title: On the stochastic SIS epidemic model in a periodic environment.
abstract: In the stochastic SIS epidemic model with a contact rate a, a recovery rate b < a, and a population size N, the mean extinction time τ is such that (log τ)/N converges to c = b/a - 1 - log(b/a) as N grows to infinity. This article considers the more realistic case where the contact rate a(t) is a periodic function whose average is bigger than b. Then log τ/N converges to a new limit C, which is linked to a time-periodic Hamilton-Jacobi equation. When a(t) is a cosine function with small amplitude or high (resp. low) frequency, approximate formulas for C 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.
authors.affiliation: IRD (Institut de Recherche pour le Développement), UMMISCO, Bondy, France, nicolas.bacaer@ird.fr.
authors.forename: Nicolas
authors.initials: N
authors.lastname: Bacaër
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology; D019295:Computational Biology; D003198:Computer Simulation; D004198:Disease Susceptibility; D004777:Environment; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D013269:Stochastic Processes