Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model

To understand the impact of spatial heterogeneity of environment and movement of individuals on the persistence and extinction of a disease, a spatial SIS reaction-diffusion model is studied, with the focus on the existence, uniqueness and particularly the asymptotic profile of the steady-states. First, the basic reproduction number $\R_{0}$ is defined for this SIS PDE model. It is shown that if $\R_{0} 1$, the unique disease-free equilibrium …