A reaction–diffusion SIS epidemic model with saturated incidence rate and logistic source

Abstract

A reaction–diffusion SIS epidemic model with saturated incidence rate and logistic source for the susceptible individuals is considered. We establish the uniform bounds of parabolic system and investigate the extinction and persistence of infectious diseases in terms of the basic reproduction number. We further analyze the asymptotic profiles of the endemic equilibrium for small and large movement rates and large saturate rate. In particular, it is shown that large saturation may cause the elimination of disease and the logistic source can enhance persistence of infectious disease.