Global behavior of SIS epidemic models with age structure and spatial heterogeneity

Abstract

In this study, we investigate two kinds of SIS epidemic models with an age structure and spatial heterogeneity. The first is the SIS epidemic model with age and patch structures, and the second is the SIS epidemic model with age structure and spatial diffusion. For both models, we prove that the global attractivity of each equilibrium is completely determined by the basic reproduction number $$R_0$$ ; that is, the disease-free equilibrium is globally attractive if $$R_0<1$$ , whereas the endemic equilibrium uniquely exists and is globally attractive if $$R_0>1$$ . In particular, we provide a theoretical justification for the basic reproduction number being the spectral radius of the next generation operator. This enables us to perform numerical simulations that verify our theoretical results, which is important from the viewpoint of applications.