Abstract
Abstract 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 R 0 {R}_{0} . Finally, we present the numerical examples simulations that clarifies and confirms the results of the study throughout the paper.
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