Periodic orbits of a seasonal SIS epidemic model with migration

We consider a seasonally forced SIS epidemic model where the population is spatially divided into two patches. We consider that periodicity occurs in the contact rates by switching between two levels. The epidemic dynamics are described by a switched system. We prove the existence of an invariant domain D containing at least one periodic solution. By considering small migrations, we rewrite the SIS model as a slow-fast dynamical system and show that it has a harmonic periodic solution which lies in a small tubular neighborhood of a curve Gamma(m). We deduce from this study the persistence or not of the disease in each patch. (C) 2014 Elsevier Inc. All rights reserved.