%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Bacaër, Nicolas
%A Gomes, M.G.M.
%T On the final size of epidemics with seasonality
%D 2009
%L fdi:010048307
%G ENG
%J Bulletin of Mathematical Biology
%@ 0092-8240
%K Basic reproduction number ; Seasonality ; Final epidemic size
%M ISI:000270826300009
%N 8
%P 1954-1966
%R 10.1007/s11538-009-9433-7
%U https://www.documentation.ird.fr/hor/fdi:010048307
%> https://www.documentation.ird.fr/intranet/publi/2009/11/010048307.pdf
%V 71
%W Horizon (IRD)
%X We first study an SIR system of differential equations with periodic coefficients describing an epidemic in a seasonal environment. Unlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number R-0 or of the initial fraction of infected people. Moreover, large epidemics can happen even if R-0 < 1. But like in a constant environment, the final epidemic size tends to 0 when R-0 < 1 and the initial fraction of infected people tends to 0. When R-0 > 1, the final epidemic size is bigger than the fraction 1-1/R-0 of the initially nonimmune population. In summary, the basic reproduction number R-0 keeps its classical threshold property but many other properties are no longer true in a seasonal environment. These theoretical results should be kept in mind when analyzing data for emerging vector-borne diseases (West-Nile, dengue, chikungunya) or air-borne diseases (SARS, pandemic influenza); all these diseases being influenced by seasonality.
%$ 020 ; 052