Qualitative analysis on a diffusive SIRS epidemic model with standard incidence infection mechanism

Abstract

In this paper, we are concerned with an SIRS epidemic reaction–diffusion system with standard incidence infection mechanism in a spatially heterogeneous environment. We first establish the uniform bounds of solutions and then derive the threshold dynamics in terms of the basic reproduction number $$\mathcal {R}_0$$ . Our main focus is on the asymptotic profile of endemic equilibria (when exists) if the diffusion (migration) rate of the susceptible, infected or recovered population is small, and our results show that the disease always exists in the entire habitat in each case of small diffusion rate. This suggests that restricting the diffusion (migration) rate of population is not an effective strategy of disease eradication.