Asymptotic behavior of a diffusive SIS epidemic model with mass action infection mechanism

In this paper, we study an SIS epidemic reaction-diffusion model with mass action infection mechanism and subject to homogeneous Dirichlet boundary conditions. We define a basic reproduction number $ \mathcal{R}_0 $ for the model and prove that there exists a unique endemic equilibrium if $ \mathcal{R}_0> 1 $. We then establish the global attractivity of the disease-free equilibrium and the endemic equilibrium for a special case. Furthermore, we analyze the asymptotic profiles of the endemic equilibrium. We show that limited movement of the individuals cannot eradicate the disease because of a varying total population, while large population mobility can cause the disease extinction due to the hostile exterior environment.