In this paper, the global stability of virus dynamics model with Beddington-DeAngelis infection rate and CTL immune response is studied by constructing Lyapunov functions. We derive the basic reproduction number R 0 and the immune response reproduction number R 0 for the virus infection model, and establish that the global dynamics are completely determined by the values of R 0 . We obtain the global stabilities of the disease-free equilibrium E 0 , immunefree equilibrium E 1 and endemic equilibrium E * when R 0 ≤ 1, R 0 > 1, R 0 > 1, respectively.

In this paper, a mathematical model for HIV-1 infection with intracellular delay and Beddington-DeAngelis functional response is investigated. We obtain a necessary and sufficient condition for the global stability of the infection-free equilibrium and give some sufficient conditions for the local stability of the infected equilibrium.

The stability of infections disease model with CTL immune response in vivo is considered in this paper. Explicit Lyapunov functions for our dynamics model with CTL immune response with nonlinear incidence of the form βVqTpfor the case q ≤ 1 are introduced, and global properties of the model are thereby established.