The Volterra-Lyapunov for global stability analysis of a model of Reaction-Diffusion system

Abstract

The aime of this work is to study the problem of global asymptotic stability for equilibria of a spatially diffusive HIV/AIDS epidemic model with homogeneous Neumann boundary condition. By discretizing the model with respect to the space variable, we first then by incorporating the theory of stable matrix of VolterraLyapunov into the classical method of the Lyapunov functional ODEs model, and then broaden the construction method into the PDEs model in which either susceptible or infective populations are diffusive. In both cases, we obtain the standard threshold dynamical behaviors, that is, if 01, then the disease-free equilibrium is globally asymptotically stable and if 01, then the (strictly positive) endemic equilibrium is globally asymptotically stable