On the stochastic SIS epidemic model in a periodic environment

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.