Global properties of the virus dynamics model with antibody and CTL immune responses

In this paper, we present the virus model with antibody and CTL immune responses. For the model, five threshold parameters are defined, which determine the dynamical behaviors of the model. We prove that, if R₀₁≤1, then the disease-free equilibrium is globally asymptotically stable and the disease eventually disappears; if R₀₁>;1, R₀₂ ≤1 and R₀₃ ≤1, then the immune-free equilibrium is globally asymptotically stable; if R₀₂>;1 and R´₀₄ ≤1, the CTL-dominant equilibrium is globally asymptotically stable; if R₀₃>;1 and R´₀₄ ≤1, the antibody-dominant equilibrium is globally asymptotically stable; if R´₀₄ >;1 and R₀₄ >;1, the positive equilibrium is globally asymptotically stable. This global asymptotic stability of the equilibria is established by using appropriate Lyapunov functions.