About stability analysis in epidemic reaction-diffusion model

Abstract

The purpose of this thesis is to study the local and global asymptotic stability of the nonnegative constant steady states of an epidemic reaction-diffusion system (susceptible-infectious) with a nonlinear incidence in the case of ordinary and partial differential equations depending on the basic reproduction number, with determining the linearity of the studied system in both cases . Where the local asymptotic stability is determined by the nature of the eigenvalues, but for the global asymptotic stability we use the Lyapunov method, in addition to illustrate the analytical results through numerical examples