Asymptotic stability of solutions for a diffusive epidemic model

The aim of this paper is to study the existence and the asymptotic stability of solutions for an epidemiologically emerging reaction-diffusion model. We show that the model has two types of equilibrium points to resolve the proposed system for a fairly broad class of nonlinearity that describes the transmission of an infectious disease between individuals. The model is analyzed by using the basic reproductive number R0{R}_{0}. Finally, we present the numerical examples simulations that clarifies and confirms the results of the study throughout the paper.