Asymptotic profile of endemic equilibrium to a diffusive epidemic model with saturated incidence rate

We study the existence and asymptotic profile of endemic equilibrium (EE) of a diffusive SIS epidemic model with saturated incidence rate. By introducing the basic reproduction number R₀, the existence of EE is established when R₀ > 1. The effects of diffusion rates and the saturated coefficient on asymptotic profile of EE are investigated. Our results indicate that when the diffusion rate of susceptible individuals is small and the total population N is below a certain level, or the saturated coefficient is large, the infected population dies out, while the two populations persist if at least one of the diffusion rates of the susceptible and infected individuals is large. Finally, we illustrate the influences of the population diffusion and the saturation coefficient on this model numerically.