Stability of a general discrete-time viral infection model with humoral immunity and cellular infection

This paper studies the global stability of a general discrete-time viral infection model with virus-to-cell and cell-to-cell transmissions and with humoral immune response. We consider both latently and actively infected cells. The model incorporates three types of intracellular time delays. The production and clearance rates of all compartments as well as incidence rates of infection are modeled by general nonlinear functions. We use the nonstandard finite difference method to discretize the continuous-time model. We show that the solutions of the discrete-time model are positive and ultimately bounded. We derive two threshold parameters, the basic reproduction number R0 and the humoral immune response activation number R1, which completely determine the existence and stability of the model’s equilibria. By using Lyapunov functions, we have proven that if R0≤1, then the virus-free equilibrium Q0 is globally asymptotically stable; if R1≤1< R0, then the persistent infection equilibrium without immune response Q* is globally asymptotically stable; and if R1>1, then the persistent infection equilibrium with immune response Q¯ is globally asymptotically stable. We illustrate our theoretical results by using numerical simulations. The effects of antiretroviral drug therapy and time delay on the virus dynamics are also studied. We have shown that the time delay has a similar effect as the antiretroviral drug therapy.