Virus Dynamics With Immune Responses And Intracellular Delay

In this paper, the virus dynamics with immune responses and intracellular delay are mainly studied in mathematics. We analyse the global dynamics of these models completely by con-structing Lyapunov function and Lyapunov functional.First, the properties of two virus dynamic models with CTL immune responses are studied. The two models imply that when the basic reproductive number R0< 1, the infection-free steady state is globally asymptotically stable. when R0>1, the trivial equilibriums lose stability, for the first model the infection steady state is globally asymptotically stable, and the second model is uniformly persistent.Second, the global properties of a virus dynamic model with intracellular delay and hu-moral immune responses are studied. We obtain that the dynamics of this model is completely determined by the basic reproductive number R0 and the humoral immune basic reproductive number R1, with R11, R1≤1 and R2≤1, the immune-free infected equi-librium is globally asymptotically stable; when R1>1 and R4≤1, the CTL immune infected equilibrium is globally asymptotically stable; when R2>1 and R3≤1, the antibody immune infected equilibrium is globally asymptotically stable; when R3>1 and R4>1, the CTL and the antibody immune infected equilibrium is globally asymptotically stable.