Analysis of Solutions for a Reaction-Diffusion Epidemic Model

Abstract

This work mainly focuses on the dynamics of an epidemiologically emerging reaction-diffusion system. We establish global presence and the outcomes of asymptotic local and global stability to resolve the proposed system for a fairly broad class of nonlinearity that describes the transmission of an infectious disease between individuals by means of the appropriate Lyapunov function. the basic reproduction number can play a role in determining whether a disease will become extinct or persistent. Finally, we present an example that clarifies and confirms the results of the study throughout the paper.