%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Bacaër, Nicolas
%T On the stochastic SIS epidemic model in a periodic environment
%D 2015
%L fdi:010071565
%G ENG
%J Journal of Mathematical Biology
%@ 0303-6812
%K EPIDEMIOLOGIE ; MODELISATION
%K MODELE STOCHASTIQUE ; EXTINCTION ; EQUATION DE HAMILTON JACOBI
%M ISI:000357672000008
%N 2
%P 494-511
%R 10.1007/s00285-014-0828-1
%U https://www.documentation.ird.fr/hor/fdi:010071565
%> https://www.documentation.ird.fr/intranet/publi/depot/2018-05-09/010071565.pdf
%V 71
%W Horizon (IRD)
%X In the stochastic SIS epidemic model with a contact rate , a recovery rate , and a population size , the mean extinction time is such that converges to as grows to infinity. This article considers the more realistic case where the contact rate is a periodic function whose average is bigger than . Then converges to a new limit , which is linked to a time-periodic Hamilton-Jacobi equation. When is a cosine function with small amplitude or high (resp. low) frequency, approximate formulas for can be obtained analytically following the method used in Assaf et al. (Phys Rev E 78:041123, 2008). These results are illustrated by numerical simulations.
%$ 020MATH01 ; 050EPID