Global stability of a diffusive and delayed virus dynamics model with Beddington–DeAngelis incidence function and CTL immune response

In this paper, we study a diffusive and delayed virus dynamics model with Beddington–DeAngelis incidence and CTL immune response. By constructing Lyapunov functionals, we show that if the basic reproductive number is less than or equal to one, then the infection-free equilibrium is globally asymptotically stable; if the immune reproductive number is less than or equal to one and the basic reproductive number is greater than one, then the immune-free equilibrium is globally asymptotically stable; if the immune reproductive number is greater than one, then the interior equilibrium is globally asymptotically stable.