Dynamics and asymptotic profiles of steady states of an SIRS epidemic model in spatially heterogenous environment

This paper performs qualitative analysis on a reaction-diffusion SIRS epidemic system with ratio-dependent incidence rate in spatially heterogeneous environment. The threshold dynamics in the term of the basic reproduction number is established. And the asymptotic profile of endemic equilibrium is determined if the diffusion rate of the susceptible individuals is small. The results show that restricting the movement of susceptible individuals can effectively control the number of infectious individuals.