Global stability of a diffusive virus dynamics model with general incidence function and time delay

Abstract

In this paper, we propose a model of virus dynamics that includes diffusion, time delay and a general incidence function. By constructing Liapunov functionals, we show that the model has threshold dynamics: if the basic reproduction number R0≤1, then the infection-free equilibrium is globally asymptotically stable; whereas if R0>1, then there exists an infection equilibrium which is globally asymptotically stable. We pay particular attention to demonstrating that solutions are sufficiently bounded away from 0 that the Liapunov functionals are well-defined. Some applications are listed. Our results improve and generalize some known results.