A Periodic Epidemic Model with Age Structure in a Patchy Environment

Abstract

In this paper, a periodic epidemic model with age structure in a patchy environment is introduced. We investigate its global dynamics in term of the basic reproduction number $\mathcal{R}_0$, and show that there exists at least one positive periodic state and the disease persists when $\mathcal{R}_0>1$ while the disease will die out if $\mathcal{R}_0<1$. Some numerical examples are given to confirm our analytic results and to show that the age and spatial heterogeneities are important factors for the global dynamics.