Analysis Of Viral Infection Dynamic Models With Saturated Immune Responses

In this paper, considering the effect of immune saturation, we develop a virus dynamics model with the immune saturation and an intracellular time delay and an HIV dynamical model with CTL immune saturation. The dynamical properties with their biological meanings are stud-ied. The relevant knowledge of virus infection and immunity, the recent study of viral dynamics and some basic theories are introduced in Chapter1.In Chapter2, a five-dimensional virus dynamics model is studied, which incorporates sat-uration effects of immune responses and an intracellular time delay. We study the global stability analysis of this model. We introduce the reproductive numbers for viral infection, for CTL immune response, for antibody immune response, for antibody invasion and for CTL immune invasion. With the aid of persistence theory and Lyapunov method, it is shown that the global stability of the model is totally determined by these reproductive numbers. When R0≤1, the infection-free equilibrium E0is globally asymptotically stable; when R0>1,R1≤1and R2≤1, the immune-free infection equilibrium E1is globally asymptotically stable; when R1>1and R4≤1, the infection equilibrium E2with only CTL immune response is globally asymptotically stable; when R2>1and R3<1, the infection equilibrium E3with only antibody immune re-sponse is globally asymptotically stable; when R3>1and R4>1, the infection equilibrium E4with both CTL response and antibody immune response is globally asymptotically stable. The results preclude the complicated behaviors such as the backward bifurcations and Hopf bifurca-tions which may be induced by saturation factors and a time delay.In Chapter3, an HIV dynamic model with CTL immune saturation is proposed. By con- structing a Lyapunov function, the infection-free equilibrium is shown to be globally asymp-totically stable. Using the symbolic computation method and the Hurwitz criterion, both the immune-free and the positive equilibria are proved to be locally asymptotically stable. More-over, we obtain that the immune-free infection equilibria is globally asymptotically stable by constructing a Lyapunov function.