Global stability of a delayed and diffusive virus model with nonlinear infection function.

Abstract

This paper studies a delayed viral infection model with diffusion and a general incidence rate. A discrete-time model was derived by applying nonstandard finite difference scheme. The positivity and boundedness of solutions are presented. We established the global stability of equilibria in terms of $R_0$ by applying Lyapunov method. The results showed that if $R_0$ is less than 1, then the infection-free equilibrium $E_0$ is globally asymptotically stable. If $R_0$ is greater than 1, then the infection equilibrium $E_{\ast }$ is globally asymptotically stable. Numerical experiments are carried out to illustrate the theoretical results.