Multigeneration Reproduction Ratios and the Effects of Clustered Unvaccinated Individuals on Epidemic Outbreak |
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Authors: | David E Hiebeler Isaac J Michaud Hamilton Hoxie Ackerman Shannon Reed Iosevich Andre Robinson |
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Institution: | 1.Department of Mathematics and Statistics,University of Maine,Orono,USA;2.Department of Mathematics and Statistics,Boston University,Boston,USA;3.Biogen Idec, 14 Cambridge Center,Cambridge,USA;4.Department of Mathematics,University of Missouri,Columbia,USA;5.Department of Mathematics,Medgar Evers College,Brooklyn,USA;6.Department of Statistics,University of California, Berkeley,Berkeley,USA;7.Warner School of Education,University of Rochester,Rochester,USA |
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Abstract: | An SIR epidemiological community-structured model is constructed to investigate the effects of clustered distributions of
unvaccinated individuals and the distribution of the primary case relative to vaccination levels. The communities here represent
groups such as neighborhoods within a city or cities within a region. The model contains two levels of mixing, where individuals
make more intra-group than inter-group contacts. Stochastic simulations and analytical results are utilized to explore the
model. An extension of the effective reproduction ratio that incorporates more spatial information by predicting the average
number of tertiary infections caused by a single infected individual is introduced to characterize the system. Using these
methods, we show that both the vaccination coverage and the variation in vaccination levels among communities affect the likelihood
and severity of epidemics. The location of the primary infectious case and the degree of mixing between communities are also
important factors in determining the dynamics of outbreaks. In some cases, increasing the efficacy of a vaccine can in fact
increase the effective reproduction ratio in early generations, due to the effects of population structure on the likely initial
location of an infection. |
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