures in West Africa has received criticism due to the fact that the quarantined areas are at risk for )] TJ ET BT 26.250 581.405 Td /F1 9.8 Tf [(crowding, lack of medical and basic services, and poor sanitation, potentially increasing the spread of disease within those )] TJ ET BT 26.250 569.500 Td /F1 9.8 Tf [(areas )] TJ ET 0.267 0.267 0.267 rg BT 53.345 571.007 Td /F4 8.7 Tf [(20)] TJ ET 0.271 0.267 0.267 rg BT 62.983 569.500 Td /F1 9.8 Tf [(. It was around the period of time that the )] TJ ET BT 242.919 569.500 Td /F5 9.8 Tf [(cordons sanitaire)] TJ ET BT 317.155 569.500 Td /F1 9.8 Tf [( were first imposed, and when the outbreak moved to the )] TJ ET BT 26.250 557.595 Td /F1 9.8 Tf [(densely populated cities of Conakry and Monrovia, that the exponential rise in new cases in Guinea and Liberia increased, )] TJ ET BT 26.250 545.691 Td /F1 9.8 Tf [(rather than went down. Again, it is unclear why the rate of exponential rise in Sierra Leone was apparently unaffected by these )] TJ ET BT 26.250 533.786 Td /F1 9.8 Tf [(events.)] TJ ET BT 26.250 514.381 Td /F1 9.8 Tf [(Based on our estimates of the exponential rise in cases between July 1st to the beginning of September, if this rise is to )] TJ ET BT 26.250 502.476 Td /F1 9.8 Tf [(continue unabated, there will be approximately 4400 new EVD cases in West Africa during the last half of the month of )] TJ ET BT 26.250 490.572 Td /F1 9.8 Tf [(September \(95% CI [3000, 6800]\), 500, 900, and 3000 of which will be in Sierra Leone, Guinea, and Liberia, respectively.)] TJ ET BT 26.250 453.969 Td /F4 12.0 Tf [(Summary)] TJ ET BT 26.250 434.015 Td /F1 9.8 Tf [(We have presented an analysis where piecewise exponential fits are employed to estimate the local rate of exponential rise in )] TJ ET BT 26.250 422.110 Td /F1 9.8 Tf [(cases in the 2014 West Africa Ebola outbreak. We have shown that these local rates of exponential rise can be used in )] TJ ET BT 26.250 410.205 Td /F1 9.8 Tf [(conjunction with a mathematical model to estimate the temporal changes in the effective reproduction number \(in the case of )] TJ ET BT 26.250 398.301 Td /F1 9.8 Tf [(this analysis, we employed an SEIR model\). Our analysis indicates that the spread of the disease to densely populated cities, )] TJ ET BT 26.250 386.396 Td /F1 9.8 Tf [(and/or the imposition of )] TJ ET BT 130.302 386.396 Td /F5 9.8 Tf [(cordons sanitaire )] TJ ET BT 207.249 386.396 Td /F1 9.8 Tf [( in West Africa may have accelerated the spread of the disease in some regions. Our )] TJ ET BT 26.250 374.491 Td /F1 9.8 Tf [(methodology is novel, and is applicable to any outbreak, and any mathematical disease model.)] TJ ET BT 26.250 337.889 Td /F4 12.0 Tf [(Competing Interests)] TJ ET BT 26.250 317.934 Td /F1 9.8 Tf [(The authors have declared that no competing interests exist.)] TJ ET BT 26.250 281.332 Td /F4 12.0 Tf [(Acknowledgements)] TJ ET BT 26.250 261.378 Td /F1 9.8 Tf [(The authors wish to acknowledge useful discussions with Gerardo Chowell regarding these studies.)] TJ ET BT 26.250 232.275 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 204.821 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 204.821 Td /F1 9.8 Tf [(Sanchez, Anthony. Ebola Viruses. John Wiley & Sons, Ltd, 2001.)] TJ ET BT 26.250 185.416 Td /F1 9.8 Tf [(2.)] TJ ET BT 38.132 185.416 Td /F1 9.8 Tf [(WHO. Ebola Virus Disease in Guinea, Mar 23 2014.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 176.930 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 158.380 Td /F1 9.8 Tf [(3.)] TJ ET BT 38.132 158.380 Td /F1 9.8 Tf [(World Health Organization. Global Alert and Response situation reports: Ebola response roadmap.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 149.894 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 131.344 Td /F1 9.8 Tf [(4.)] TJ ET BT 38.132 131.344 Td /F1 9.8 Tf [(Brownstein, John S., et al. "Surveillance Sans Frontieres: Internet-based emerging infectious disease intelligence and the )] TJ ET BT 26.250 119.439 Td /F1 9.8 Tf [(HealthMap project." PLoS medicine 5.7 \(2008\): e151.)] TJ ET BT 26.250 100.035 Td /F1 9.8 Tf [(5.)] TJ ET BT 38.132 100.035 Td /F1 9.8 Tf [(Hamilton, James Douglas. Time series analysis. Vol. 2. Princeton: Princeton university press, 1994.)] TJ ET BT 26.250 80.630 Td /F1 9.8 Tf [(6.)] TJ ET BT 38.132 80.630 Td /F1 9.8 Tf [(Casella, George, and Roger L. Berger. Statistical inference. Vol. 2. Pacific Grove, CA: Duxbury, 2002.)] TJ ET BT 26.250 61.225 Td /F1 9.8 Tf [(7.)] TJ ET BT 38.132 61.225 Td /F1 9.8 Tf [(Lloyd-Smith, James O. "Maximum likelihood estimation of the negative binomial dispersion parameter for highly )] TJ ET BT 26.250 49.320 Td /F1 9.8 Tf [(overdispersed data, with applications to infectious diseases." PloS one 2.2 \(2007\): e180.)] TJ ET Q q 15.000 39.439 577.500 737.561 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(central value, and rising. None of the estimates of )] TJ ET q 24.000 0 0 9.000 243.022 768.000 cm /I202 Do Q BT 267.022 767.476 Td /F1 9.8 Tf [( from the Sierra Leone data and combined data for all countries are )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(significantly different than the central value.)] TJ ET BT 26.250 736.167 Td /F1 9.8 Tf [(It is unclear why the transmission rate of the disease apparently rose for both Guinea and Liberia between mid July to mid )] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(August, and why the transmission rate in Sierra Leone is systematically lower, although is important to note that the WHO data )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(are obtained from rudimentary surveillance systems in under-developed countries, under the stress of a rapidly evolving )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(outbreak situation. The temporal patterns we observe may thus partly be due to variations in surveillance during the outbreak, )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(under-reporting, and/or reporting delays. In addition, serial passage of the disease as the outbreak progresses may be leading )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(to increased pathogenicity, and a subsequent increasingly larger rate of increase in case counts . However, it also must be )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(considered that otherwise well intentioned attempts at intervention may in fact be making the situation worse, at least in some )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(regions; in a joint meeting of officials from Guinea, Liberia, and Sierra Leone on Aug 1st , it was announced that )] TJ ET BT 509.665 652.833 Td /F5 9.8 Tf [(cordons )] TJ ET BT 26.250 640.929 Td /F5 9.8 Tf [(sanitaire)] TJ ET BT 63.095 640.929 Td /F1 9.8 Tf [( would be implemented, to seal off the villages and regions worst hit by the outbreak, in an attempt to limit its spread )] TJ ET BT 26.250 629.024 Td /F1 9.8 Tf [(outside those areas )] TJ ET 0.267 0.267 0.267 rg BT 114.049 630.531 Td /F4 8.7 Tf [(17)] TJ ET 0.271 0.267 0.267 rg BT 123.686 629.024 Td /F1 9.8 Tf [(. In addition, at that time Liberia closed all schools and non-essential government offices )] TJ ET 0.267 0.267 0.267 rg BT 506.286 630.531 Td /F4 8.7 Tf [(18)] TJ ET 0.271 0.267 0.267 rg BT 515.923 629.024 Td /F1 9.8 Tf [(, and two )] TJ ET BT 26.250 617.119 Td /F1 9.8 Tf [(weeks later imposed a military-enforced )] TJ ET BT 200.716 617.119 Td /F5 9.8 Tf [(cordon sanitaire)] TJ ET BT 270.078 617.119 Td /F1 9.8 Tf [( on the West Point slum of Monrovia, sparking riots )] TJ ET 0.267 0.267 0.267 rg BT 492.788 618.626 Td /F4 8.7 Tf [(19)] TJ ET 0.271 0.267 0.267 rg BT 502.425 617.119 Td /F1 9.8 Tf [(. It must be )] TJ ET BT 26.250 605.214 Td /F1 9.8 Tf [(stressed that )] TJ ET BT 84.779 605.214 Td /F5 9.8 Tf [(cordons sanitaire)] TJ ET BT 159.016 605.214 Td /F1 9.8 Tf [( do not generally attempt to limit disease spread within the quarantined areas, and the )] TJ ET BT 26.250 593.310 Td /F1 9.8 Tf [(implementation of these measures in West Africa has received criticism due to the fact that the quarantined areas are at risk for )] TJ ET BT 26.250 581.405 Td /F1 9.8 Tf [(crowding, lack of medical and basic services, and poor sanitation, potentially increasing the spread of disease within those )] TJ ET BT 26.250 569.500 Td /F1 9.8 Tf [(areas )] TJ ET 0.267 0.267 0.267 rg BT 53.345 571.007 Td /F4 8.7 Tf [(20)] TJ ET 0.271 0.267 0.267 rg BT 62.983 569.500 Td /F1 9.8 Tf [(. It was around the period of time that the )] TJ ET BT 242.919 569.500 Td /F5 9.8 Tf [(cordons sanitaire)] TJ ET BT 317.155 569.500 Td /F1 9.8 Tf [( were first imposed, and when the outbreak moved to the )] TJ ET BT 26.250 557.595 Td /F1 9.8 Tf [(densely populated cities of Conakry and Monrovia, that the exponential rise in new cases in Guinea and Liberia increased, )] TJ ET BT 26.250 545.691 Td /F1 9.8 Tf [(rather than went down. Again, it is unclear why the rate of exponential rise in Sierra Leone was apparently unaffected by these )] TJ ET BT 26.250 533.786 Td /F1 9.8 Tf [(events.)] TJ ET BT 26.250 514.381 Td /F1 9.8 Tf [(Based on our estimates of the exponential rise in cases between July 1st to the beginning of September, if this rise is to )] TJ ET BT 26.250 502.476 Td /F1 9.8 Tf [(continue unabated, there will be approximately 4400 new EVD cases in West Africa during the last half of the month of )] TJ ET BT 26.250 490.572 Td /F1 9.8 Tf [(September \(95% CI [3000, 6800]\), 500, 900, and 3000 of which will be in Sierra Leone, Guinea, and Liberia, respectively.)] TJ ET BT 26.250 453.969 Td /F4 12.0 Tf [(Summary)] TJ ET BT 26.250 434.015 Td /F1 9.8 Tf [(We have presented an analysis where piecewise exponential fits are employed to estimate the local rate of exponential rise in )] TJ ET BT 26.250 422.110 Td /F1 9.8 Tf [(cases in the 2014 West Africa Ebola outbreak. We have shown that these local rates of exponential rise can be used in )] TJ ET BT 26.250 410.205 Td /F1 9.8 Tf [(conjunction with a mathematical model to estimate the temporal changes in the effective reproduction number \(in the case of )] TJ ET BT 26.250 398.301 Td /F1 9.8 Tf [(this analysis, we employed an SEIR model\). Our analysis indicates that the spread of the disease to densely populated cities, )] TJ ET BT 26.250 386.396 Td /F1 9.8 Tf [(and/or the imposition of )] TJ ET BT 130.302 386.396 Td /F5 9.8 Tf [(cordons sanitaire )] TJ ET BT 207.249 386.396 Td /F1 9.8 Tf [( in West Africa may have accelerated the spread of the disease in some regions. Our )] TJ ET BT 26.250 374.491 Td /F1 9.8 Tf [(methodology is novel, and is applicable to any outbreak, and any mathematical disease model.)] TJ ET BT 26.250 337.889 Td /F4 12.0 Tf [(Competing Interests)] TJ ET BT 26.250 317.934 Td /F1 9.8 Tf [(The authors have declared that no competing interests exist.)] TJ ET BT 26.250 281.332 Td /F4 12.0 Tf [(Acknowledgements)] TJ ET BT 26.250 261.378 Td /F1 9.8 Tf [(The authors wish to acknowledge useful discussions with Gerardo Chowell regarding these studies.)] TJ ET BT 26.250 232.275 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 204.821 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 204.821 Td /F1 9.8 Tf [(Sanchez, Anthony. Ebola Viruses. John Wiley & Sons, Ltd, 2001.)] TJ ET BT 26.250 185.416 Td /F1 9.8 Tf [(2.)] TJ ET BT 38.132 185.416 Td /F1 9.8 Tf [(WHO. Ebola Virus Disease in Guinea, Mar 23 2014.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 176.930 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 158.380 Td /F1 9.8 Tf [(3.)] TJ ET BT 38.132 158.380 Td /F1 9.8 Tf [(World Health Organization. Global Alert and Response situation reports: Ebola response roadmap.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 149.894 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 131.344 Td /F1 9.8 Tf [(4.)] TJ ET BT 38.132 131.344 Td /F1 9.8 Tf [(Brownstein, John S., et al. "Surveillance Sans Frontieres: Internet-based emerging infectious disease intelligence and the )] TJ ET BT 26.250 119.439 Td /F1 9.8 Tf [(HealthMap project." PLoS medicine 5.7 \(2008\): e151.)] TJ ET BT 26.250 100.035 Td /F1 9.8 Tf [(5.)] TJ ET BT 38.132 100.035 Td /F1 9.8 Tf [(Hamilton, James Douglas. Time series analysis. Vol. 2. Princeton: Princeton university press, 1994.)] TJ ET BT 26.250 80.630 Td /F1 9.8 Tf [(6.)] TJ ET BT 38.132 80.630 Td /F1 9.8 Tf [(Casella, George, and Roger L. Berger. Statistical inference. Vol. 2. Pacific Grove, CA: Duxbury, 2002.)] TJ ET BT 26.250 61.225 Td /F1 9.8 Tf [(7.)] TJ ET BT 38.132 61.225 Td /F1 9.8 Tf [(Lloyd-Smith, James O. "Maximum likelihood estimation of the negative binomial dispersion parameter for highly )] TJ ET BT 26.250 49.320 Td /F1 9.8 Tf [(overdispersed data, with applications to infectious diseases." 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"The influence of climatic conditions on the transmission dynamics of the 2009 A/H1N1 influenza )] TJ ET BT 26.250 748.071 Td /F1 9.8 Tf [(pandemic in Chile." BMC infectious diseases 12.1 \(2012\): 298.)] TJ ET BT 26.250 728.667 Td /F1 9.8 Tf [(9.)] TJ ET BT 38.132 728.667 Td /F1 9.8 Tf [(Fenichel, Eli P., et al. "Adaptive human behavior in epidemiological models." Proceedings of the National Academy of )] TJ ET BT 26.250 716.762 Td /F1 9.8 Tf [(Sciences 108.15 \(2011\): 6306-6311.)] TJ ET BT 26.250 697.357 Td /F1 9.8 Tf [(10.)] TJ ET BT 43.553 697.357 Td /F1 9.8 Tf [(de Jong, Mart CM, Odo Diekmann, and Hans Heesterbeek. "How does transmission of infection depend on population )] TJ ET BT 26.250 685.452 Td /F1 9.8 Tf [(size." Epidemic models: their structure and relation to data 5.2 \(1995\): 84-94.)] TJ ET BT 26.250 666.048 Td /F1 9.8 Tf [(11.)] TJ ET BT 43.553 666.048 Td /F1 9.8 Tf [(Wallinga, Jacco, and Marc Lipsitch. "How generation intervals shape the relationship between growth rates and )] TJ ET BT 26.250 654.143 Td /F1 9.8 Tf [(reproductive numbers." Proceedings of the Royal Society B: Biological Sciences 274.1609 \(2007\): 599-604.)] TJ ET BT 26.250 634.738 Td /F1 9.8 Tf [(12.)] TJ ET BT 43.553 634.738 Td /F1 9.8 Tf [(Yan, Ping, and Zhilan Feng. "Variability order of the latent and the infectious periods in a deterministic SEIR epidemic model )] TJ ET BT 26.250 622.833 Td /F1 9.8 Tf [(and evaluation of control effectiveness." Mathematical biosciences 224.1 \(2010\): 43-52.)] TJ ET BT 26.250 603.429 Td /F1 9.8 Tf [(13.)] TJ ET BT 43.553 603.429 Td /F1 9.8 Tf [(Legrand, J., et al. "Understanding the dynamics of Ebola epidemics." Epidemiology and infection 135.04 \(2007\): 610-621.)] TJ ET BT 26.250 584.024 Td /F1 9.8 Tf [(14.)] TJ ET BT 43.553 584.024 Td /F1 9.8 Tf [(Chowell, Gerardo, et al. "The basic reproductive number of Ebola and the effects of public health measures: the cases of )] TJ ET BT 26.250 572.119 Td /F1 9.8 Tf [(Congo and Uganda." Journal of Theoretical Biology 229.1 \(2004\): 119-126.)] TJ ET BT 26.250 552.714 Td /F1 9.8 Tf [(15.)] TJ ET BT 43.553 552.714 Td /F1 9.8 Tf [(Christian Althaus. "Estimating the reproduction number of Ebola virus \(EBOV\) during the 2014 outbreak in West Africa." )] TJ ET BT 26.250 540.810 Td /F1 9.8 Tf [(PLoS currents, 1, Sep 2, 2014.)] TJ ET BT 26.250 521.405 Td /F1 9.8 Tf [(16.)] TJ ET BT 43.553 521.405 Td /F1 9.8 Tf [(Fisman, David, Khoo, Edwin, and Tuite, Ashleigh. "Early epidemic dynamics of the West African 2014 Ebola outbreak: )] TJ ET BT 26.250 509.500 Td /F1 9.8 Tf [(Estimates derived with a simple two-parameter model." PLoS currents, 1, Sep 8, 2014.)] TJ ET BT 26.250 490.095 Td /F1 9.8 Tf [(17.)] TJ ET BT 43.553 490.095 Td /F1 9.8 Tf [(Agence France-Presse." Ebola-hit African states seal off outbreak epicentre." Aug 1 2014.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 481.609 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 463.059 Td /F1 9.8 Tf [(18.)] TJ ET BT 43.553 463.059 Td /F1 9.8 Tf [(Agence France-Presse. "Liberia shuts schools in battle against Ebola: president", Jul 30 2014.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 454.573 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 436.023 Td /F1 9.8 Tf [(19.)] TJ ET BT 43.553 436.023 Td /F1 9.8 Tf [(The Guardian. "Ebola quarantine in Liberias capital sparks violence in slum", Aug 21 2014.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 427.537 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 408.987 Td /F1 9.8 Tf [(20.)] TJ ET BT 43.553 408.987 Td /F1 9.8 Tf [(Washington Post. "Quarantining an entire liberian slum to fight Ebola is a recipe for disaster", Aug 28 2014.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 400.501 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 381.951 Td /F1 9.8 Tf [(21.)] TJ ET BT 43.553 381.951 Td /F1 9.8 Tf [(Agence France-Presse. "Sierra Leone to visit every home to track down Ebola dead", Sep 8 2014.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 373.465 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 354.915 Td /F1 9.8 Tf [(22.)] TJ ET BT 43.553 354.915 Td /F1 9.8 Tf [(Gomes MFC, Pastore y Piontti A, Rossi L, Chao D, Longini I, Halloran ME, Vespignani A. Assessing the International )] TJ ET BT 26.250 343.011 Td /F1 9.8 Tf [(Spreading Risk Associated with the 2014 West African Ebola Outbreak. PLOS Currents Outbreaks. 2014 Sep 2. Edition 1. )] TJ ET BT 26.250 331.106 Td /F1 9.8 Tf [(doi:10.1371/currents.outbreaks.cd818f63d40e24aef769dda7df9e0da5.)] TJ ET BT 26.250 311.701 Td /F1 9.8 Tf [(23.)] TJ ET BT 43.553 311.701 Td /F1 9.8 Tf [(United States Centers for Disease Control and Prevention "Ebola Outbreaks 2000-2014", Sep 10, 2014)] TJ ET 0.267 0.267 0.267 rg BT 26.250 303.215 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 284.665 Td /F1 9.8 Tf [(24.)] TJ ET BT 43.553 284.665 Td /F1 9.8 Tf [(Weyer, Jacqueline, Lucille H. Blumberg, and Janusz T. Paweska. "Ebola virus disease in West Africa-an unprecedented )] TJ ET BT 26.250 272.760 Td /F1 9.8 Tf [(outbreak: editorial." South African Medical Journal 104.8 \(2014\): 555-556.)] TJ ET BT 26.250 253.356 Td /F1 9.8 Tf [(25.)] TJ ET BT 43.553 253.356 Td /F1 9.8 Tf [(World Health Organization "Media centre: Ebola virus disease fact sheet". 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BMC infectious diseases 12.1 \(2012\): 298.)] TJ ET BT 26.250 728.667 Td /F1 9.8 Tf [(9.)] TJ ET BT 38.132 728.667 Td /F1 9.8 Tf [(Fenichel, Eli P., et al. "Adaptive human behavior in epidemiological models." Proceedings of the National Academy of )] TJ ET BT 26.250 716.762 Td /F1 9.8 Tf [(Sciences 108.15 \(2011\): 6306-6311.)] TJ ET BT 26.250 697.357 Td /F1 9.8 Tf [(10.)] TJ ET BT 43.553 697.357 Td /F1 9.8 Tf [(de Jong, Mart CM, Odo Diekmann, and Hans Heesterbeek. "How does transmission of infection depend on population )] TJ ET BT 26.250 685.452 Td /F1 9.8 Tf [(size." Epidemic models: their structure and relation to data 5.2 \(1995\): 84-94.)] TJ ET BT 26.250 666.048 Td /F1 9.8 Tf [(11.)] TJ ET BT 43.553 666.048 Td /F1 9.8 Tf [(Wallinga, Jacco, and Marc Lipsitch. "How generation intervals shape the relationship between growth rates and )] TJ ET BT 26.250 654.143 Td /F1 9.8 Tf [(reproductive numbers." Proceedings of the Royal Society B: Biological Sciences 274.1609 \(2007\): 599-604.)] TJ ET BT 26.250 634.738 Td /F1 9.8 Tf [(12.)] TJ ET BT 43.553 634.738 Td /F1 9.8 Tf [(Yan, Ping, and Zhilan Feng. "Variability order of the latent and the infectious periods in a deterministic SEIR epidemic model )] TJ ET BT 26.250 622.833 Td /F1 9.8 Tf [(and evaluation of control effectiveness." Mathematical biosciences 224.1 \(2010\): 43-52.)] TJ ET BT 26.250 603.429 Td /F1 9.8 Tf [(13.)] TJ ET BT 43.553 603.429 Td /F1 9.8 Tf [(Legrand, J., et al. "Understanding the dynamics of Ebola epidemics." Epidemiology and infection 135.04 \(2007\): 610-621.)] TJ ET BT 26.250 584.024 Td /F1 9.8 Tf [(14.)] TJ ET BT 43.553 584.024 Td /F1 9.8 Tf [(Chowell, Gerardo, et al. "The basic reproductive number of Ebola and the effects of public health measures: the cases of )] TJ ET BT 26.250 572.119 Td /F1 9.8 Tf [(Congo and Uganda." Journal of Theoretical Biology 229.1 \(2004\): 119-126.)] TJ ET BT 26.250 552.714 Td /F1 9.8 Tf [(15.)] TJ ET BT 43.553 552.714 Td /F1 9.8 Tf [(Christian Althaus. "Estimating the reproduction number of Ebola virus \(EBOV\) during the 2014 outbreak in West Africa." )] TJ ET BT 26.250 540.810 Td /F1 9.8 Tf [(PLoS currents, 1, Sep 2, 2014.)] TJ ET BT 26.250 521.405 Td /F1 9.8 Tf [(16.)] TJ ET BT 43.553 521.405 Td /F1 9.8 Tf [(Fisman, David, Khoo, Edwin, and Tuite, Ashleigh. "Early epidemic dynamics of the West African 2014 Ebola outbreak: )] TJ ET BT 26.250 509.500 Td /F1 9.8 Tf [(Estimates derived with a simple two-parameter model." PLoS currents, 1, Sep 8, 2014.)] TJ ET BT 26.250 490.095 Td /F1 9.8 Tf [(17.)] TJ ET BT 43.553 490.095 Td /F1 9.8 Tf [(Agence France-Presse." Ebola-hit African states seal off outbreak epicentre." Aug 1 2014.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 481.609 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 463.059 Td /F1 9.8 Tf [(18.)] TJ ET BT 43.553 463.059 Td /F1 9.8 Tf [(Agence France-Presse. "Liberia shuts schools in battle against Ebola: president", Jul 30 2014.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 454.573 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 436.023 Td /F1 9.8 Tf [(19.)] TJ ET BT 43.553 436.023 Td /F1 9.8 Tf [(The Guardian. "Ebola quarantine in Liberias capital sparks violence in slum", Aug 21 2014.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 427.537 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 408.987 Td /F1 9.8 Tf [(20.)] TJ ET BT 43.553 408.987 Td /F1 9.8 Tf [(Washington Post. 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Edition 1. )] TJ ET BT 26.250 331.106 Td /F1 9.8 Tf [(doi:10.1371/currents.outbreaks.cd818f63d40e24aef769dda7df9e0da5.)] TJ ET BT 26.250 311.701 Td /F1 9.8 Tf [(23.)] TJ ET BT 43.553 311.701 Td /F1 9.8 Tf [(United States Centers for Disease Control and Prevention "Ebola Outbreaks 2000-2014", Sep 10, 2014)] TJ ET 0.267 0.267 0.267 rg BT 26.250 303.215 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 284.665 Td /F1 9.8 Tf [(24.)] TJ ET BT 43.553 284.665 Td /F1 9.8 Tf [(Weyer, Jacqueline, Lucille H. Blumberg, and Janusz T. Paweska. "Ebola virus disease in West Africa-an unprecedented )] TJ ET BT 26.250 272.760 Td /F1 9.8 Tf [(outbreak: editorial." South African Medical Journal 104.8 \(2014\): 555-556.)] TJ ET BT 26.250 253.356 Td /F1 9.8 Tf [(25.)] TJ ET BT 43.553 253.356 Td /F1 9.8 Tf [(World Health Organization "Media centre: Ebola virus disease fact sheet". 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Journal of Theoretical Biology 229.1 \(2004\): 119-126.)] TJ ET BT 26.250 552.714 Td /F1 9.8 Tf [(15.)] TJ ET BT 43.553 552.714 Td /F1 9.8 Tf [(Christian Althaus. "Estimating the reproduction number of Ebola virus \(EBOV\) during the 2014 outbreak in West Africa." )] TJ ET BT 26.250 540.810 Td /F1 9.8 Tf [(PLoS currents, 1, Sep 2, 2014.)] TJ ET BT 26.250 521.405 Td /F1 9.8 Tf [(16.)] TJ ET BT 43.553 521.405 Td /F1 9.8 Tf [(Fisman, David, Khoo, Edwin, and Tuite, Ashleigh. "Early epidemic dynamics of the West African 2014 Ebola outbreak: )] TJ ET BT 26.250 509.500 Td /F1 9.8 Tf [(Estimates derived with a simple two-parameter model." PLoS currents, 1, Sep 8, 2014.)] TJ ET BT 26.250 490.095 Td /F1 9.8 Tf [(17.)] TJ ET BT 43.553 490.095 Td /F1 9.8 Tf [(Agence France-Presse." Ebola-hit African states seal off outbreak epicentre." 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