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

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≤1R0≤1, then the infection-free equilibrium is globally asymptotically stable; whereas if R0>1R0>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 00 that the Liapunov functionals are well-defined. Some applications are listed. Our results improve and generalize some known results.