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 $ \mathfrak {R}_0 $ by applying Lyapunov method. The results showed that if $ \mathfrak {R}_0 $ is less than 1, then the infection-free equilibrium $ E_0 $ is globally asymptotically stable. If $ \mathfrak {R}_0 $ is greater than 1, then the infection equilibrium $ E_* $ is globally asymptotically stable. Numerical experiments are carried out to illustrate the theoretical results.

Keywords

• diffusion
• nonlinear incidence
• delay
• lyapunov method
• global stability