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Assessing Measles Transmission )] TJ ET BT 570.807 639.438 Td /F1 9.8 Tf [(in )] TJ ET BT 26.250 627.533 Td /F1 9.8 Tf [(the United States Following a Large Outbreak in California. PLOS Currents Outbreaks. 2015 May 7 . Edition 1. doi: )] TJ ET BT 26.250 615.628 Td /F1 9.8 Tf [(10.1371/currents.outbreaks.b497624d7043b1aecfbfd3dfda3e344a.)] TJ ET q 15.000 29.878 577.500 583.370 re W n 0.271 0.267 0.267 rg BT 26.250 586.526 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 566.571 Td /F1 9.8 Tf [(The recent increase in measles cases in California may raise questions regarding the continuing success of measles control. To )] TJ ET BT 26.250 554.667 Td /F1 9.8 Tf [(determine whether the dynamics of measles is qualitatively different in comparison to previous years, we assess whether the )] TJ ET BT 26.250 542.762 Td /F1 9.8 Tf [(2014-2015 measles outbreak associated with an Anaheim theme park is consistent with subcriticality by calculating maximum-)] TJ ET BT 26.250 530.857 Td /F1 9.8 Tf [(likelihood estimates for the effective reproduction number given this years outbreak, using the Galton-Watson branching )] TJ ET BT 26.250 518.952 Td /F1 9.8 Tf [(process model. We find that the dynamics after the initial transmission event are consistent with prior transmission, but does not )] TJ ET BT 26.250 507.048 Td /F1 9.8 Tf [(exclude the possibility that the effective reproduction number has increased.)] TJ ET BT 26.250 470.445 Td /F4 12.0 Tf [(Funding Statement)] TJ ET BT 26.250 450.491 Td /F1 9.8 Tf [(This study was supported by a Models of Infectious Disease Agent Study \(MIDAS\) grant from the US NIH/NIGMS to the )] TJ ET BT 26.250 438.586 Td /F1 9.8 Tf [(University of California, San Francisco \(U01GM087728\). SB was also funded by the RAPIDD program of the Science and )] TJ ET BT 26.250 426.681 Td /F1 9.8 Tf [(Technology Directorate, Department of Homeland Security \(Research and Policy for Infectious Disease Dynamics\). The )] TJ ET BT 26.250 414.777 Td /F1 9.8 Tf [(sponsor played no role in the analysis or decision to publish.)] TJ ET BT 26.250 385.674 Td /F4 12.0 Tf [(Introduction)] TJ ET BT 26.250 365.720 Td /F1 9.8 Tf [(A recent outbreak of measles linked with one or more Disney theme parks has reinvigorated discussion of measles vaccination.)] TJ ET 0.267 0.267 0.267 rg BT 575.175 367.227 Td /F4 8.7 Tf [(1)] TJ ET 0.271 0.267 0.267 rg BT 26.250 357.703 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 28.659 355.322 Td /F4 8.7 Tf [(2)] TJ ET 0.271 0.267 0.267 rg BT 33.478 357.703 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 35.887 355.322 Td /F4 8.7 Tf [(18)] TJ ET 0.271 0.267 0.267 rg BT 45.525 353.815 Td /F1 9.8 Tf [( By April 10, 2015, 131 confirmed measles cases were reported in the outbreak in California, with 40 cases in California )] TJ ET BT 26.250 341.910 Td /F1 9.8 Tf [(having traveled to the parks in December.)] TJ ET 0.267 0.267 0.267 rg BT 206.703 343.418 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 211.522 345.799 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 213.931 343.418 Td /F4 8.7 Tf [(16)] TJ ET 0.271 0.267 0.267 rg BT 223.568 341.910 Td /F1 9.8 Tf [( An additional 16 cases linked to this outbreak have been reported elsewhere in )] TJ ET BT 26.250 330.006 Td /F1 9.8 Tf [(the US, in six other states)] TJ ET 0.267 0.267 0.267 rg BT 137.341 331.513 Td /F4 8.7 Tf [(12)] TJ ET 0.271 0.267 0.267 rg BT 146.979 330.006 Td /F1 9.8 Tf [( by April 10, 2015, for a total of 147.)] TJ ET 0.267 0.267 0.267 rg BT 301.448 331.513 Td /F4 8.7 Tf [(18)] TJ ET 0.271 0.267 0.267 rg BT 311.085 330.006 Td /F1 9.8 Tf [( In Quebec, a total of 158 cases of the same genotype \(B3\) )] TJ ET BT 26.250 318.101 Td /F1 9.8 Tf [(were reported in a non-immunizing religious community)] TJ ET 0.267 0.267 0.267 rg BT 265.193 319.608 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 274.831 318.101 Td /F1 9.8 Tf [( by March 28, and the importation to Canada is linked to travel to )] TJ ET BT 26.250 306.196 Td /F1 9.8 Tf [(Disneyland. Cases from this outbreak also were observed in Mexico.)] TJ ET 0.267 0.267 0.267 rg BT 322.104 307.703 Td /F4 8.7 Tf [(12)] TJ ET 0.271 0.267 0.267 rg BT 331.741 306.196 Td /F1 9.8 Tf [( This outbreak, larger than those typically seen in recent )] TJ ET BT 26.250 294.291 Td /F1 9.8 Tf [(years in North America, may raise questions regarding the continuing success of measles control.)] TJ ET BT 26.250 274.887 Td /F1 9.8 Tf [(Between 2001 and 2011, the average number of individuals who became infected by one infectious case \(the effective )] TJ ET BT 26.250 262.982 Td /F1 9.8 Tf [(reproduction number, )] TJ ET BT 121.624 262.982 Td /F5 9.8 Tf [(R)] TJ ET BT 128.664 260.918 Td /F5 8.7 Tf [(eff)] TJ ET BT 138.301 262.982 Td /F1 9.8 Tf [(\) in the United States was estimated to be 0.52 individuals \(95% CI: 0.44, 0.60\).)] TJ ET 0.267 0.267 0.267 rg BT 481.345 264.489 Td /F4 8.7 Tf [(4)] TJ ET 0.271 0.267 0.267 rg BT 486.164 262.982 Td /F1 9.8 Tf [( If )] TJ ET BT 497.006 262.982 Td /F5 9.8 Tf [(R)] TJ ET BT 504.046 260.918 Td /F5 8.7 Tf [(eff)] TJ ET BT 513.683 262.982 Td /F1 9.8 Tf [( is less than )] TJ ET BT 26.250 251.077 Td /F1 9.8 Tf [(one, transmission is subcritical; each infectious case, on average, directly infects fewer than one person; all outbreaks die out )] TJ ET BT 26.250 239.172 Td /F1 9.8 Tf [(under subcritical conditions.)] TJ ET 0.267 0.267 0.267 rg BT 146.546 240.680 Td /F4 8.7 Tf [(19)] TJ ET 0.271 0.267 0.267 rg BT 156.183 239.172 Td /F1 9.8 Tf [( Thus, our prior findings implied that measles could not sustain itself in the United States. Here, )] TJ ET BT 26.250 227.268 Td /F1 9.8 Tf [(we use the 131 confirmed cases from the California outbreak to assess whether )] TJ ET BT 373.067 227.268 Td /F5 9.8 Tf [(R)] TJ ET BT 380.107 225.203 Td /F5 8.7 Tf [(eff)] TJ ET BT 389.744 227.268 Td /F1 9.8 Tf [( has increased significantly.)] TJ ET BT 26.250 190.665 Td /F4 12.0 Tf [(Methods)] TJ ET BT 26.250 170.711 Td /F1 9.8 Tf [(We used the Galton-Watson branching process model with our previously inferred dispersion parameter for measles, )] TJ ET BT 26.250 158.806 Td /F1 9.8 Tf [(supplemented by sensitivity analysis. The number of new cases caused by each case is modeled by the negative binomial )] TJ ET BT 26.250 146.901 Td /F1 9.8 Tf [(distribution, with parameters )] TJ ET BT 150.875 146.901 Td /F5 9.8 Tf [(R)] TJ ET BT 157.914 144.837 Td /F1 8.7 Tf [(eff)] TJ ET BT 167.551 146.901 Td /F1 9.8 Tf [( and a dispersion parameter )] TJ ET BT 291.649 146.901 Td /F5 9.8 Tf [(k.)] TJ ET 0.267 0.267 0.267 rg BT 299.235 148.409 Td /F4 8.7 Tf [(6)] TJ ET 0.271 0.267 0.267 rg BT 304.054 150.790 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 306.463 148.409 Td /F4 8.7 Tf [(17)] TJ ET 0.271 0.267 0.267 rg BT 316.100 146.901 Td /F1 9.8 Tf [( The dispersion parameter permits explicit modeling of )] TJ ET BT 26.250 134.997 Td /F1 9.8 Tf [(heterogeneity of disease transmission as occurs when superspreading is present. Estimates of these two parameters for the )] TJ ET BT 26.250 123.092 Td /F1 9.8 Tf [(US, as well as the rate of introduction of measles into the US, were used to assess the current outbreak.)] TJ ET BT 26.250 103.687 Td /F1 9.8 Tf [(While heterogeneity and superspreading are key features of measles which must be taken into account, analysis of )] TJ ET BT 26.250 91.782 Td /F1 9.8 Tf [(transmission at the very beginning of the epidemicin the theme parkis subject to severe selection bias)] TJ ET 0.267 0.267 0.267 rg BT 483.067 93.290 Td /F4 8.7 Tf [(5)] TJ ET 0.271 0.267 0.267 rg BT 487.885 91.782 Td /F1 9.8 Tf [(; analysis of an )] TJ ET BT 26.250 79.878 Td /F1 9.8 Tf [(outbreak chosen specifically because of its size can hardly yield other than an upwardly biased assessment of transmission. )] TJ ET BT 26.250 67.973 Td /F1 9.8 Tf [(Moreover, the relatively quiet years from 2001 and 2011 \(where cluster data are available\) may not be sufficient to fully )] TJ ET BT 26.250 56.068 Td /F1 9.8 Tf [(characterize the tail of the transmission distribution. Instead of modeling the initial transmission in the theme park, we instead )] TJ ET BT 26.250 44.163 Td /F1 9.8 Tf [(follow the subsequent transmission from cases exposed in Disneyland. These subsequent cases may be considered a kind of )] 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 [(Assessing Measles Transmission in the United States Following )] TJ ET BT 15.000 693.094 Td /F2 21.0 Tf [(a Large Outbreak in California)] TJ ET Q 0.271 0.267 0.267 rg BT 15.000 675.088 Td /F3 9.8 Tf [(May 7, 2015)] TJ ET BT 68.888 675.088 Td /F3 9.8 Tf [()] TJ ET 0.267 0.267 0.267 rg BT 73.763 675.088 Td /F3 9.8 Tf [(Research Article)] TJ ET BT 26.250 663.247 Td /F1 9.8 Tf [(Seth Blumberg)] TJ ET 0.271 0.267 0.267 rg BT 90.737 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 96.158 663.247 Td /F1 9.8 Tf [(Lee Worden)] TJ ET 0.271 0.267 0.267 rg BT 149.266 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 154.687 663.247 Td /F1 9.8 Tf [(Wayne Enanoria)] TJ ET 0.271 0.267 0.267 rg BT 226.759 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 232.180 663.247 Td /F1 9.8 Tf [(Sarah Ackley)] TJ ET 0.271 0.267 0.267 rg BT 289.617 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 295.038 663.247 Td /F1 9.8 Tf [(Michael Deiner)] TJ ET 0.271 0.267 0.267 rg BT 360.051 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 365.472 663.247 Td /F1 9.8 Tf [(Fengchen Liu)] TJ ET 0.271 0.267 0.267 rg BT 424.547 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 429.968 663.247 Td /F1 9.8 Tf [(Daozhou Gao)] TJ ET 0.271 0.267 0.267 rg BT 490.126 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 495.547 663.247 Td /F1 9.8 Tf [(Thomas Lietman)] TJ ET 0.271 0.267 0.267 rg BT 568.155 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 26.250 651.342 Td /F1 9.8 Tf [(Travis Porco)] TJ ET 0.271 0.267 0.267 rg BT 26.250 639.438 Td /F1 9.8 Tf [(Blumberg S, Worden L, Enanoria W, Ackley S, Deiner M, Liu F, Gao D, Lietman T, Porco T. Assessing Measles Transmission )] TJ ET BT 570.807 639.438 Td /F1 9.8 Tf [(in )] TJ ET BT 26.250 627.533 Td /F1 9.8 Tf [(the United States Following a Large Outbreak in California. PLOS Currents Outbreaks. 2015 May 7 . Edition 1. doi: )] TJ ET BT 26.250 615.628 Td /F1 9.8 Tf [(10.1371/currents.outbreaks.b497624d7043b1aecfbfd3dfda3e344a.)] TJ ET q 15.000 29.878 577.500 583.370 re W n 0.271 0.267 0.267 rg BT 26.250 586.526 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 566.571 Td /F1 9.8 Tf [(The recent increase in measles cases in California may raise questions regarding the continuing success of measles control. To )] TJ ET BT 26.250 554.667 Td /F1 9.8 Tf [(determine whether the dynamics of measles is qualitatively different in comparison to previous years, we assess whether the )] TJ ET BT 26.250 542.762 Td /F1 9.8 Tf [(2014-2015 measles outbreak associated with an Anaheim theme park is consistent with subcriticality by calculating maximum-)] TJ ET BT 26.250 530.857 Td /F1 9.8 Tf [(likelihood estimates for the effective reproduction number given this years outbreak, using the Galton-Watson branching )] TJ ET BT 26.250 518.952 Td /F1 9.8 Tf [(process model. We find that the dynamics after the initial transmission event are consistent with prior transmission, but does not )] TJ ET BT 26.250 507.048 Td /F1 9.8 Tf [(exclude the possibility that the effective reproduction number has increased.)] TJ ET BT 26.250 470.445 Td /F4 12.0 Tf [(Funding Statement)] TJ ET BT 26.250 450.491 Td /F1 9.8 Tf [(This study was supported by a Models of Infectious Disease Agent Study \(MIDAS\) grant from the US NIH/NIGMS to the )] TJ ET BT 26.250 438.586 Td /F1 9.8 Tf [(University of California, San Francisco \(U01GM087728\). SB was also funded by the RAPIDD program of the Science and )] TJ ET BT 26.250 426.681 Td /F1 9.8 Tf [(Technology Directorate, Department of Homeland Security \(Research and Policy for Infectious Disease Dynamics\). The )] TJ ET BT 26.250 414.777 Td /F1 9.8 Tf [(sponsor played no role in the analysis or decision to publish.)] TJ ET BT 26.250 385.674 Td /F4 12.0 Tf [(Introduction)] TJ ET BT 26.250 365.720 Td /F1 9.8 Tf [(A recent outbreak of measles linked with one or more Disney theme parks has reinvigorated discussion of measles vaccination.)] TJ ET 0.267 0.267 0.267 rg BT 575.175 367.227 Td /F4 8.7 Tf [(1)] TJ ET 0.271 0.267 0.267 rg BT 26.250 357.703 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 28.659 355.322 Td /F4 8.7 Tf [(2)] TJ ET 0.271 0.267 0.267 rg BT 33.478 357.703 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 35.887 355.322 Td /F4 8.7 Tf [(18)] TJ ET 0.271 0.267 0.267 rg BT 45.525 353.815 Td /F1 9.8 Tf [( By April 10, 2015, 131 confirmed measles cases were reported in the outbreak in California, with 40 cases in California )] TJ ET BT 26.250 341.910 Td /F1 9.8 Tf [(having traveled to the parks in December.)] TJ ET 0.267 0.267 0.267 rg BT 206.703 343.418 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 211.522 345.799 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 213.931 343.418 Td /F4 8.7 Tf [(16)] TJ ET 0.271 0.267 0.267 rg BT 223.568 341.910 Td /F1 9.8 Tf [( An additional 16 cases linked to this outbreak have been reported elsewhere in )] TJ ET BT 26.250 330.006 Td /F1 9.8 Tf [(the US, in six other states)] TJ ET 0.267 0.267 0.267 rg BT 137.341 331.513 Td /F4 8.7 Tf [(12)] TJ ET 0.271 0.267 0.267 rg BT 146.979 330.006 Td /F1 9.8 Tf [( by April 10, 2015, for a total of 147.)] TJ ET 0.267 0.267 0.267 rg BT 301.448 331.513 Td /F4 8.7 Tf [(18)] TJ ET 0.271 0.267 0.267 rg BT 311.085 330.006 Td /F1 9.8 Tf [( In Quebec, a total of 158 cases of the same genotype \(B3\) )] TJ ET BT 26.250 318.101 Td /F1 9.8 Tf [(were reported in a non-immunizing religious community)] TJ ET 0.267 0.267 0.267 rg BT 265.193 319.608 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 274.831 318.101 Td /F1 9.8 Tf [( by March 28, and the importation to Canada is linked to travel to )] TJ ET BT 26.250 306.196 Td /F1 9.8 Tf [(Disneyland. Cases from this outbreak also were observed in Mexico.)] TJ ET 0.267 0.267 0.267 rg BT 322.104 307.703 Td /F4 8.7 Tf [(12)] TJ ET 0.271 0.267 0.267 rg BT 331.741 306.196 Td /F1 9.8 Tf [( This outbreak, larger than those typically seen in recent )] TJ ET BT 26.250 294.291 Td /F1 9.8 Tf [(years in North America, may raise questions regarding the continuing success of measles control.)] TJ ET BT 26.250 274.887 Td /F1 9.8 Tf [(Between 2001 and 2011, the average number of individuals who became infected by one infectious case \(the effective )] TJ ET BT 26.250 262.982 Td /F1 9.8 Tf [(reproduction number, )] TJ ET BT 121.624 262.982 Td /F5 9.8 Tf [(R)] TJ ET BT 128.664 260.918 Td /F5 8.7 Tf [(eff)] TJ ET BT 138.301 262.982 Td /F1 9.8 Tf [(\) in the United States was estimated to be 0.52 individuals \(95% CI: 0.44, 0.60\).)] TJ ET 0.267 0.267 0.267 rg BT 481.345 264.489 Td /F4 8.7 Tf [(4)] TJ ET 0.271 0.267 0.267 rg BT 486.164 262.982 Td /F1 9.8 Tf [( If )] TJ ET BT 497.006 262.982 Td /F5 9.8 Tf [(R)] TJ ET BT 504.046 260.918 Td /F5 8.7 Tf [(eff)] TJ ET BT 513.683 262.982 Td /F1 9.8 Tf [( is less than )] TJ ET BT 26.250 251.077 Td /F1 9.8 Tf [(one, transmission is subcritical; each infectious case, on average, directly infects fewer than one person; all outbreaks die out )] TJ ET BT 26.250 239.172 Td /F1 9.8 Tf [(under subcritical conditions.)] TJ ET 0.267 0.267 0.267 rg BT 146.546 240.680 Td /F4 8.7 Tf [(19)] TJ ET 0.271 0.267 0.267 rg BT 156.183 239.172 Td /F1 9.8 Tf [( Thus, our prior findings implied that measles could not sustain itself in the United States. Here, )] TJ ET BT 26.250 227.268 Td /F1 9.8 Tf [(we use the 131 confirmed cases from the California outbreak to assess whether )] TJ ET BT 373.067 227.268 Td /F5 9.8 Tf [(R)] TJ ET BT 380.107 225.203 Td /F5 8.7 Tf [(eff)] TJ ET BT 389.744 227.268 Td /F1 9.8 Tf [( has increased significantly.)] TJ ET BT 26.250 190.665 Td /F4 12.0 Tf [(Methods)] TJ ET BT 26.250 170.711 Td /F1 9.8 Tf [(We used the Galton-Watson branching process model with our previously inferred dispersion parameter for measles, )] TJ ET BT 26.250 158.806 Td /F1 9.8 Tf [(supplemented by sensitivity analysis. The number of new cases caused by each case is modeled by the negative binomial )] TJ ET BT 26.250 146.901 Td /F1 9.8 Tf [(distribution, with parameters )] TJ ET BT 150.875 146.901 Td /F5 9.8 Tf [(R)] TJ ET BT 157.914 144.837 Td /F1 8.7 Tf [(eff)] TJ ET BT 167.551 146.901 Td /F1 9.8 Tf [( and a dispersion parameter )] TJ ET BT 291.649 146.901 Td /F5 9.8 Tf [(k.)] TJ ET 0.267 0.267 0.267 rg BT 299.235 148.409 Td /F4 8.7 Tf [(6)] TJ ET 0.271 0.267 0.267 rg BT 304.054 150.790 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 306.463 148.409 Td /F4 8.7 Tf [(17)] TJ ET 0.271 0.267 0.267 rg BT 316.100 146.901 Td /F1 9.8 Tf [( The dispersion parameter permits explicit modeling of )] TJ ET BT 26.250 134.997 Td /F1 9.8 Tf [(heterogeneity of disease transmission as occurs when superspreading is present. Estimates of these two parameters for the )] TJ ET BT 26.250 123.092 Td /F1 9.8 Tf [(US, as well as the rate of introduction of measles into the US, were used to assess the current outbreak.)] TJ ET BT 26.250 103.687 Td /F1 9.8 Tf [(While heterogeneity and superspreading are key features of measles which must be taken into account, analysis of )] TJ ET BT 26.250 91.782 Td /F1 9.8 Tf [(transmission at the very beginning of the epidemicin the theme parkis subject to severe selection bias)] TJ ET 0.267 0.267 0.267 rg BT 483.067 93.290 Td /F4 8.7 Tf [(5)] TJ ET 0.271 0.267 0.267 rg BT 487.885 91.782 Td /F1 9.8 Tf [(; analysis of an )] TJ ET BT 26.250 79.878 Td /F1 9.8 Tf [(outbreak chosen specifically because of its size can hardly yield other than an upwardly biased assessment of transmission. )] TJ ET BT 26.250 67.973 Td /F1 9.8 Tf [(Moreover, the relatively quiet years from 2001 and 2011 \(where cluster data are available\) may not be sufficient to fully )] TJ ET BT 26.250 56.068 Td /F1 9.8 Tf [(characterize the tail of the transmission distribution. Instead of modeling the initial transmission in the theme park, we instead )] TJ ET BT 26.250 44.163 Td /F1 9.8 Tf [(follow the subsequent transmission from cases exposed in Disneyland. These subsequent cases may be considered a kind of )] 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 [(Assessing Measles Transmission in the United States Following )] TJ ET BT 15.000 693.094 Td /F2 21.0 Tf [(a Large Outbreak in California)] TJ ET Q 0.271 0.267 0.267 rg BT 15.000 675.088 Td /F3 9.8 Tf [(May 7, 2015)] TJ ET BT 68.888 675.088 Td /F3 9.8 Tf [()] TJ ET 0.267 0.267 0.267 rg BT 73.763 675.088 Td /F3 9.8 Tf [(Research Article)] TJ ET BT 26.250 663.247 Td /F1 9.8 Tf [(Seth Blumberg)] TJ ET 0.271 0.267 0.267 rg BT 90.737 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 96.158 663.247 Td /F1 9.8 Tf [(Lee Worden)] TJ ET 0.271 0.267 0.267 rg BT 149.266 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 154.687 663.247 Td /F1 9.8 Tf [(Wayne Enanoria)] TJ ET 0.271 0.267 0.267 rg BT 226.759 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 232.180 663.247 Td /F1 9.8 Tf [(Sarah Ackley)] TJ ET 0.271 0.267 0.267 rg BT 289.617 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 295.038 663.247 Td /F1 9.8 Tf [(Michael Deiner)] TJ ET 0.271 0.267 0.267 rg BT 360.051 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 365.472 663.247 Td /F1 9.8 Tf [(Fengchen Liu)] TJ ET 0.271 0.267 0.267 rg BT 424.547 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 429.968 663.247 Td /F1 9.8 Tf [(Daozhou Gao)] TJ ET 0.271 0.267 0.267 rg BT 490.126 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 495.547 663.247 Td /F1 9.8 Tf [(Thomas Lietman)] TJ ET 0.271 0.267 0.267 rg BT 568.155 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 26.250 651.342 Td /F1 9.8 Tf [(Travis Porco)] TJ ET 0.271 0.267 0.267 rg BT 26.250 639.438 Td /F1 9.8 Tf [(Blumberg S, Worden L, Enanoria W, Ackley S, Deiner M, Liu F, Gao D, Lietman T, Porco T. Assessing Measles Transmission )] TJ ET BT 570.807 639.438 Td /F1 9.8 Tf [(in )] TJ ET BT 26.250 627.533 Td /F1 9.8 Tf [(the United States Following a Large Outbreak in California. PLOS Currents Outbreaks. 2015 May 7 . Edition 1. doi: )] TJ ET BT 26.250 615.628 Td /F1 9.8 Tf [(10.1371/currents.outbreaks.b497624d7043b1aecfbfd3dfda3e344a.)] TJ ET q 15.000 29.878 577.500 583.370 re W n 0.271 0.267 0.267 rg BT 26.250 586.526 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 566.571 Td /F1 9.8 Tf [(The recent increase in measles cases in California may raise questions regarding the continuing success of measles control. To )] TJ ET BT 26.250 554.667 Td /F1 9.8 Tf [(determine whether the dynamics of measles is qualitatively different in comparison to previous years, we assess whether the )] TJ ET BT 26.250 542.762 Td /F1 9.8 Tf [(2014-2015 measles outbreak associated with an Anaheim theme park is consistent with subcriticality by calculating maximum-)] TJ ET BT 26.250 530.857 Td /F1 9.8 Tf [(likelihood estimates for the effective reproduction number given this years outbreak, using the Galton-Watson branching )] TJ ET BT 26.250 518.952 Td /F1 9.8 Tf [(process model. We find that the dynamics after the initial transmission event are consistent with prior transmission, but does not )] TJ ET BT 26.250 507.048 Td /F1 9.8 Tf [(exclude the possibility that the effective reproduction number has increased.)] TJ ET BT 26.250 470.445 Td /F4 12.0 Tf [(Funding Statement)] TJ ET BT 26.250 450.491 Td /F1 9.8 Tf [(This study was supported by a Models of Infectious Disease Agent Study \(MIDAS\) grant from the US NIH/NIGMS to the )] TJ ET BT 26.250 438.586 Td /F1 9.8 Tf [(University of California, San Francisco \(U01GM087728\). SB was also funded by the RAPIDD program of the Science and )] TJ ET BT 26.250 426.681 Td /F1 9.8 Tf [(Technology Directorate, Department of Homeland Security \(Research and Policy for Infectious Disease Dynamics\). The )] TJ ET BT 26.250 414.777 Td /F1 9.8 Tf [(sponsor played no role in the analysis or decision to publish.)] TJ ET BT 26.250 385.674 Td /F4 12.0 Tf [(Introduction)] TJ ET BT 26.250 365.720 Td /F1 9.8 Tf [(A recent outbreak of measles linked with one or more Disney theme parks has reinvigorated discussion of measles vaccination.)] TJ ET 0.267 0.267 0.267 rg BT 575.175 367.227 Td /F4 8.7 Tf [(1)] TJ ET 0.271 0.267 0.267 rg BT 26.250 357.703 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 28.659 355.322 Td /F4 8.7 Tf [(2)] TJ ET 0.271 0.267 0.267 rg BT 33.478 357.703 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 35.887 355.322 Td /F4 8.7 Tf [(18)] TJ ET 0.271 0.267 0.267 rg BT 45.525 353.815 Td /F1 9.8 Tf [( By April 10, 2015, 131 confirmed measles cases were reported in the outbreak in California, with 40 cases in California )] TJ ET BT 26.250 341.910 Td /F1 9.8 Tf [(having traveled to the parks in December.)] TJ ET 0.267 0.267 0.267 rg BT 206.703 343.418 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 211.522 345.799 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 213.931 343.418 Td /F4 8.7 Tf [(16)] TJ ET 0.271 0.267 0.267 rg BT 223.568 341.910 Td /F1 9.8 Tf [( An additional 16 cases linked to this outbreak have been reported elsewhere in )] TJ ET BT 26.250 330.006 Td /F1 9.8 Tf [(the US, in six other states)] TJ ET 0.267 0.267 0.267 rg BT 137.341 331.513 Td /F4 8.7 Tf [(12)] TJ ET 0.271 0.267 0.267 rg BT 146.979 330.006 Td /F1 9.8 Tf [( by April 10, 2015, for a total of 147.)] TJ ET 0.267 0.267 0.267 rg BT 301.448 331.513 Td /F4 8.7 Tf [(18)] TJ ET 0.271 0.267 0.267 rg BT 311.085 330.006 Td /F1 9.8 Tf [( In Quebec, a total of 158 cases of the same genotype \(B3\) )] TJ ET BT 26.250 318.101 Td /F1 9.8 Tf [(were reported in a non-immunizing religious community)] TJ ET 0.267 0.267 0.267 rg BT 265.193 319.608 Td /F4 8.7 Tf [(13)] TJ ET 0.271 0.267 0.267 rg BT 274.831 318.101 Td /F1 9.8 Tf [( by March 28, and the importation to Canada is linked to travel to )] TJ ET BT 26.250 306.196 Td /F1 9.8 Tf [(Disneyland. Cases from this outbreak also were observed in Mexico.)] TJ ET 0.267 0.267 0.267 rg BT 322.104 307.703 Td /F4 8.7 Tf [(12)] TJ ET 0.271 0.267 0.267 rg BT 331.741 306.196 Td /F1 9.8 Tf [( This outbreak, larger than those typically seen in recent )] TJ ET BT 26.250 294.291 Td /F1 9.8 Tf [(years in North America, may raise questions regarding the continuing success of measles control.)] TJ ET BT 26.250 274.887 Td /F1 9.8 Tf [(Between 2001 and 2011, the average number of individuals who became infected by one infectious case \(the effective )] TJ ET BT 26.250 262.982 Td /F1 9.8 Tf [(reproduction number, )] TJ ET BT 121.624 262.982 Td /F5 9.8 Tf [(R)] TJ ET BT 128.664 260.918 Td /F5 8.7 Tf [(eff)] TJ ET BT 138.301 262.982 Td /F1 9.8 Tf [(\) in the United States was estimated to be 0.52 individuals \(95% CI: 0.44, 0.60\).)] TJ ET 0.267 0.267 0.267 rg BT 481.345 264.489 Td /F4 8.7 Tf [(4)] TJ ET 0.271 0.267 0.267 rg BT 486.164 262.982 Td /F1 9.8 Tf [( If )] TJ ET BT 497.006 262.982 Td /F5 9.8 Tf [(R)] TJ ET BT 504.046 260.918 Td /F5 8.7 Tf [(eff)] TJ ET BT 513.683 262.982 Td /F1 9.8 Tf [( is less than )] TJ ET BT 26.250 251.077 Td /F1 9.8 Tf [(one, transmission is subcritical; each infectious case, on average, directly infects fewer than one person; all outbreaks die out )] TJ ET BT 26.250 239.172 Td /F1 9.8 Tf [(under subcritical conditions.)] TJ ET 0.267 0.267 0.267 rg BT 146.546 240.680 Td /F4 8.7 Tf [(19)] TJ ET 0.271 0.267 0.267 rg BT 156.183 239.172 Td /F1 9.8 Tf [( Thus, our prior findings implied that measles could not sustain itself in the United States. Here, )] TJ ET BT 26.250 227.268 Td /F1 9.8 Tf [(we use the 131 confirmed cases from the California outbreak to assess whether )] TJ ET BT 373.067 227.268 Td /F5 9.8 Tf [(R)] TJ ET BT 380.107 225.203 Td /F5 8.7 Tf [(eff)] TJ ET BT 389.744 227.268 Td /F1 9.8 Tf [( has increased significantly.)] TJ ET BT 26.250 190.665 Td /F4 12.0 Tf [(Methods)] TJ ET BT 26.250 170.711 Td /F1 9.8 Tf [(We used the Galton-Watson branching process model with our previously inferred dispersion parameter for measles, )] TJ ET BT 26.250 158.806 Td /F1 9.8 Tf [(supplemented by sensitivity analysis. The number of new cases caused by each case is modeled by the negative binomial )] TJ ET BT 26.250 146.901 Td /F1 9.8 Tf [(distribution, with parameters )] TJ ET BT 150.875 146.901 Td /F5 9.8 Tf [(R)] TJ ET BT 157.914 144.837 Td /F1 8.7 Tf [(eff)] TJ ET BT 167.551 146.901 Td /F1 9.8 Tf [( and a dispersion parameter )] TJ ET BT 291.649 146.901 Td /F5 9.8 Tf [(k.)] TJ ET 0.267 0.267 0.267 rg BT 299.235 148.409 Td /F4 8.7 Tf [(6)] TJ ET 0.271 0.267 0.267 rg BT 304.054 150.790 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 306.463 148.409 Td /F4 8.7 Tf [(17)] TJ ET 0.271 0.267 0.267 rg BT 316.100 146.901 Td /F1 9.8 Tf [( The dispersion parameter permits explicit modeling of )] TJ ET BT 26.250 134.997 Td /F1 9.8 Tf [(heterogeneity of disease transmission as occurs when superspreading is present. Estimates of these two parameters for the )] TJ ET BT 26.250 123.092 Td /F1 9.8 Tf [(US, as well as the rate of introduction of measles into the US, were used to assess the current outbreak.)] TJ ET BT 26.250 103.687 Td /F1 9.8 Tf [(While heterogeneity and superspreading are key features of measles which must be taken into account, analysis of )] TJ ET BT 26.250 91.782 Td /F1 9.8 Tf [(transmission at the very beginning of the epidemicin the theme parkis subject to severe selection bias)] TJ ET 0.267 0.267 0.267 rg BT 483.067 93.290 Td /F4 8.7 Tf [(5)] TJ ET 0.271 0.267 0.267 rg BT 487.885 91.782 Td /F1 9.8 Tf [(; analysis of an )] TJ ET BT 26.250 79.878 Td /F1 9.8 Tf [(outbreak chosen specifically because of its size can hardly yield other than an upwardly biased assessment of transmission. )] TJ ET BT 26.250 67.973 Td /F1 9.8 Tf [(Moreover, the relatively quiet years from 2001 and 2011 \(where cluster data are available\) may not be sufficient to fully )] TJ ET BT 26.250 56.068 Td /F1 9.8 Tf [(characterize the tail of the transmission distribution. Instead of modeling the initial transmission in the theme park, we instead )] TJ ET BT 26.250 44.163 Td /F1 9.8 Tf [(follow the subsequent transmission from cases exposed in Disneyland. These subsequent cases may be considered a kind of )] TJ ET Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(1)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Outbreaks)] TJ ET Q endstream endobj 8 0 obj << /Type /Font /Subtype /Type1 /Name /F1 /BaseFont /Helvetica /Encoding /WinAnsiEncoding >> endobj 9 0 obj << /Type /Font /Subtype /Type1 /Name /F2 /BaseFont /Times-Bold /Encoding /WinAnsiEncoding >> endobj 10 0 obj << /Type /Font /Subtype /Type1 /Name /F3 /BaseFont /Times-Italic /Encoding /WinAnsiEncoding >> endobj 11 0 obj << /Type /Font /Subtype /Type1 /Name /F4 /BaseFont /Helvetica-Bold /Encoding /WinAnsiEncoding >> endobj 12 0 obj << /Type /Font /Subtype /Type1 /Name /F5 /BaseFont /Helvetica-Oblique /Encoding /WinAnsiEncoding >> endobj 13 0 obj << /Type /XObject /Subtype /Image /Width 500 /Height 52 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 500 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 144>> stream x1 0 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Assuming the negative binomial distribution )] TJ ET 0.267 0.267 0.267 rg BT 417.508 713.864 Td /F4 8.7 Tf [(6)] TJ ET 0.271 0.267 0.267 rg BT 422.326 716.245 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 424.736 713.864 Td /F4 8.7 Tf [(17)] TJ ET 0.271 0.267 0.267 rg BT 434.373 712.357 Td /F1 9.8 Tf [( for the number of new cases )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(caused by each case in one generation, the probability of )] TJ ET BT 275.558 700.452 Td /F5 9.8 Tf [(i)] TJ ET BT 277.722 700.452 Td /F1 9.8 Tf [( cases causing )] TJ ET BT 344.919 700.452 Td /F5 9.8 Tf [(j)] TJ ET BT 347.083 700.452 Td /F1 9.8 Tf [( cases in the subsequent generation is )] TJ ET 0.267 0.267 0.267 rg BT 516.178 701.960 Td /F4 8.7 Tf [(7)] TJ ET q 241.500 0 0 46.500 26.250 644.072 cm /I4 Do Q 0.271 0.267 0.267 rg BT 26.250 627.048 Td /F1 9.8 Tf [(These )] TJ ET BT 56.056 627.048 Td /F5 9.8 Tf [(j)] TJ ET BT 58.220 627.048 Td /F1 9.8 Tf [( cases go on to cause, in general, further cases. If eventually transmission terminates, with no new cases arising in )] TJ ET BT 26.250 615.143 Td /F1 9.8 Tf [(subsequent generations, we can compute the total number of cases so far, i.e., the total cluster size. The probability of )] TJ ET BT 538.924 615.143 Td /F5 9.8 Tf [(i)] TJ ET BT 541.089 615.143 Td /F1 9.8 Tf [( cases )] TJ ET BT 26.250 603.238 Td /F1 9.8 Tf [(causing a cluster of size )] TJ ET BT 133.003 603.238 Td /F5 9.8 Tf [(j)] TJ ET BT 135.167 603.238 Td /F1 9.8 Tf [( is given by )] TJ ET 0.267 0.267 0.267 rg BT 186.647 604.745 Td /F4 8.7 Tf [(7)] TJ ET q 201.000 0 0 24.750 26.250 568.607 cm /I6 Do Q 0.271 0.267 0.267 rg BT 26.250 551.583 Td /F1 9.8 Tf [(The probability )] TJ ET BT 92.901 551.583 Td /F5 9.8 Tf [(p)] TJ ET BT 98.322 549.519 Td /F5 8.7 Tf [(i)] TJ ET BT 100.246 551.583 Td /F1 9.8 Tf [(of observing a chain of size )] TJ ET BT 221.097 551.583 Td /F5 9.8 Tf [(M)] TJ ET BT 229.219 551.583 Td /F1 9.8 Tf [( \(or greater\) after )] TJ ET BT 305.620 551.583 Td /F5 9.8 Tf [(N)] TJ ET BT 312.659 549.519 Td /F5 8.7 Tf [(i)] TJ ET BT 314.584 551.583 Td /F1 9.8 Tf [( introductions is one minus the probability that all clusters are )] TJ ET BT 26.250 539.679 Td /F1 9.8 Tf [(smaller than )] TJ ET BT 82.059 539.679 Td /F5 9.8 Tf [(M)] TJ ET BT 90.181 539.679 Td /F1 9.8 Tf [(:)] TJ ET q 141.000 0 0 48.000 26.250 481.798 cm /I8 Do Q BT 26.250 464.774 Td /F1 9.8 Tf [(Given )] TJ ET BT 54.427 464.774 Td /F5 9.8 Tf [(N)] TJ ET BT 61.467 462.710 Td /F5 8.7 Tf [(i)] TJ ET BT 63.391 464.774 Td /F1 9.8 Tf [(introductions per year, we can compute the expected number of years between events of size at least )] TJ ET BT 503.984 464.774 Td /F5 9.8 Tf [(M)] TJ ET BT 512.106 464.774 Td /F1 9.8 Tf [( as )] TJ ET BT 527.822 464.774 Td /F5 9.8 Tf [(1/p)] TJ ET BT 541.375 462.710 Td /F5 8.7 Tf [(i)] TJ ET BT 543.299 464.774 Td /F5 9.8 Tf [(.)] TJ ET BT 26.250 445.369 Td /F1 9.8 Tf [(We use values of the dispersion parameter )] TJ ET BT 214.288 445.369 Td /F5 9.8 Tf [(k)] TJ ET BT 219.163 445.369 Td /F1 9.8 Tf [( derived from US national data in this estimation; although the estimate of )] TJ ET BT 538.359 445.369 Td /F5 9.8 Tf [(R)] TJ ET BT 545.398 443.305 Td /F5 8.7 Tf [(eff)] TJ ET BT 26.250 433.464 Td /F1 9.8 Tf [(does not depend on )] TJ ET BT 115.150 433.464 Td /F5 9.8 Tf [(k)] TJ ET BT 120.025 433.464 Td /F1 9.8 Tf [(, the confidence interval does. Our central estimate of the dispersion parameter was 0.27, with 95% )] TJ ET BT 26.250 421.560 Td /F1 9.8 Tf [(confidence interval of 0.18 to 0.41.)] TJ ET 0.267 0.267 0.267 rg BT 175.298 423.067 Td /F4 8.7 Tf [(4)] TJ ET 0.271 0.267 0.267 rg BT 180.117 421.560 Td /F1 9.8 Tf [( Note that there is no evidence distinguishing Californias MMR vaccination rate \(90.7 5.3\) )] TJ ET BT 26.250 409.655 Td /F1 9.8 Tf [(from the national vaccination rate \(91.9 0.9\), so that US national estimates11 \(with sensitivity analysis\) provide a plausible )] TJ ET BT 26.250 397.750 Td /F1 9.8 Tf [(choice of )] TJ ET BT 67.980 397.750 Td /F5 9.8 Tf [(k)] TJ ET BT 72.855 397.750 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 378.345 Td /F1 9.8 Tf [(To estimate an overall maximum likelihood effective reproduction number from an initial number of cases and a total cluster )] TJ ET BT 26.250 366.441 Td /F1 9.8 Tf [(size, we use this assumed value of )] TJ ET BT 179.608 366.441 Td /F5 9.8 Tf [(k)] TJ ET BT 184.483 366.441 Td /F1 9.8 Tf [( and maximize the right hand side of the second equation above. To jointly estimate the )] TJ ET BT 26.250 354.536 Td /F1 9.8 Tf [(maximum likelihood estimate of an effective reproduction number in the first generation and then in the subsequent rounds of )] TJ ET BT 26.250 342.631 Td /F1 9.8 Tf [(transmission, we compute the probability that an initial number of cases gives rise to the next generation size \(using the first )] TJ ET BT 26.250 330.726 Td /F1 9.8 Tf [(equation\), and that this number of cases in the next generation give rise to the remaining number of cases using the second )] TJ ET BT 26.250 318.822 Td /F1 9.8 Tf [(equation. We assume independent transmissions, and add the log likelihoods for the first generation and the subsequent )] TJ ET BT 26.250 306.917 Td /F1 9.8 Tf [(generations. Confidence intervals for these are computed using the likelihood ratio method.)] TJ ET 0.267 0.267 0.267 rg BT 419.146 308.424 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 428.783 306.917 Td /F1 9.8 Tf [( All computations were conducted )] TJ ET BT 26.250 295.012 Td /F1 9.8 Tf [(using the statistics package R 3.1 for Ubuntu Linux \(R Foundation for Statistical Computing, Vienna, Austria\).)] TJ ET BT 26.250 258.410 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 238.455 Td /F1 9.8 Tf [(The outbreak began with individuals exposed in Disneyland between December 17 and 20, 2014; 40 Californians were believed )] TJ ET BT 26.250 226.551 Td /F1 9.8 Tf [(exposed during that period.)] TJ ET 0.267 0.267 0.267 rg BT 144.400 228.058 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 149.219 226.551 Td /F1 9.8 Tf [( Subsequently, 91 additional cases \(of the outbreak strain\) are known to have occurred in the state. )] TJ ET BT 26.250 214.646 Td /F1 9.8 Tf [(The epidemiology of the initial exposure has not been completely characterized, and even the number of index cases in )] TJ ET BT 26.250 202.741 Td /F1 9.8 Tf [(December has not been reported. The initial exposure, occurring in a crowded theme park, may be considered a possible )] TJ ET BT 26.250 190.836 Td /F1 9.8 Tf [(superspreading event.)] TJ ET BT 26.250 171.432 Td /F1 9.8 Tf [(When 40 first-generation measles cases produce 91 additional linked secondary cases \(for a total chain size of 131 including a )] TJ ET BT 26.250 159.527 Td /F1 9.8 Tf [(putative single index case\), )] TJ ET BT 146.555 159.527 Td /F5 9.8 Tf [(R)] TJ ET BT 153.595 159.527 Td /F1 9.8 Tf [( is estimated to be 0.69 \(95% CI: 0.48, 1.04; likelihood ratio CI assuming)] TJ ET 0.267 0.267 0.267 rg BT 465.741 161.034 Td /F4 8.7 Tf [(7)] TJ ET 0.271 0.267 0.267 rg BT 470.560 159.527 Td /F5 9.8 Tf [( k)] TJ ET BT 478.145 159.527 Td /F1 9.8 Tf [( = 0.27\). If we use the )] TJ ET BT 26.250 147.622 Td /F1 9.8 Tf [(95% upper confidence bound for the estimated aggregation parameter )] TJ ET BT 332.459 147.622 Td /F5 9.8 Tf [(k)] TJ ET BT 337.334 147.622 Td /F1 9.8 Tf [(, 0.41, then we obtain a confidence interval for R of )] TJ ET BT 26.250 135.717 Td /F1 9.8 Tf [(0.50 to 0.98; using the 95% lower bound of )] TJ ET BT 214.327 135.717 Td /F5 9.8 Tf [(k)] TJ ET BT 219.202 135.717 Td /F1 9.8 Tf [(=0.18, we obtain a confidence interval of 0.45 to 1.12. Smaller values of )] TJ ET BT 531.105 135.717 Td /F5 9.8 Tf [(k)] TJ ET BT 535.980 135.717 Td /F1 9.8 Tf [( yield )] TJ ET BT 26.250 123.813 Td /F1 9.8 Tf [(wider confidence limits still; )] TJ ET BT 146.526 123.813 Td /F5 9.8 Tf [(k)] TJ ET BT 151.401 123.813 Td /F1 9.8 Tf [(=0.05 provides a confidence interval of 0.34 to 1.71.)] TJ ET BT 26.250 104.408 Td /F1 9.8 Tf [(We conducted an additional sensitivity analysis in which we no longer assumed that the effective reproduction number was )] TJ ET BT 26.250 92.503 Td /F1 9.8 Tf [(constant. Assuming that the approximately 48 cases reported in the two weeks immediately following the last of the 40 Disney-)] TJ ET BT 26.250 80.598 Td /F1 9.8 Tf [(exposed cases to be the next generation of transmission outside Disneyland, we find maximum likelihood estimates of the )] TJ ET BT 26.250 68.694 Td /F1 9.8 Tf [(effective reproduction number to be 1.20 \(=48/40\) \(95% CI: 0.65, 2.45, assuming )] TJ ET BT 377.162 68.694 Td /F5 9.8 Tf [(k)] TJ ET BT 382.037 68.694 Td /F1 9.8 Tf [(=0.27\) in the first generation and 0.47 \(95% )] TJ ET BT 26.250 56.789 Td /F1 9.8 Tf [(CI: 0.29, 0.79, assuming )] TJ ET BT 134.641 56.789 Td /F5 9.8 Tf [(k)] TJ ET BT 139.516 56.789 Td /F1 9.8 Tf [(=0.27\) for the remaining transmission events. This difference is not statistically significant \()] TJ ET BT 529.389 56.789 Td /F5 9.8 Tf [(P)] TJ ET BT 535.892 56.789 Td /F1 9.8 Tf [(=0.09, )] TJ ET BT 26.250 44.884 Td /F1 9.8 Tf [(likelihood ratio test\). Assuming a smaller )] TJ ET BT 203.427 44.884 Td /F5 9.8 Tf [(k)] TJ ET BT 208.302 44.884 Td /F1 9.8 Tf [( value of 0.18 widens the confidence intervals on these estimates, and increases the )] TJ ET BT 574.658 44.884 Td /F5 9.8 Tf [(P)] TJ ET Q q 15.000 30.598 577.500 746.402 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(natural experiment in seeding measles throughout the state, while recognizing that contacts of cases exposed at the theme park )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(may systematically differ from the California population. Because the number of California cases exposed in Disneyland is )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(known to be 40, we used California case counts to derive a current estimate of the effective reproduction number.)] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(Our analysis of the epidemic using the Galton-Watson process will assume a negative binomial distribution for the number of )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(secondary cases caused by each active case. Assuming the negative binomial distribution )] TJ ET 0.267 0.267 0.267 rg BT 417.508 713.864 Td /F4 8.7 Tf [(6)] TJ ET 0.271 0.267 0.267 rg BT 422.326 716.245 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 424.736 713.864 Td /F4 8.7 Tf [(17)] TJ ET 0.271 0.267 0.267 rg BT 434.373 712.357 Td /F1 9.8 Tf [( for the number of new cases )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(caused by each case in one generation, the probability of )] TJ ET BT 275.558 700.452 Td /F5 9.8 Tf [(i)] TJ ET BT 277.722 700.452 Td /F1 9.8 Tf [( cases causing )] TJ ET BT 344.919 700.452 Td /F5 9.8 Tf [(j)] TJ ET BT 347.083 700.452 Td /F1 9.8 Tf [( cases in the subsequent generation is )] TJ ET 0.267 0.267 0.267 rg BT 516.178 701.960 Td /F4 8.7 Tf [(7)] TJ ET q 241.500 0 0 46.500 26.250 644.072 cm /I10 Do Q 0.271 0.267 0.267 rg BT 26.250 627.048 Td /F1 9.8 Tf [(These )] TJ ET BT 56.056 627.048 Td /F5 9.8 Tf [(j)] TJ ET BT 58.220 627.048 Td /F1 9.8 Tf [( cases go on to cause, in general, further cases. If eventually transmission terminates, with no new cases arising in )] TJ ET BT 26.250 615.143 Td /F1 9.8 Tf [(subsequent generations, we can compute the total number of cases so far, i.e., the total cluster size. The probability of )] TJ ET BT 538.924 615.143 Td /F5 9.8 Tf [(i)] TJ ET BT 541.089 615.143 Td /F1 9.8 Tf [( cases )] TJ ET BT 26.250 603.238 Td /F1 9.8 Tf [(causing a cluster of size )] TJ ET BT 133.003 603.238 Td /F5 9.8 Tf [(j)] TJ ET BT 135.167 603.238 Td /F1 9.8 Tf [( is given by )] TJ ET 0.267 0.267 0.267 rg BT 186.647 604.745 Td /F4 8.7 Tf [(7)] TJ ET q 201.000 0 0 24.750 26.250 568.607 cm /I12 Do Q 0.271 0.267 0.267 rg BT 26.250 551.583 Td /F1 9.8 Tf [(The probability )] TJ ET BT 92.901 551.583 Td /F5 9.8 Tf [(p)] TJ ET BT 98.322 549.519 Td /F5 8.7 Tf [(i)] TJ ET BT 100.246 551.583 Td /F1 9.8 Tf [(of observing a chain of size )] TJ ET BT 221.097 551.583 Td /F5 9.8 Tf [(M)] TJ ET BT 229.219 551.583 Td /F1 9.8 Tf [( \(or greater\) after )] TJ ET BT 305.620 551.583 Td /F5 9.8 Tf [(N)] TJ ET BT 312.659 549.519 Td /F5 8.7 Tf [(i)] TJ ET BT 314.584 551.583 Td /F1 9.8 Tf [( introductions is one minus the probability that all clusters are )] TJ ET BT 26.250 539.679 Td /F1 9.8 Tf [(smaller than )] TJ ET BT 82.059 539.679 Td /F5 9.8 Tf [(M)] TJ ET BT 90.181 539.679 Td /F1 9.8 Tf [(:)] TJ ET q 141.000 0 0 48.000 26.250 481.798 cm /I14 Do Q BT 26.250 464.774 Td /F1 9.8 Tf [(Given )] TJ ET BT 54.427 464.774 Td /F5 9.8 Tf [(N)] TJ ET BT 61.467 462.710 Td /F5 8.7 Tf [(i)] TJ ET BT 63.391 464.774 Td /F1 9.8 Tf [(introductions per year, we can compute the expected number of years between events of size at least )] TJ ET BT 503.984 464.774 Td /F5 9.8 Tf [(M)] TJ ET BT 512.106 464.774 Td /F1 9.8 Tf [( as )] TJ ET BT 527.822 464.774 Td /F5 9.8 Tf [(1/p)] TJ ET BT 541.375 462.710 Td /F5 8.7 Tf [(i)] TJ ET BT 543.299 464.774 Td /F5 9.8 Tf [(.)] TJ ET BT 26.250 445.369 Td /F1 9.8 Tf [(We use values of the dispersion parameter )] TJ ET BT 214.288 445.369 Td /F5 9.8 Tf [(k)] TJ ET BT 219.163 445.369 Td /F1 9.8 Tf [( derived from US national data in this estimation; although the estimate of )] TJ ET BT 538.359 445.369 Td /F5 9.8 Tf [(R)] TJ ET BT 545.398 443.305 Td /F5 8.7 Tf [(eff)] TJ ET BT 26.250 433.464 Td /F1 9.8 Tf [(does not depend on )] TJ ET BT 115.150 433.464 Td /F5 9.8 Tf [(k)] TJ ET BT 120.025 433.464 Td /F1 9.8 Tf [(, the confidence interval does. Our central estimate of the dispersion parameter was 0.27, with 95% )] TJ ET BT 26.250 421.560 Td /F1 9.8 Tf [(confidence interval of 0.18 to 0.41.)] TJ ET 0.267 0.267 0.267 rg BT 175.298 423.067 Td /F4 8.7 Tf [(4)] TJ ET 0.271 0.267 0.267 rg BT 180.117 421.560 Td /F1 9.8 Tf [( Note that there is no evidence distinguishing Californias MMR vaccination rate \(90.7 5.3\) )] TJ ET BT 26.250 409.655 Td /F1 9.8 Tf [(from the national vaccination rate \(91.9 0.9\), so that US national estimates11 \(with sensitivity analysis\) provide a plausible )] TJ ET BT 26.250 397.750 Td /F1 9.8 Tf [(choice of )] TJ ET BT 67.980 397.750 Td /F5 9.8 Tf [(k)] TJ ET BT 72.855 397.750 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 378.345 Td /F1 9.8 Tf [(To estimate an overall maximum likelihood effective reproduction number from an initial number of cases and a total cluster )] TJ ET BT 26.250 366.441 Td /F1 9.8 Tf [(size, we use this assumed value of )] TJ ET BT 179.608 366.441 Td /F5 9.8 Tf [(k)] TJ ET BT 184.483 366.441 Td /F1 9.8 Tf [( and maximize the right hand side of the second equation above. To jointly estimate the )] TJ ET BT 26.250 354.536 Td /F1 9.8 Tf [(maximum likelihood estimate of an effective reproduction number in the first generation and then in the subsequent rounds of )] TJ ET BT 26.250 342.631 Td /F1 9.8 Tf [(transmission, we compute the probability that an initial number of cases gives rise to the next generation size \(using the first )] TJ ET BT 26.250 330.726 Td /F1 9.8 Tf [(equation\), and that this number of cases in the next generation give rise to the remaining number of cases using the second )] TJ ET BT 26.250 318.822 Td /F1 9.8 Tf [(equation. We assume independent transmissions, and add the log likelihoods for the first generation and the subsequent )] TJ ET BT 26.250 306.917 Td /F1 9.8 Tf [(generations. Confidence intervals for these are computed using the likelihood ratio method.)] TJ ET 0.267 0.267 0.267 rg BT 419.146 308.424 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 428.783 306.917 Td /F1 9.8 Tf [( All computations were conducted )] TJ ET BT 26.250 295.012 Td /F1 9.8 Tf [(using the statistics package R 3.1 for Ubuntu Linux \(R Foundation for Statistical Computing, Vienna, Austria\).)] TJ ET BT 26.250 258.410 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 238.455 Td /F1 9.8 Tf [(The outbreak began with individuals exposed in Disneyland between December 17 and 20, 2014; 40 Californians were believed )] TJ ET BT 26.250 226.551 Td /F1 9.8 Tf [(exposed during that period.)] TJ ET 0.267 0.267 0.267 rg BT 144.400 228.058 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 149.219 226.551 Td /F1 9.8 Tf [( Subsequently, 91 additional cases \(of the outbreak strain\) are known to have occurred in the state. )] TJ ET BT 26.250 214.646 Td /F1 9.8 Tf [(The epidemiology of the initial exposure has not been completely characterized, and even the number of index cases in )] TJ ET BT 26.250 202.741 Td /F1 9.8 Tf [(December has not been reported. The initial exposure, occurring in a crowded theme park, may be considered a possible )] TJ ET BT 26.250 190.836 Td /F1 9.8 Tf [(superspreading event.)] TJ ET BT 26.250 171.432 Td /F1 9.8 Tf [(When 40 first-generation measles cases produce 91 additional linked secondary cases \(for a total chain size of 131 including a )] TJ ET BT 26.250 159.527 Td /F1 9.8 Tf [(putative single index case\), )] TJ ET BT 146.555 159.527 Td /F5 9.8 Tf [(R)] TJ ET BT 153.595 159.527 Td /F1 9.8 Tf [( is estimated to be 0.69 \(95% CI: 0.48, 1.04; likelihood ratio CI assuming)] TJ ET 0.267 0.267 0.267 rg BT 465.741 161.034 Td /F4 8.7 Tf [(7)] TJ ET 0.271 0.267 0.267 rg BT 470.560 159.527 Td /F5 9.8 Tf [( k)] TJ ET BT 478.145 159.527 Td /F1 9.8 Tf [( = 0.27\). If we use the )] TJ ET BT 26.250 147.622 Td /F1 9.8 Tf [(95% upper confidence bound for the estimated aggregation parameter )] TJ ET BT 332.459 147.622 Td /F5 9.8 Tf [(k)] TJ ET BT 337.334 147.622 Td /F1 9.8 Tf [(, 0.41, then we obtain a confidence interval for R of )] TJ ET BT 26.250 135.717 Td /F1 9.8 Tf [(0.50 to 0.98; using the 95% lower bound of )] TJ ET BT 214.327 135.717 Td /F5 9.8 Tf [(k)] TJ ET BT 219.202 135.717 Td /F1 9.8 Tf [(=0.18, we obtain a confidence interval of 0.45 to 1.12. Smaller values of )] TJ ET BT 531.105 135.717 Td /F5 9.8 Tf [(k)] TJ ET BT 535.980 135.717 Td /F1 9.8 Tf [( yield )] TJ ET BT 26.250 123.813 Td /F1 9.8 Tf [(wider confidence limits still; )] TJ ET BT 146.526 123.813 Td /F5 9.8 Tf [(k)] TJ ET BT 151.401 123.813 Td /F1 9.8 Tf [(=0.05 provides a confidence interval of 0.34 to 1.71.)] TJ ET BT 26.250 104.408 Td /F1 9.8 Tf [(We conducted an additional sensitivity analysis in which we no longer assumed that the effective reproduction number was )] TJ ET BT 26.250 92.503 Td /F1 9.8 Tf [(constant. Assuming that the approximately 48 cases reported in the two weeks immediately following the last of the 40 Disney-)] TJ ET BT 26.250 80.598 Td /F1 9.8 Tf [(exposed cases to be the next generation of transmission outside Disneyland, we find maximum likelihood estimates of the )] TJ ET BT 26.250 68.694 Td /F1 9.8 Tf [(effective reproduction number to be 1.20 \(=48/40\) \(95% CI: 0.65, 2.45, assuming )] TJ ET BT 377.162 68.694 Td /F5 9.8 Tf [(k)] TJ ET BT 382.037 68.694 Td /F1 9.8 Tf [(=0.27\) in the first generation and 0.47 \(95% )] TJ ET BT 26.250 56.789 Td /F1 9.8 Tf [(CI: 0.29, 0.79, assuming )] TJ ET BT 134.641 56.789 Td /F5 9.8 Tf [(k)] TJ ET BT 139.516 56.789 Td /F1 9.8 Tf [(=0.27\) for the remaining transmission events. This difference is not statistically significant \()] TJ ET BT 529.389 56.789 Td /F5 9.8 Tf [(P)] TJ ET BT 535.892 56.789 Td /F1 9.8 Tf [(=0.09, )] TJ ET BT 26.250 44.884 Td /F1 9.8 Tf [(likelihood ratio test\). Assuming a smaller )] TJ ET BT 203.427 44.884 Td /F5 9.8 Tf [(k)] TJ ET BT 208.302 44.884 Td /F1 9.8 Tf [( value of 0.18 widens the confidence intervals on these estimates, and increases the )] TJ ET BT 574.658 44.884 Td /F5 9.8 Tf [(P)] TJ ET Q q 15.000 30.598 577.500 746.402 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(natural experiment in seeding measles throughout the state, while recognizing that contacts of cases exposed at the theme park )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(may systematically differ from the California population. Because the number of California cases exposed in Disneyland is )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(known to be 40, we used California case counts to derive a current estimate of the effective reproduction number.)] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(Our analysis of the epidemic using the Galton-Watson process will assume a negative binomial distribution for the number of )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(secondary cases caused by each active case. Assuming the negative binomial distribution )] TJ ET 0.267 0.267 0.267 rg BT 417.508 713.864 Td /F4 8.7 Tf [(6)] TJ ET 0.271 0.267 0.267 rg BT 422.326 716.245 Td /F1 8.7 Tf [(,)] TJ ET 0.267 0.267 0.267 rg BT 424.736 713.864 Td /F4 8.7 Tf [(17)] TJ ET 0.271 0.267 0.267 rg BT 434.373 712.357 Td /F1 9.8 Tf [( for the number of new cases )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(caused by each case in one generation, the probability of )] TJ ET BT 275.558 700.452 Td /F5 9.8 Tf [(i)] TJ ET BT 277.722 700.452 Td /F1 9.8 Tf [( cases causing )] TJ ET BT 344.919 700.452 Td /F5 9.8 Tf [(j)] TJ ET BT 347.083 700.452 Td /F1 9.8 Tf [( cases in the subsequent generation is )] TJ ET 0.267 0.267 0.267 rg BT 516.178 701.960 Td /F4 8.7 Tf [(7)] TJ ET q 241.500 0 0 46.500 26.250 644.072 cm /I16 Do Q 0.271 0.267 0.267 rg BT 26.250 627.048 Td /F1 9.8 Tf [(These )] TJ ET BT 56.056 627.048 Td /F5 9.8 Tf [(j)] TJ ET BT 58.220 627.048 Td /F1 9.8 Tf [( cases go on to cause, in general, further cases. If eventually transmission terminates, with no new cases arising in )] TJ ET BT 26.250 615.143 Td /F1 9.8 Tf [(subsequent generations, we can compute the total number of cases so far, i.e., the total cluster size. The probability of )] TJ ET BT 538.924 615.143 Td /F5 9.8 Tf [(i)] TJ ET BT 541.089 615.143 Td /F1 9.8 Tf [( cases )] TJ ET BT 26.250 603.238 Td /F1 9.8 Tf [(causing a cluster of size )] TJ ET BT 133.003 603.238 Td /F5 9.8 Tf [(j)] TJ ET BT 135.167 603.238 Td /F1 9.8 Tf [( is given by )] TJ ET 0.267 0.267 0.267 rg BT 186.647 604.745 Td /F4 8.7 Tf [(7)] TJ ET q 201.000 0 0 24.750 26.250 568.607 cm /I18 Do Q 0.271 0.267 0.267 rg BT 26.250 551.583 Td /F1 9.8 Tf [(The probability )] TJ ET BT 92.901 551.583 Td /F5 9.8 Tf [(p)] TJ ET BT 98.322 549.519 Td /F5 8.7 Tf [(i)] TJ ET BT 100.246 551.583 Td /F1 9.8 Tf [(of observing a chain of size )] TJ ET BT 221.097 551.583 Td /F5 9.8 Tf [(M)] TJ ET BT 229.219 551.583 Td /F1 9.8 Tf [( \(or greater\) after )] TJ ET BT 305.620 551.583 Td /F5 9.8 Tf [(N)] TJ ET BT 312.659 549.519 Td /F5 8.7 Tf [(i)] TJ ET BT 314.584 551.583 Td /F1 9.8 Tf [( introductions is one minus the probability that all clusters are )] TJ ET BT 26.250 539.679 Td /F1 9.8 Tf [(smaller than )] TJ ET BT 82.059 539.679 Td /F5 9.8 Tf [(M)] TJ ET BT 90.181 539.679 Td /F1 9.8 Tf [(:)] TJ ET q 141.000 0 0 48.000 26.250 481.798 cm /I20 Do Q BT 26.250 464.774 Td /F1 9.8 Tf [(Given )] TJ ET BT 54.427 464.774 Td /F5 9.8 Tf [(N)] TJ ET BT 61.467 462.710 Td /F5 8.7 Tf [(i)] TJ ET BT 63.391 464.774 Td /F1 9.8 Tf [(introductions per year, we can compute the expected number of years between events of size at least )] TJ ET BT 503.984 464.774 Td /F5 9.8 Tf [(M)] TJ ET BT 512.106 464.774 Td /F1 9.8 Tf [( as )] TJ ET BT 527.822 464.774 Td /F5 9.8 Tf [(1/p)] TJ ET BT 541.375 462.710 Td /F5 8.7 Tf [(i)] TJ ET BT 543.299 464.774 Td /F5 9.8 Tf [(.)] TJ ET BT 26.250 445.369 Td /F1 9.8 Tf [(We use values of the dispersion parameter )] TJ ET BT 214.288 445.369 Td /F5 9.8 Tf [(k)] TJ ET BT 219.163 445.369 Td /F1 9.8 Tf [( derived from US national data in this estimation; although the estimate of )] TJ ET BT 538.359 445.369 Td /F5 9.8 Tf [(R)] TJ ET BT 545.398 443.305 Td /F5 8.7 Tf [(eff)] TJ ET BT 26.250 433.464 Td /F1 9.8 Tf [(does not depend on )] TJ ET BT 115.150 433.464 Td /F5 9.8 Tf [(k)] TJ ET BT 120.025 433.464 Td /F1 9.8 Tf [(, the confidence interval does. Our central estimate of the dispersion parameter was 0.27, with 95% )] TJ ET BT 26.250 421.560 Td /F1 9.8 Tf [(confidence interval of 0.18 to 0.41.)] TJ ET 0.267 0.267 0.267 rg BT 175.298 423.067 Td /F4 8.7 Tf [(4)] TJ ET 0.271 0.267 0.267 rg BT 180.117 421.560 Td /F1 9.8 Tf [( Note that there is no evidence distinguishing Californias MMR vaccination rate \(90.7 5.3\) )] TJ ET BT 26.250 409.655 Td /F1 9.8 Tf [(from the national vaccination rate \(91.9 0.9\), so that US national estimates11 \(with sensitivity analysis\) provide a plausible )] TJ ET BT 26.250 397.750 Td /F1 9.8 Tf [(choice of )] TJ ET BT 67.980 397.750 Td /F5 9.8 Tf [(k)] TJ ET BT 72.855 397.750 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 378.345 Td /F1 9.8 Tf [(To estimate an overall maximum likelihood effective reproduction number from an initial number of cases and a total cluster )] TJ ET BT 26.250 366.441 Td /F1 9.8 Tf [(size, we use this assumed value of )] TJ ET BT 179.608 366.441 Td /F5 9.8 Tf [(k)] TJ ET BT 184.483 366.441 Td /F1 9.8 Tf [( and maximize the right hand side of the second equation above. To jointly estimate the )] TJ ET BT 26.250 354.536 Td /F1 9.8 Tf [(maximum likelihood estimate of an effective reproduction number in the first generation and then in the subsequent rounds of )] TJ ET BT 26.250 342.631 Td /F1 9.8 Tf [(transmission, we compute the probability that an initial number of cases gives rise to the next generation size \(using the first )] TJ ET BT 26.250 330.726 Td /F1 9.8 Tf [(equation\), and that this number of cases in the next generation give rise to the remaining number of cases using the second )] TJ ET BT 26.250 318.822 Td /F1 9.8 Tf [(equation. We assume independent transmissions, and add the log likelihoods for the first generation and the subsequent )] TJ ET BT 26.250 306.917 Td /F1 9.8 Tf [(generations. Confidence intervals for these are computed using the likelihood ratio method.)] TJ ET 0.267 0.267 0.267 rg BT 419.146 308.424 Td /F4 8.7 Tf [(14)] TJ ET 0.271 0.267 0.267 rg BT 428.783 306.917 Td /F1 9.8 Tf [( All computations were conducted )] TJ ET BT 26.250 295.012 Td /F1 9.8 Tf [(using the statistics package R 3.1 for Ubuntu Linux \(R Foundation for Statistical Computing, Vienna, Austria\).)] TJ ET BT 26.250 258.410 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 238.455 Td /F1 9.8 Tf [(The outbreak began with individuals exposed in Disneyland between December 17 and 20, 2014; 40 Californians were believed )] TJ ET BT 26.250 226.551 Td /F1 9.8 Tf [(exposed during that period.)] TJ ET 0.267 0.267 0.267 rg BT 144.400 228.058 Td /F4 8.7 Tf [(3)] TJ ET 0.271 0.267 0.267 rg BT 149.219 226.551 Td /F1 9.8 Tf [( Subsequently, 91 additional cases \(of the outbreak strain\) are known to have occurred in the state. )] TJ ET BT 26.250 214.646 Td /F1 9.8 Tf [(The epidemiology of the initial exposure has not been completely characterized, and even the number of index cases in )] TJ ET BT 26.250 202.741 Td /F1 9.8 Tf [(December has not been reported. The initial exposure, occurring in a crowded theme park, may be considered a possible )] TJ ET BT 26.250 190.836 Td /F1 9.8 Tf [(superspreading event.)] TJ ET BT 26.250 171.432 Td /F1 9.8 Tf [(When 40 first-generation measles cases produce 91 additional linked secondary cases \(for a total chain size of 131 including a )] TJ ET BT 26.250 159.527 Td /F1 9.8 Tf [(putative single index case\), )] TJ ET BT 146.555 159.527 Td /F5 9.8 Tf [(R)] TJ ET BT 153.595 159.527 Td /F1 9.8 Tf [( is estimated to be 0.69 \(95% CI: 0.48, 1.04; likelihood ratio CI assuming)] TJ ET 0.267 0.267 0.267 rg BT 465.741 161.034 Td /F4 8.7 Tf [(7)] TJ ET 0.271 0.267 0.267 rg BT 470.560 159.527 Td /F5 9.8 Tf [( k)] TJ ET BT 478.145 159.527 Td /F1 9.8 Tf [( = 0.27\). If we use the )] TJ ET BT 26.250 147.622 Td /F1 9.8 Tf [(95% upper confidence bound for the estimated aggregation parameter )] TJ ET BT 332.459 147.622 Td /F5 9.8 Tf [(k)] TJ ET BT 337.334 147.622 Td /F1 9.8 Tf [(, 0.41, then we obtain a confidence interval for R of )] TJ ET BT 26.250 135.717 Td /F1 9.8 Tf [(0.50 to 0.98; using the 95% lower bound of )] TJ ET BT 214.327 135.717 Td /F5 9.8 Tf [(k)] TJ ET BT 219.202 135.717 Td /F1 9.8 Tf [(=0.18, we obtain a confidence interval of 0.45 to 1.12. Smaller values of )] TJ ET BT 531.105 135.717 Td /F5 9.8 Tf [(k)] TJ ET BT 535.980 135.717 Td /F1 9.8 Tf [( yield )] TJ ET BT 26.250 123.813 Td /F1 9.8 Tf [(wider confidence limits still; )] TJ ET BT 146.526 123.813 Td /F5 9.8 Tf [(k)] TJ ET BT 151.401 123.813 Td /F1 9.8 Tf [(=0.05 provides a confidence interval of 0.34 to 1.71.)] TJ ET BT 26.250 104.408 Td /F1 9.8 Tf [(We conducted an additional sensitivity analysis in which we no longer assumed that the effective reproduction number was )] TJ ET BT 26.250 92.503 Td /F1 9.8 Tf [(constant. Assuming that the approximately 48 cases reported in the two weeks immediately following the last of the 40 Disney-)] TJ ET BT 26.250 80.598 Td /F1 9.8 Tf [(exposed cases to be the next generation of transmission outside Disneyland, we find maximum likelihood estimates of the )] TJ ET BT 26.250 68.694 Td /F1 9.8 Tf [(effective reproduction number to be 1.20 \(=48/40\) \(95% CI: 0.65, 2.45, assuming )] TJ ET BT 377.162 68.694 Td /F5 9.8 Tf [(k)] TJ ET BT 382.037 68.694 Td /F1 9.8 Tf [(=0.27\) in the first generation and 0.47 \(95% )] TJ ET BT 26.250 56.789 Td /F1 9.8 Tf [(CI: 0.29, 0.79, assuming )] TJ ET BT 134.641 56.789 Td /F5 9.8 Tf [(k)] TJ ET BT 139.516 56.789 Td /F1 9.8 Tf [(=0.27\) for the remaining transmission events. This difference is not statistically significant \()] TJ ET BT 529.389 56.789 Td /F5 9.8 Tf [(P)] TJ ET BT 535.892 56.789 Td /F1 9.8 Tf [(=0.09, )] TJ ET BT 26.250 44.884 Td /F1 9.8 Tf [(likelihood ratio test\). Assuming a smaller )] TJ ET BT 203.427 44.884 Td /F5 9.8 Tf [(k)] TJ ET BT 208.302 44.884 Td /F1 9.8 Tf [( value of 0.18 widens the confidence intervals on these estimates, and increases the )] TJ ET BT 574.658 44.884 Td /F5 9.8 Tf [(P)] TJ ET Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(2)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Outbreaks)] TJ ET Q endstream endobj 173 0 obj << /Type /Annot /Subtype /Link /A 174 0 R /Border [0 0 0] /H /I /Rect [ 417.5077 713.0627 422.3264 721.8810 ] >> endobj 174 0 obj << /Type /Action >> endobj 175 0 obj << /Type /Annot /Subtype /Link /A 176 0 R /Border [0 0 0] /H /I /Rect [ 424.7357 713.0627 434.3731 721.8810 ] >> endobj 176 0 obj << /Type /Action >> endobj 177 0 obj << /Type /Annot /Subtype /Link /A 178 0 R /Border [0 0 0] /H /I /Rect [ 516.1777 701.1579 520.9964 709.9762 ] >> endobj 178 0 obj << /Type /Action >> endobj 179 0 obj << /Type /XObject /Subtype /Image /Width 322 /Height 62 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 322 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 4682>> stream xGq/333333$Wr%+Ir]L$I2IfLf&3$d2$33I&33}e۫C]/s9Ϸs|||||#9N>E? 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A smaller )] TJ ET BT 517.747 724.262 Td /F5 9.8 Tf [(k)] TJ ET BT 522.622 724.262 Td /F1 9.8 Tf [( of 0.18 \(the )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(lower confidence limit from the earlier analysis\) and larger )] TJ ET BT 278.200 712.357 Td /F5 9.8 Tf [(R)] TJ ET BT 285.239 710.293 Td /F5 8.7 Tf [(eff)] TJ ET BT 294.877 712.357 Td /F1 9.8 Tf [( \(0.60, the upper confidence bound\) would yield a frequency of )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(once every 140 years.)] TJ ET 0.965 0.965 0.965 rg 26.250 434.958 555.000 255.614 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 690.572 m 581.250 690.572 l 581.250 689.822 l 26.250 689.822 l f 26.250 434.958 m 581.250 434.958 l 581.250 435.708 l 26.250 435.708 l f q 216.000 0 0 162.000 35.250 518.822 cm /I22 Do Q q 35.250 446.208 537.000 66.614 re W n 0.271 0.267 0.267 rg BT 35.250 503.298 Td /F4 9.8 Tf [(Fig. 1: Probability of observed transmission chain vs. reproduction number)] TJ ET BT 35.250 483.928 Td /F1 9.8 Tf [(Probability of at least 131 cases \(the chain size restricted to California\) following 20, 40, or 60 first generation cases in )] TJ ET BT 35.250 470.191 Td /F1 9.8 Tf [(California as a function of reproduction number )] TJ ET BT 240.634 470.191 Td /F5 9.8 Tf [(R)] TJ ET BT 247.673 469.043 Td /F1 8.7 Tf [(eff)] TJ ET BT 257.311 470.191 Td /F1 9.8 Tf [(, with )] TJ ET BT 282.778 470.191 Td /F5 9.8 Tf [(k)] TJ ET BT 287.653 470.191 Td /F1 9.8 Tf [(=0.27. Gray vertical line and shading depict the estimated )] TJ ET BT 538.842 470.191 Td /F5 9.8 Tf [(R)] TJ ET BT 545.881 469.043 Td /F1 8.7 Tf [(eff)] TJ ET BT 35.250 456.455 Td /F1 9.8 Tf [(and 95% CI based on data for measles transmission in the United States from 20012011.)] TJ ET Q BT 26.250 400.736 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 380.782 Td /F1 9.8 Tf [(Except for the substantial initial transmission event that occurred within the Disney theme parks, the transmission of measles )] TJ ET BT 26.250 368.877 Td /F1 9.8 Tf [(seen in the recent outbreak is relatively consistent with data from the past decade. In particular, amplification from 40 cases to )] TJ ET BT 26.250 356.973 Td /F1 9.8 Tf [(91 additional cases is consistent with subcritical transmission, with each case failing, on average, to replace itself, but playing )] TJ ET BT 26.250 345.068 Td /F1 9.8 Tf [(out over several generations of transmission. Our primary estimate of the reproduction number, 0.69, is higher than the number )] TJ ET BT 26.250 333.163 Td /F1 9.8 Tf [(obtained from US national data for 2001-2011 \(0.52\), but the difference is not statistically significant. Our second estimate \(in )] TJ ET BT 26.250 321.258 Td /F1 9.8 Tf [(which we allowed the effective reproduction number)] TJ ET BT 250.052 321.258 Td /F1 9.8 Tf [( to be larger in the first generation outside Disneyland\) suggested the )] TJ ET BT 26.250 309.354 Td /F1 9.8 Tf [(possibility of an effective reproduction number over one, but inaccuracy in classifying cases as being in this next generation, )] TJ ET BT 26.250 297.449 Td /F1 9.8 Tf [(together with wide confidence bands, limits our ability to draw firm conclusions from this result.)] TJ ET BT 26.250 278.044 Td /F1 9.8 Tf [(Use of the Galton-Watson process with a negative binomial distribution accounts for heterogeneity in transmission, but we are )] TJ ET BT 26.250 266.139 Td /F1 9.8 Tf [(limited in that our estimated dispersion parameter \()] TJ ET BT 245.703 266.139 Td /F5 9.8 Tf [(k)] TJ ET BT 250.578 266.139 Td /F1 9.8 Tf [(\) was derived from an observation period \(2001-2011\) which may not be )] TJ ET BT 26.250 254.235 Td /F1 9.8 Tf [(sufficient to characterize superspreading events. We found that the current outbreak does seem to be unusual based on our US )] TJ ET BT 26.250 242.330 Td /F1 9.8 Tf [(national model of 2001-2011, in the sense that outbreaks as large or larger should occur with a frequency of less than once per )] TJ ET BT 26.250 230.425 Td /F1 9.8 Tf [(century. Of course, such estimates are difficult to interpret in the absence of a prespecified analysis plan.)] TJ ET BT 26.250 211.020 Td /F1 9.8 Tf [(Our primary analysis also assumed a constant value for the reproduction number during the entire outbreak. However, the onset )] TJ ET BT 26.250 199.116 Td /F1 9.8 Tf [(of rash of the first case was on Dec. 28, 2014, while the outbreak proper did not come to the attention of the public until Jan. 6)] TJ ET 0.267 0.267 0.267 rg BT 568.213 200.623 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 26.250 187.211 Td /F1 9.8 Tf [(, so that at least for a few cases, more transmission may have been likely for several days than later in the outbreak, once )] TJ ET BT 26.250 175.306 Td /F1 9.8 Tf [(widespread public awareness could contribute to rapid diagnosis. While we failed to find evidence of a change in the effective )] TJ ET BT 26.250 163.401 Td /F1 9.8 Tf [(reproduction number, the results suggest that further investigation is warranted to determine whether or not there was more )] TJ ET BT 26.250 151.497 Td /F1 9.8 Tf [(transmission during the earlier part of the epidemic. It should also be asked whether such transmission is due to clustering of )] TJ ET BT 26.250 139.592 Td /F1 9.8 Tf [(unvaccinated individuals, or to a time lag in the intensification of contact investigation and public awareness. An alternative )] TJ ET BT 26.250 127.687 Td /F1 9.8 Tf [(analysis suggested a more substantial decline.)] TJ ET 0.267 0.267 0.267 rg BT 227.841 129.194 Td /F4 8.7 Tf [(15)] TJ ET 0.271 0.267 0.267 rg BT 26.250 108.282 Td /F1 9.8 Tf [(It is important to note that the epidemiology of recent years post-elimination illustrates that even with the absence of endemic )] TJ ET BT 26.250 96.378 Td /F1 9.8 Tf [(measles, transmission can still occur with imported infections and susceptible individuals.)] TJ ET 0.267 0.267 0.267 rg BT 410.420 97.885 Td /F4 8.7 Tf [(8)] TJ ET 0.271 0.267 0.267 rg BT 415.238 96.378 Td /F1 9.8 Tf [( High vaccination coverage remains )] TJ ET BT 26.250 84.473 Td /F1 9.8 Tf [(the best method of measles control and prevention.)] TJ ET 0.267 0.267 0.267 rg BT 247.906 85.980 Td /F4 8.7 Tf [(9)] TJ ET Q q 15.000 37.440 577.500 739.560 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(-value to 0.12.)] TJ ET BT 26.250 748.071 Td /F1 9.8 Tf [(Finally, if we assume 60 introductions per year into the US, and use the estimated effective reproduction number 0.52 and )] TJ ET BT 26.250 736.167 Td /F1 9.8 Tf [(dispersion parameter 0.27 from the 2001-2011 data)] TJ ET 0.267 0.267 0.267 rg BT 248.989 737.674 Td /F4 8.7 Tf [(4)] TJ ET 0.271 0.267 0.267 rg BT 253.807 736.167 Td /F1 9.8 Tf [(, then we would expect clusters of size at least 147 \(the size of the )] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(outbreak in the US, including the 131 California cases\) to occur approximately once every 14200 years. A smaller )] TJ ET BT 517.747 724.262 Td /F5 9.8 Tf [(k)] TJ ET BT 522.622 724.262 Td /F1 9.8 Tf [( of 0.18 \(the )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(lower confidence limit from the earlier analysis\) and larger )] TJ ET BT 278.200 712.357 Td /F5 9.8 Tf [(R)] TJ ET BT 285.239 710.293 Td /F5 8.7 Tf [(eff)] TJ ET BT 294.877 712.357 Td /F1 9.8 Tf [( \(0.60, the upper confidence bound\) would yield a frequency of )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(once every 140 years.)] TJ ET 0.965 0.965 0.965 rg 26.250 434.958 555.000 255.614 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 690.572 m 581.250 690.572 l 581.250 689.822 l 26.250 689.822 l f 26.250 434.958 m 581.250 434.958 l 581.250 435.708 l 26.250 435.708 l f q 216.000 0 0 162.000 35.250 518.822 cm /I24 Do Q q 35.250 446.208 537.000 66.614 re W n 0.271 0.267 0.267 rg BT 35.250 503.298 Td /F4 9.8 Tf [(Fig. 1: Probability of observed transmission chain vs. reproduction number)] TJ ET BT 35.250 483.928 Td /F1 9.8 Tf [(Probability of at least 131 cases \(the chain size restricted to California\) following 20, 40, or 60 first generation cases in )] TJ ET BT 35.250 470.191 Td /F1 9.8 Tf [(California as a function of reproduction number )] TJ ET BT 240.634 470.191 Td /F5 9.8 Tf [(R)] TJ ET BT 247.673 469.043 Td /F1 8.7 Tf [(eff)] TJ ET BT 257.311 470.191 Td /F1 9.8 Tf [(, with )] TJ ET BT 282.778 470.191 Td /F5 9.8 Tf [(k)] TJ ET BT 287.653 470.191 Td /F1 9.8 Tf [(=0.27. Gray vertical line and shading depict the estimated )] TJ ET BT 538.842 470.191 Td /F5 9.8 Tf [(R)] TJ ET BT 545.881 469.043 Td /F1 8.7 Tf [(eff)] TJ ET BT 35.250 456.455 Td /F1 9.8 Tf [(and 95% CI based on data for measles transmission in the United States from 20012011.)] TJ ET Q BT 26.250 400.736 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 380.782 Td /F1 9.8 Tf [(Except for the substantial initial transmission event that occurred within the Disney theme parks, the transmission of measles )] TJ ET BT 26.250 368.877 Td /F1 9.8 Tf [(seen in the recent outbreak is relatively consistent with data from the past decade. In particular, amplification from 40 cases to )] TJ ET BT 26.250 356.973 Td /F1 9.8 Tf [(91 additional cases is consistent with subcritical transmission, with each case failing, on average, to replace itself, but playing )] TJ ET BT 26.250 345.068 Td /F1 9.8 Tf [(out over several generations of transmission. Our primary estimate of the reproduction number, 0.69, is higher than the number )] TJ ET BT 26.250 333.163 Td /F1 9.8 Tf [(obtained from US national data for 2001-2011 \(0.52\), but the difference is not statistically significant. Our second estimate \(in )] TJ ET BT 26.250 321.258 Td /F1 9.8 Tf [(which we allowed the effective reproduction number)] TJ ET BT 250.052 321.258 Td /F1 9.8 Tf [( to be larger in the first generation outside Disneyland\) suggested the )] TJ ET BT 26.250 309.354 Td /F1 9.8 Tf [(possibility of an effective reproduction number over one, but inaccuracy in classifying cases as being in this next generation, )] TJ ET BT 26.250 297.449 Td /F1 9.8 Tf [(together with wide confidence bands, limits our ability to draw firm conclusions from this result.)] TJ ET BT 26.250 278.044 Td /F1 9.8 Tf [(Use of the Galton-Watson process with a negative binomial distribution accounts for heterogeneity in transmission, but we are )] TJ ET BT 26.250 266.139 Td /F1 9.8 Tf [(limited in that our estimated dispersion parameter \()] TJ ET BT 245.703 266.139 Td /F5 9.8 Tf [(k)] TJ ET BT 250.578 266.139 Td /F1 9.8 Tf [(\) was derived from an observation period \(2001-2011\) which may not be )] TJ ET BT 26.250 254.235 Td /F1 9.8 Tf [(sufficient to characterize superspreading events. We found that the current outbreak does seem to be unusual based on our US )] TJ ET BT 26.250 242.330 Td /F1 9.8 Tf [(national model of 2001-2011, in the sense that outbreaks as large or larger should occur with a frequency of less than once per )] TJ ET BT 26.250 230.425 Td /F1 9.8 Tf [(century. Of course, such estimates are difficult to interpret in the absence of a prespecified analysis plan.)] TJ ET BT 26.250 211.020 Td /F1 9.8 Tf [(Our primary analysis also assumed a constant value for the reproduction number during the entire outbreak. However, the onset )] TJ ET BT 26.250 199.116 Td /F1 9.8 Tf [(of rash of the first case was on Dec. 28, 2014, while the outbreak proper did not come to the attention of the public until Jan. 6)] TJ ET 0.267 0.267 0.267 rg BT 568.213 200.623 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 26.250 187.211 Td /F1 9.8 Tf [(, so that at least for a few cases, more transmission may have been likely for several days than later in the outbreak, once )] TJ ET BT 26.250 175.306 Td /F1 9.8 Tf [(widespread public awareness could contribute to rapid diagnosis. While we failed to find evidence of a change in the effective )] TJ ET BT 26.250 163.401 Td /F1 9.8 Tf [(reproduction number, the results suggest that further investigation is warranted to determine whether or not there was more )] TJ ET BT 26.250 151.497 Td /F1 9.8 Tf [(transmission during the earlier part of the epidemic. It should also be asked whether such transmission is due to clustering of )] TJ ET BT 26.250 139.592 Td /F1 9.8 Tf [(unvaccinated individuals, or to a time lag in the intensification of contact investigation and public awareness. An alternative )] TJ ET BT 26.250 127.687 Td /F1 9.8 Tf [(analysis suggested a more substantial decline.)] TJ ET 0.267 0.267 0.267 rg BT 227.841 129.194 Td /F4 8.7 Tf [(15)] TJ ET 0.271 0.267 0.267 rg BT 26.250 108.282 Td /F1 9.8 Tf [(It is important to note that the epidemiology of recent years post-elimination illustrates that even with the absence of endemic )] TJ ET BT 26.250 96.378 Td /F1 9.8 Tf [(measles, transmission can still occur with imported infections and susceptible individuals.)] TJ ET 0.267 0.267 0.267 rg BT 410.420 97.885 Td /F4 8.7 Tf [(8)] TJ ET 0.271 0.267 0.267 rg BT 415.238 96.378 Td /F1 9.8 Tf [( High vaccination coverage remains )] TJ ET BT 26.250 84.473 Td /F1 9.8 Tf [(the best method of measles control and prevention.)] TJ ET 0.267 0.267 0.267 rg BT 247.906 85.980 Td /F4 8.7 Tf [(9)] TJ ET Q q 15.000 37.440 577.500 739.560 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(-value to 0.12.)] TJ ET BT 26.250 748.071 Td /F1 9.8 Tf [(Finally, if we assume 60 introductions per year into the US, and use the estimated effective reproduction number 0.52 and )] TJ ET BT 26.250 736.167 Td /F1 9.8 Tf [(dispersion parameter 0.27 from the 2001-2011 data)] TJ ET 0.267 0.267 0.267 rg BT 248.989 737.674 Td /F4 8.7 Tf [(4)] TJ ET 0.271 0.267 0.267 rg BT 253.807 736.167 Td /F1 9.8 Tf [(, then we would expect clusters of size at least 147 \(the size of the )] TJ ET BT 26.250 724.262 Td /F1 9.8 Tf [(outbreak in the US, including the 131 California cases\) to occur approximately once every 14200 years. A smaller )] TJ ET BT 517.747 724.262 Td /F5 9.8 Tf [(k)] TJ ET BT 522.622 724.262 Td /F1 9.8 Tf [( of 0.18 \(the )] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(lower confidence limit from the earlier analysis\) and larger )] TJ ET BT 278.200 712.357 Td /F5 9.8 Tf [(R)] TJ ET BT 285.239 710.293 Td /F5 8.7 Tf [(eff)] TJ ET BT 294.877 712.357 Td /F1 9.8 Tf [( \(0.60, the upper confidence bound\) would yield a frequency of )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(once every 140 years.)] TJ ET 0.965 0.965 0.965 rg 26.250 434.958 555.000 255.614 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 690.572 m 581.250 690.572 l 581.250 689.822 l 26.250 689.822 l f 26.250 434.958 m 581.250 434.958 l 581.250 435.708 l 26.250 435.708 l f q 216.000 0 0 162.000 35.250 518.822 cm /I26 Do Q q 35.250 446.208 537.000 66.614 re W n 0.271 0.267 0.267 rg BT 35.250 503.298 Td /F4 9.8 Tf [(Fig. 1: Probability of observed transmission chain vs. reproduction number)] TJ ET BT 35.250 483.928 Td /F1 9.8 Tf [(Probability of at least 131 cases \(the chain size restricted to California\) following 20, 40, or 60 first generation cases in )] TJ ET BT 35.250 470.191 Td /F1 9.8 Tf [(California as a function of reproduction number )] TJ ET BT 240.634 470.191 Td /F5 9.8 Tf [(R)] TJ ET BT 247.673 469.043 Td /F1 8.7 Tf [(eff)] TJ ET BT 257.311 470.191 Td /F1 9.8 Tf [(, with )] TJ ET BT 282.778 470.191 Td /F5 9.8 Tf [(k)] TJ ET BT 287.653 470.191 Td /F1 9.8 Tf [(=0.27. Gray vertical line and shading depict the estimated )] TJ ET BT 538.842 470.191 Td /F5 9.8 Tf [(R)] TJ ET BT 545.881 469.043 Td /F1 8.7 Tf [(eff)] TJ ET BT 35.250 456.455 Td /F1 9.8 Tf [(and 95% CI based on data for measles transmission in the United States from 20012011.)] TJ ET Q BT 26.250 400.736 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 380.782 Td /F1 9.8 Tf [(Except for the substantial initial transmission event that occurred within the Disney theme parks, the transmission of measles )] TJ ET BT 26.250 368.877 Td /F1 9.8 Tf [(seen in the recent outbreak is relatively consistent with data from the past decade. In particular, amplification from 40 cases to )] TJ ET BT 26.250 356.973 Td /F1 9.8 Tf [(91 additional cases is consistent with subcritical transmission, with each case failing, on average, to replace itself, but playing )] TJ ET BT 26.250 345.068 Td /F1 9.8 Tf [(out over several generations of transmission. Our primary estimate of the reproduction number, 0.69, is higher than the number )] TJ ET BT 26.250 333.163 Td /F1 9.8 Tf [(obtained from US national data for 2001-2011 \(0.52\), but the difference is not statistically significant. Our second estimate \(in )] TJ ET BT 26.250 321.258 Td /F1 9.8 Tf [(which we allowed the effective reproduction number)] TJ ET BT 250.052 321.258 Td /F1 9.8 Tf [( to be larger in the first generation outside Disneyland\) suggested the )] TJ ET BT 26.250 309.354 Td /F1 9.8 Tf [(possibility of an effective reproduction number over one, but inaccuracy in classifying cases as being in this next generation, )] TJ ET BT 26.250 297.449 Td /F1 9.8 Tf [(together with wide confidence bands, limits our ability to draw firm conclusions from this result.)] TJ ET BT 26.250 278.044 Td /F1 9.8 Tf [(Use of the Galton-Watson process with a negative binomial distribution accounts for heterogeneity in transmission, but we are )] TJ ET BT 26.250 266.139 Td /F1 9.8 Tf [(limited in that our estimated dispersion parameter \()] TJ ET BT 245.703 266.139 Td /F5 9.8 Tf [(k)] TJ ET BT 250.578 266.139 Td /F1 9.8 Tf [(\) was derived from an observation period \(2001-2011\) which may not be )] TJ ET BT 26.250 254.235 Td /F1 9.8 Tf [(sufficient to characterize superspreading events. We found that the current outbreak does seem to be unusual based on our US )] TJ ET BT 26.250 242.330 Td /F1 9.8 Tf [(national model of 2001-2011, in the sense that outbreaks as large or larger should occur with a frequency of less than once per )] TJ ET BT 26.250 230.425 Td /F1 9.8 Tf [(century. Of course, such estimates are difficult to interpret in the absence of a prespecified analysis plan.)] TJ ET BT 26.250 211.020 Td /F1 9.8 Tf [(Our primary analysis also assumed a constant value for the reproduction number during the entire outbreak. However, the onset )] TJ ET BT 26.250 199.116 Td /F1 9.8 Tf [(of rash of the first case was on Dec. 28, 2014, while the outbreak proper did not come to the attention of the public until Jan. 6)] TJ ET 0.267 0.267 0.267 rg BT 568.213 200.623 Td /F4 8.7 Tf [(10)] TJ ET 0.271 0.267 0.267 rg BT 26.250 187.211 Td /F1 9.8 Tf [(, so that at least for a few cases, more transmission may have been likely for several days than later in the outbreak, once )] TJ ET BT 26.250 175.306 Td /F1 9.8 Tf [(widespread public awareness could contribute to rapid diagnosis. While we failed to find evidence of a change in the effective )] TJ ET BT 26.250 163.401 Td /F1 9.8 Tf [(reproduction number, the results suggest that further investigation is warranted to determine whether or not there was more )] TJ ET BT 26.250 151.497 Td /F1 9.8 Tf [(transmission during the earlier part of the epidemic. It should also be asked whether such transmission is due to clustering of )] TJ ET BT 26.250 139.592 Td /F1 9.8 Tf [(unvaccinated individuals, or to a time lag in the intensification of contact investigation and public awareness. An alternative )] TJ ET BT 26.250 127.687 Td /F1 9.8 Tf [(analysis suggested a more substantial decline.)] TJ ET 0.267 0.267 0.267 rg BT 227.841 129.194 Td /F4 8.7 Tf [(15)] TJ ET 0.271 0.267 0.267 rg BT 26.250 108.282 Td /F1 9.8 Tf [(It is important to note that the epidemiology of recent years post-elimination illustrates that even with the absence of endemic )] TJ ET BT 26.250 96.378 Td /F1 9.8 Tf [(measles, transmission can still occur with imported infections and susceptible individuals.)] TJ ET 0.267 0.267 0.267 rg BT 410.420 97.885 Td /F4 8.7 Tf [(8)] TJ ET 0.271 0.267 0.267 rg BT 415.238 96.378 Td /F1 9.8 Tf [( High vaccination coverage remains )] TJ ET BT 26.250 84.473 Td /F1 9.8 Tf [(the best method of measles control and prevention.)] TJ ET 0.267 0.267 0.267 rg BT 247.906 85.980 Td /F4 8.7 Tf [(9)] TJ ET Q q 216.000 0 0 162.000 35.250 518.822 cm /I28 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 241 0 obj << /Type /Annot /Subtype /Link /A 242 0 R /Border [0 0 0] /H /I /Rect [ 248.9888 736.8722 253.8074 745.6905 ] >> endobj 242 0 obj << /Type /Action >> endobj 243 0 obj << /Type /Annot /Subtype /Link /A 244 0 R /Border [0 0 0] /H /I /Rect [ 35.2500 518.8215 251.2500 680.8215 ] >> endobj 244 0 obj << /Type /Action /S /URI /URI (http://currents.plos.org/outbreaks/files/2015/03/plosco1-fig12.png) >> endobj 245 0 obj << /Type /XObject /Subtype /Image /Width 288 /Height 216 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 288 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 434>> stream x1 0 =Asn V:wA`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0( A`P0(\( endstream endobj 246 0 obj << /Type /XObject /Subtype /Image /Width 288 /Height 216 /SMask 245 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 288 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 11742>> stream x{|ىȱc2n)&#m؆r-*SzܲuٳMm?h Bvєd!44`,8NV"ź?g"tFҌ|{}}.T* jhd1&` 0c04 !L a`h0CC1А", HِAI|0$jj=2)|(z^vAͦŘ<O$ѢeCnݪN$I2Ap%K!HD033ёqQE%NLLXr7nܨ^Q䜋b1ɤu/u:~pvI$IlGEJ 4(ڃY,@ `6zAkZUQ0VDv- әsy6i\.jZe,J-ZQ0:;;u: lZb ^Afe_a4o))cI͆rx\gT3ãqz}%\w*+0Al6bEQ^V&yrc$뮻_htffgAƮP(TZ/)g.Ò^A>uR?yR]B2?OmfGk]VoBkL0Th ųp8<s0ɌkLI74YڒTLj5͒$~LqIQ00|}`Ȝ)1LbFى9mXr-X4iпkjkb,ŢVCR,$Ό~?GGN 'NV.w [|skͦOQe% 2'J;<ϓlxނʡ v=Jy<% Ñq C$ă87F[ ΈA6Xd*Z'b!14"L ~w[|͢ ê֞.+ X[rRC|!9A9[ELwl5<<,׫+L-Ob9Y䎅X̸݅d%ѝrb!azHy/;IT_۪.]|u2Œ-\J:~iZiĨy|`~C ?{] pɊ뒊3#=7OXs⋸\BE^f"51LN|$5y<5y=>eUW$`<;At:n( ԑ4 -Ç<~%ԇ.p!zsǢVݰ*c2yS&ƓS& &( 1!6}9z?^@o;>l^[ b!د9xzfX]j]"J\(]W[w UXئ[Vٷ80_f蚏`dN<#[H>:/J#NON'dƧ&nٹ5.yt+Wi7`@ξwe)*\EuN={ķ?tyʵ]u=WW /?&f|֯DlR+" [Q Xk:n浘z\oȟ޶ܱPb19YN'4Sʀ W Zc(t,*\^c_hza)kN>l\.:*<00@-,GUaf5@i^!WϿZ^ɽ{t夀@ a8f)8gG:|>"$Ifhۇ>-H$R'h4ZrE3F;93Y4r@i]j}odRWZBVwHg`2:>}:WUE9EEu4Zl^;U p8j']nӏڶnݪnrJu. 85߽ pťM\\:S50xU}WeJV7e:M+3 :{<T`LrCUQSSsfuq\ QݞJȶT4jLF[ƻ;Ft2PZa${'+yӓ t f 7+lH^A4%LQo~*Cًx'tCMozbuKVZ{Gs&UU6']\ߴ~J(krox\Y-5z/{{֪$v e.7\U7WVEFf/g^sڴ[V4?kh%SXR\?5W<n;640=DZIcx6Eq$jpfpo@Bru1Q*9iaX $IOUKļ!L:o=?@/nds0a%I$fy<nXDBRT *9h`! 9O A΋8bR9y%УnU9 ;`._&TDQ=f K}xLLLPe>:tª.nT+9 (StPnIh*f}S][TF ;k*iCԓCLreXeh#`rLK*|Ņ䴡L9TEFyB=p\J^;apeVݖpOr>ҕC]{*iãa6lAMbl&:p^i@asek0ڮU&K9[7y8H?l5$TX#c2q_Ϧ-1&b4't |gVʎT @eR㉝w9KfaT!GInYqmb tT(Mp8c|.e(Cد)i?YnS$v LO3ˡ(E'*͐j|~z[H Dž-,ӆ(0a6<,󽽽6m3Vh^_fu[I|`4oBf@5^oS嫣eVr@~9Qs5'reQgYN&%:;;-q䏟$^#0 ߨ/ك/l%_YePuFL zvkY?T}^>\Tl6'/Я|ijsAY6f6hTͣh<V Mb.J +E.ja/"M3|뇚&ey@ @ݩUE{0JAcz Tp(q&H8I4i>vߏi˯|tΤu=-EfX^yJ2ՐzY?]"!OˢݗFc.YoO/) AIi{.Šh66 ѣ@ҏfħdW,`d|v'U^:gMMYdPjU*<88hd[Z(0I<r8~dr|K/nómVن,hӸjDMREAQ=-EF".˕LX$utekuϗ6_\Eu뼜i^9(ANoA^-i&K|dLVtfE)MvAeĜWW, ǟy,Yod;!iZOK|馘Tg,6H+rjfT,?[V\|\UfidJP_NSLyʢfL7;;H$4(^Yvt;8*N'H̾3߿h2]x\Itv(sK =V/)&bލS~kWO@K >lWe0eX8QL1et.[nUY% FyVZ?G|ϩ\;8|i%*^7L5.RE g2fy~ bA:/LU5 l`]dmʉ"aoۨS *>_ˢc'-_0=DeSSj "Ԅ~uJa1v]yQZ+10dF:|-o]nٔ=}Y6*b  j8pVV:p@ŤJUƆΗ-vhˎMi|ŅFĮw,P]("fYobuWo勢- FWrtԛZBŖr-C/?(Šxɷz ƍDu;sloA+?0]WFHO-=uݵ[2 þ.dYKC/_1Q2}Vm\*w{[) 5p)"cccdX'/'ܷ*lg?Tn P{:k9ƒe '*HA~|<[K,N\QLǼA( <换Aw\b^*DZm6%<588(l6ÇGFFPKYE*1-\yӁ$h@uݍXYEd=l6jZe4D[C({c&~(`k٠lׯSj|ΤiedܬEch]t>!E[\7bH`&pGU=SnӪɘVY|> r (~~xd/7NܲR_V9"?A, [Yz̾6- R@W]VCbcϟiwݲP'S9z1|StvvMUX,bkd2ɐQ#uKgތpGۖ]x<^8S/<_/K2襨T 4x<^"Ǒƙ fF|/_&O; m>ƂEؽ+W[LD*k*KeRhWfx<p%BzKQ@ϓuTCE7?-1ZCތ2Q3T8uZ#}La9&lۿ DqIQӵ Gw߀XWbrLjbXIW4TBV*m o CXTdC2ӧKWY[H8?J1e=/۶)ϟ}\\jF477K#x }.ǻd鲵l(G? 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Zipprich and K. Harriman at the California Department of Public Health.)] TJ ET BT 26.250 644.665 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 617.211 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 617.211 Td /F1 9.8 Tf [(McCarthy M. Measles outbreak linked to Disney theme parks reaches five states and Mexico. BMJ. 2015 Jan 23;350:h436. )] TJ ET BT 26.250 605.306 Td /F1 9.8 Tf [(PubMed PMID:25616478.)] TJ ET BT 26.250 585.901 Td /F1 9.8 Tf [(2.)] TJ ET BT 38.132 585.901 Td /F1 9.8 Tf [(McCarthy M. Measles cases exceed 100 in US outbreak. BMJ. 2015 Feb 3;350:h622. PubMed PMID:25646696.)] TJ ET BT 26.250 566.496 Td /F1 9.8 Tf [(3.)] TJ ET BT 38.132 566.496 Td /F1 9.8 Tf [(California Department of Public Health. California Measles Surveillance Update. April 10, 2015.; 2015. Last accessed on April )] TJ ET BT 26.250 554.592 Td /F1 9.8 Tf [(10, 2015. )] TJ ET 0.267 0.267 0.267 rg BT 26.250 546.106 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 527.556 Td /F1 9.8 Tf [(4.)] TJ ET BT 38.132 527.556 Td /F1 9.8 Tf [(Blumberg S, Enanoria WT, Lloyd-Smith JO, Lietman TM, Porco TC. Identifying postelimination trends for the introduction and )] TJ ET BT 26.250 515.651 Td /F1 9.8 Tf [(transmissibility of measles in the United States. Am J Epidemiol. 2014 Jun 1;179\(11\):1375-82. PubMed PMID:24786800.)] TJ ET BT 26.250 496.246 Td /F1 9.8 Tf [(5.)] TJ ET BT 38.132 496.246 Td /F1 9.8 Tf [(Blumberg S, Lloyd-Smith JO. Comparing methods for estimating R0 from the size distribution of subcritical transmission )] TJ ET BT 26.250 484.341 Td /F1 9.8 Tf [(chains. Epidemics. 2013 Sep;5\(3\):131-45. PubMed PMID:24021520.)] TJ ET BT 26.250 464.937 Td /F1 9.8 Tf [(6.)] TJ ET BT 38.132 464.937 Td /F1 9.8 Tf [(Lloyd-Smith JO, Schreiber SJ, Kopp PE, Getz WM. Superspreading and the effect of individual variation on disease )] TJ ET BT 26.250 453.032 Td /F1 9.8 Tf [(emergence. Nature. 2005 Nov 17;438\(7066\):355-9. PubMed PMID:16292310.)] TJ ET BT 26.250 433.627 Td /F1 9.8 Tf [(7.)] TJ ET BT 38.132 433.627 Td /F1 9.8 Tf [(Blumberg S, Funk S, Pulliam JR. Detecting differential transmissibilities that affect the size of self-limited outbreaks. PLoS )] TJ ET BT 26.250 421.722 Td /F1 9.8 Tf [(Pathog. 2014 Oct;10\(10\):e1004452. PubMed PMID:25356657.)] TJ ET BT 26.250 402.318 Td /F1 9.8 Tf [(8.)] TJ ET BT 38.132 402.318 Td /F1 9.8 Tf [(De Serres G, Gay NJ, Farrington CP. Epidemiology of transmissible diseases after elimination. Am J Epidemiol. 2000 Jun )] TJ ET BT 26.250 390.413 Td /F1 9.8 Tf [(1;151\(11\):1039-48; discussion 1049-52. PubMed PMID:10873127.)] TJ ET BT 26.250 371.008 Td /F1 9.8 Tf [(9.)] TJ ET BT 38.132 371.008 Td /F1 9.8 Tf [(Parker Fiebelkorn A, Redd SB, Gallagher K, Rota PA, Rota J, Bellini W, Seward J. Measles in the United States during the )] TJ ET BT 26.250 359.103 Td /F1 9.8 Tf [(postelimination era. J Infect Dis. 2010 Nov 15;202\(10\):1520-8. PubMed PMID:20929352.)] TJ ET BT 26.250 339.699 Td /F1 9.8 Tf [(10.)] TJ ET BT 43.553 339.699 Td /F1 9.8 Tf [(County of Orange Health Care Agency, Measles Advisory, Jan. 6 2015)] TJ ET 0.267 0.267 0.267 rg BT 26.250 331.213 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 312.663 Td /F1 9.8 Tf [(11.)] TJ ET BT 43.553 312.663 Td /F1 9.8 Tf [(Elam-Evans, L. D., D. Yankey, J. A. Singleton, M. Kolasa, National, State, and Selected Local Area Vaccination Coverage )] TJ ET BT 26.250 300.758 Td /F1 9.8 Tf [(Among Children Aged 1935 Months United States, 2013, CDC Morbidity and Mortality Weekly Report, Aug. 29, 2014.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 292.272 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 273.722 Td /F1 9.8 Tf [(12.)] TJ ET BT 43.553 273.722 Td /F1 9.8 Tf [(CDC, Accessed April 15, 2015.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 265.236 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 246.686 Td /F1 9.8 Tf [(13.)] TJ ET BT 43.553 246.686 Td /F1 9.8 Tf [(Health Canada, Accessed April 15, 2015)] TJ ET 0.267 0.267 0.267 rg BT 26.250 238.200 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 219.650 Td /F1 9.8 Tf [(14.)] TJ ET BT 43.553 219.650 Td /F1 9.8 Tf [(Selvin S. Statistical analysis of epidemiologic data. Oxford, Second Edition, 2004.)] TJ ET BT 26.250 200.245 Td /F1 9.8 Tf [(15.)] TJ ET BT 43.553 200.245 Td /F1 9.8 Tf [(Majumder MS, Cohn EL, Mekaru SR, Huston JE, Brownstein JS. Substandard vaccination compliance and the 2015 )] TJ ET BT 26.250 188.340 Td /F1 9.8 Tf [(measles outbreak. JAMA Pediatrics, epub, 2015 Mar 16. doi: 10.1001/jamapediatrics.2015.0384.)] TJ ET BT 26.250 168.936 Td /F1 9.8 Tf [(16.)] TJ ET BT 43.553 168.936 Td /F1 9.8 Tf [(Zipprich J, Winter K, Hacker J, Xia DX, Watt J, Harriman K. Measles Outbreak California, December 2014February )] TJ ET BT 26.250 157.031 Td /F1 9.8 Tf [(2015. MMWR 64\(06\);153-154, 2015.)] TJ ET BT 26.250 137.626 Td /F1 9.8 Tf [(17.)] TJ ET BT 43.553 137.626 Td /F1 9.8 Tf [(Blumberg S, Lloyd-Smith JO. Inference of R\(0\) and transmission heterogeneity from the size distribution of stuttering )] TJ ET BT 26.250 125.721 Td /F1 9.8 Tf [(chains. PLoS Comput Biol. 2013;9\(5\):e1002993. PubMed PMID:23658504.)] TJ ET BT 26.250 106.317 Td /F1 9.8 Tf [(18.)] TJ ET BT 43.553 106.317 Td /F1 9.8 Tf [(Clemmons NS, Gastanaduy PA, Fiebelkorn AP, Wallace GS. Measles-United States, January 4-April 2, 2015. MMWR )] TJ ET BT 26.250 94.412 Td /F1 9.8 Tf [(64\(14\):372-376, 2015.)] TJ ET BT 26.250 75.007 Td /F1 9.8 Tf [(19.)] TJ ET BT 43.553 75.007 Td /F1 9.8 Tf [(Diekmann O, Heesterbeek H. Mathematical epidemiology of infectious diseases. Model building, analysis, and )] TJ ET BT 26.250 63.102 Td /F1 9.8 Tf [(interpretation. West Sussex: John Wiley, 2000.)] TJ ET Q q 15.000 45.722 577.500 731.278 re W n 0.271 0.267 0.267 rg BT 26.250 750.278 Td /F4 12.0 Tf [(Competing Interests)] TJ ET BT 26.250 730.324 Td /F1 9.8 Tf [(All authors have confirmed that they have no financial, personal or professional competing interests to report.)] TJ ET BT 26.250 693.722 Td /F4 12.0 Tf [(Acknowledgements)] TJ ET BT 26.250 673.767 Td /F1 9.8 Tf [(We gratefully acknowledge useful discussions with J. Zipprich and K. Harriman at the California Department of Public Health.)] TJ ET BT 26.250 644.665 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 617.211 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 617.211 Td /F1 9.8 Tf [(McCarthy M. Measles outbreak linked to Disney theme parks reaches five states and Mexico. BMJ. 2015 Jan 23;350:h436. )] TJ ET BT 26.250 605.306 Td /F1 9.8 Tf [(PubMed PMID:25616478.)] TJ ET BT 26.250 585.901 Td /F1 9.8 Tf [(2.)] TJ ET BT 38.132 585.901 Td /F1 9.8 Tf [(McCarthy M. Measles cases exceed 100 in US outbreak. BMJ. 2015 Feb 3;350:h622. PubMed PMID:25646696.)] TJ ET BT 26.250 566.496 Td /F1 9.8 Tf [(3.)] TJ ET BT 38.132 566.496 Td /F1 9.8 Tf [(California Department of Public Health. California Measles Surveillance Update. April 10, 2015.; 2015. Last accessed on April )] TJ ET BT 26.250 554.592 Td /F1 9.8 Tf [(10, 2015. )] TJ ET 0.267 0.267 0.267 rg BT 26.250 546.106 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 527.556 Td /F1 9.8 Tf [(4.)] TJ ET BT 38.132 527.556 Td /F1 9.8 Tf [(Blumberg S, Enanoria WT, Lloyd-Smith JO, Lietman TM, Porco TC. Identifying postelimination trends for the introduction and )] TJ ET BT 26.250 515.651 Td /F1 9.8 Tf [(transmissibility of measles in the United States. Am J Epidemiol. 2014 Jun 1;179\(11\):1375-82. PubMed PMID:24786800.)] TJ ET BT 26.250 496.246 Td /F1 9.8 Tf [(5.)] TJ ET BT 38.132 496.246 Td /F1 9.8 Tf [(Blumberg S, Lloyd-Smith JO. Comparing methods for estimating R0 from the size distribution of subcritical transmission )] TJ ET BT 26.250 484.341 Td /F1 9.8 Tf [(chains. Epidemics. 2013 Sep;5\(3\):131-45. PubMed PMID:24021520.)] TJ ET BT 26.250 464.937 Td /F1 9.8 Tf [(6.)] TJ ET BT 38.132 464.937 Td /F1 9.8 Tf [(Lloyd-Smith JO, Schreiber SJ, Kopp PE, Getz WM. Superspreading and the effect of individual variation on disease )] TJ ET BT 26.250 453.032 Td /F1 9.8 Tf [(emergence. Nature. 2005 Nov 17;438\(7066\):355-9. PubMed PMID:16292310.)] TJ ET BT 26.250 433.627 Td /F1 9.8 Tf [(7.)] TJ ET BT 38.132 433.627 Td /F1 9.8 Tf [(Blumberg S, Funk S, Pulliam JR. Detecting differential transmissibilities that affect the size of self-limited outbreaks. PLoS )] TJ ET BT 26.250 421.722 Td /F1 9.8 Tf [(Pathog. 2014 Oct;10\(10\):e1004452. PubMed PMID:25356657.)] TJ ET BT 26.250 402.318 Td /F1 9.8 Tf [(8.)] TJ ET BT 38.132 402.318 Td /F1 9.8 Tf [(De Serres G, Gay NJ, Farrington CP. Epidemiology of transmissible diseases after elimination. Am J Epidemiol. 2000 Jun )] TJ ET BT 26.250 390.413 Td /F1 9.8 Tf [(1;151\(11\):1039-48; discussion 1049-52. PubMed PMID:10873127.)] TJ ET BT 26.250 371.008 Td /F1 9.8 Tf [(9.)] TJ ET BT 38.132 371.008 Td /F1 9.8 Tf [(Parker Fiebelkorn A, Redd SB, Gallagher K, Rota PA, Rota J, Bellini W, Seward J. Measles in the United States during the )] TJ ET BT 26.250 359.103 Td /F1 9.8 Tf [(postelimination era. J Infect Dis. 2010 Nov 15;202\(10\):1520-8. PubMed PMID:20929352.)] TJ ET BT 26.250 339.699 Td /F1 9.8 Tf [(10.)] TJ ET BT 43.553 339.699 Td /F1 9.8 Tf [(County of Orange Health Care Agency, Measles Advisory, Jan. 6 2015)] TJ ET 0.267 0.267 0.267 rg BT 26.250 331.213 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 312.663 Td /F1 9.8 Tf [(11.)] TJ ET BT 43.553 312.663 Td /F1 9.8 Tf [(Elam-Evans, L. D., D. Yankey, J. A. Singleton, M. Kolasa, National, State, and Selected Local Area Vaccination Coverage )] TJ ET BT 26.250 300.758 Td /F1 9.8 Tf [(Among Children Aged 1935 Months United States, 2013, CDC Morbidity and Mortality Weekly Report, Aug. 29, 2014.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 292.272 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 273.722 Td /F1 9.8 Tf [(12.)] TJ ET BT 43.553 273.722 Td /F1 9.8 Tf [(CDC, Accessed April 15, 2015.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 265.236 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 246.686 Td /F1 9.8 Tf [(13.)] TJ ET BT 43.553 246.686 Td /F1 9.8 Tf [(Health Canada, Accessed April 15, 2015)] TJ ET 0.267 0.267 0.267 rg BT 26.250 238.200 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 219.650 Td /F1 9.8 Tf [(14.)] TJ ET BT 43.553 219.650 Td /F1 9.8 Tf [(Selvin S. Statistical analysis of epidemiologic data. Oxford, Second Edition, 2004.)] TJ ET BT 26.250 200.245 Td /F1 9.8 Tf [(15.)] TJ ET BT 43.553 200.245 Td /F1 9.8 Tf [(Majumder MS, Cohn EL, Mekaru SR, Huston JE, Brownstein JS. Substandard vaccination compliance and the 2015 )] TJ ET BT 26.250 188.340 Td /F1 9.8 Tf [(measles outbreak. JAMA Pediatrics, epub, 2015 Mar 16. doi: 10.1001/jamapediatrics.2015.0384.)] TJ ET BT 26.250 168.936 Td /F1 9.8 Tf [(16.)] TJ ET BT 43.553 168.936 Td /F1 9.8 Tf [(Zipprich J, Winter K, Hacker J, Xia DX, Watt J, Harriman K. Measles Outbreak California, December 2014February )] TJ ET BT 26.250 157.031 Td /F1 9.8 Tf [(2015. MMWR 64\(06\);153-154, 2015.)] TJ ET BT 26.250 137.626 Td /F1 9.8 Tf [(17.)] TJ ET BT 43.553 137.626 Td /F1 9.8 Tf [(Blumberg S, Lloyd-Smith JO. Inference of R\(0\) and transmission heterogeneity from the size distribution of stuttering )] TJ ET BT 26.250 125.721 Td /F1 9.8 Tf [(chains. PLoS Comput Biol. 2013;9\(5\):e1002993. PubMed PMID:23658504.)] TJ ET BT 26.250 106.317 Td /F1 9.8 Tf [(18.)] TJ ET BT 43.553 106.317 Td /F1 9.8 Tf [(Clemmons NS, Gastanaduy PA, Fiebelkorn AP, Wallace GS. Measles-United States, January 4-April 2, 2015. MMWR )] TJ ET BT 26.250 94.412 Td /F1 9.8 Tf [(64\(14\):372-376, 2015.)] TJ ET BT 26.250 75.007 Td /F1 9.8 Tf [(19.)] TJ ET BT 43.553 75.007 Td /F1 9.8 Tf [(Diekmann O, Heesterbeek H. Mathematical epidemiology of infectious diseases. Model building, analysis, and )] TJ ET BT 26.250 63.102 Td /F1 9.8 Tf [(interpretation. West Sussex: John Wiley, 2000.)] TJ ET Q q 15.000 45.722 577.500 731.278 re W n 0.271 0.267 0.267 rg BT 26.250 750.278 Td /F4 12.0 Tf [(Competing Interests)] TJ ET BT 26.250 730.324 Td /F1 9.8 Tf [(All authors have confirmed that they have no financial, personal or professional competing interests to report.)] TJ ET BT 26.250 693.722 Td /F4 12.0 Tf [(Acknowledgements)] TJ ET BT 26.250 673.767 Td /F1 9.8 Tf [(We gratefully acknowledge useful discussions with J. Zipprich and K. Harriman at the California Department of Public Health.)] TJ ET BT 26.250 644.665 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 617.211 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 617.211 Td /F1 9.8 Tf [(McCarthy M. Measles outbreak linked to Disney theme parks reaches five states and Mexico. BMJ. 2015 Jan 23;350:h436. )] TJ ET BT 26.250 605.306 Td /F1 9.8 Tf [(PubMed PMID:25616478.)] TJ ET BT 26.250 585.901 Td /F1 9.8 Tf [(2.)] TJ ET BT 38.132 585.901 Td /F1 9.8 Tf [(McCarthy M. Measles cases exceed 100 in US outbreak. BMJ. 2015 Feb 3;350:h622. PubMed PMID:25646696.)] TJ ET BT 26.250 566.496 Td /F1 9.8 Tf [(3.)] TJ ET BT 38.132 566.496 Td /F1 9.8 Tf [(California Department of Public Health. California Measles Surveillance Update. April 10, 2015.; 2015. Last accessed on April )] TJ ET BT 26.250 554.592 Td /F1 9.8 Tf [(10, 2015. )] TJ ET 0.267 0.267 0.267 rg BT 26.250 546.106 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 527.556 Td /F1 9.8 Tf [(4.)] TJ ET BT 38.132 527.556 Td /F1 9.8 Tf [(Blumberg S, Enanoria WT, Lloyd-Smith JO, Lietman TM, Porco TC. Identifying postelimination trends for the introduction and )] TJ ET BT 26.250 515.651 Td /F1 9.8 Tf [(transmissibility of measles in the United States. Am J Epidemiol. 2014 Jun 1;179\(11\):1375-82. PubMed PMID:24786800.)] TJ ET BT 26.250 496.246 Td /F1 9.8 Tf [(5.)] TJ ET BT 38.132 496.246 Td /F1 9.8 Tf [(Blumberg S, Lloyd-Smith JO. Comparing methods for estimating R0 from the size distribution of subcritical transmission )] TJ ET BT 26.250 484.341 Td /F1 9.8 Tf [(chains. Epidemics. 2013 Sep;5\(3\):131-45. PubMed PMID:24021520.)] TJ ET BT 26.250 464.937 Td /F1 9.8 Tf [(6.)] TJ ET BT 38.132 464.937 Td /F1 9.8 Tf [(Lloyd-Smith JO, Schreiber SJ, Kopp PE, Getz WM. Superspreading and the effect of individual variation on disease )] TJ ET BT 26.250 453.032 Td /F1 9.8 Tf [(emergence. Nature. 2005 Nov 17;438\(7066\):355-9. PubMed PMID:16292310.)] TJ ET BT 26.250 433.627 Td /F1 9.8 Tf [(7.)] TJ ET BT 38.132 433.627 Td /F1 9.8 Tf [(Blumberg S, Funk S, Pulliam JR. Detecting differential transmissibilities that affect the size of self-limited outbreaks. PLoS )] TJ ET BT 26.250 421.722 Td /F1 9.8 Tf [(Pathog. 2014 Oct;10\(10\):e1004452. PubMed PMID:25356657.)] TJ ET BT 26.250 402.318 Td /F1 9.8 Tf [(8.)] TJ ET BT 38.132 402.318 Td /F1 9.8 Tf [(De Serres G, Gay NJ, Farrington CP. Epidemiology of transmissible diseases after elimination. Am J Epidemiol. 2000 Jun )] TJ ET BT 26.250 390.413 Td /F1 9.8 Tf [(1;151\(11\):1039-48; discussion 1049-52. PubMed PMID:10873127.)] TJ ET BT 26.250 371.008 Td /F1 9.8 Tf [(9.)] TJ ET BT 38.132 371.008 Td /F1 9.8 Tf [(Parker Fiebelkorn A, Redd SB, Gallagher K, Rota PA, Rota J, Bellini W, Seward J. Measles in the United States during the )] TJ ET BT 26.250 359.103 Td /F1 9.8 Tf [(postelimination era. J Infect Dis. 2010 Nov 15;202\(10\):1520-8. PubMed PMID:20929352.)] TJ ET BT 26.250 339.699 Td /F1 9.8 Tf [(10.)] TJ ET BT 43.553 339.699 Td /F1 9.8 Tf [(County of Orange Health Care Agency, Measles Advisory, Jan. 6 2015)] TJ ET 0.267 0.267 0.267 rg BT 26.250 331.213 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 312.663 Td /F1 9.8 Tf [(11.)] TJ ET BT 43.553 312.663 Td /F1 9.8 Tf [(Elam-Evans, L. D., D. Yankey, J. A. Singleton, M. Kolasa, National, State, and Selected Local Area Vaccination Coverage )] TJ ET BT 26.250 300.758 Td /F1 9.8 Tf [(Among Children Aged 1935 Months United States, 2013, CDC Morbidity and Mortality Weekly Report, Aug. 29, 2014.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 292.272 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 273.722 Td /F1 9.8 Tf [(12.)] TJ ET BT 43.553 273.722 Td /F1 9.8 Tf [(CDC, Accessed April 15, 2015.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 265.236 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 246.686 Td /F1 9.8 Tf [(13.)] TJ ET BT 43.553 246.686 Td /F1 9.8 Tf [(Health Canada, Accessed April 15, 2015)] TJ ET 0.267 0.267 0.267 rg BT 26.250 238.200 Td /F1 7.5 Tf [(REFERENCE LINK)] TJ ET 0.271 0.267 0.267 rg BT 26.250 219.650 Td /F1 9.8 Tf [(14.)] TJ ET BT 43.553 219.650 Td /F1 9.8 Tf [(Selvin S. Statistical analysis of epidemiologic data. Oxford, Second Edition, 2004.)] TJ ET BT 26.250 200.245 Td /F1 9.8 Tf [(15.)] TJ ET BT 43.553 200.245 Td /F1 9.8 Tf [(Majumder MS, Cohn EL, Mekaru SR, Huston JE, Brownstein JS. Substandard vaccination compliance and the 2015 )] TJ ET BT 26.250 188.340 Td /F1 9.8 Tf [(measles outbreak. JAMA Pediatrics, epub, 2015 Mar 16. doi: 10.1001/jamapediatrics.2015.0384.)] TJ ET BT 26.250 168.936 Td /F1 9.8 Tf [(16.)] TJ ET BT 43.553 168.936 Td /F1 9.8 Tf [(Zipprich J, Winter K, Hacker J, Xia DX, Watt J, Harriman K. Measles Outbreak California, December 2014February )] TJ ET BT 26.250 157.031 Td /F1 9.8 Tf [(2015. MMWR 64\(06\);153-154, 2015.)] TJ ET BT 26.250 137.626 Td /F1 9.8 Tf [(17.)] TJ ET BT 43.553 137.626 Td /F1 9.8 Tf [(Blumberg S, Lloyd-Smith JO. Inference of R\(0\) and transmission heterogeneity from the size distribution of stuttering )] TJ ET BT 26.250 125.721 Td /F1 9.8 Tf [(chains. PLoS Comput Biol. 2013;9\(5\):e1002993. PubMed PMID:23658504.)] TJ ET BT 26.250 106.317 Td /F1 9.8 Tf [(18.)] TJ ET BT 43.553 106.317 Td /F1 9.8 Tf [(Clemmons NS, Gastanaduy PA, Fiebelkorn AP, Wallace GS. Measles-United States, January 4-April 2, 2015. MMWR )] TJ ET BT 26.250 94.412 Td /F1 9.8 Tf [(64\(14\):372-376, 2015.)] TJ ET BT 26.250 75.007 Td /F1 9.8 Tf [(19.)] TJ ET BT 43.553 75.007 Td /F1 9.8 Tf [(Diekmann O, Heesterbeek H. Mathematical epidemiology of infectious diseases. Model building, analysis, and )] TJ ET BT 26.250 63.102 Td /F1 9.8 Tf [(interpretation. 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