In this paper, we study the global properties of a class of human immunodeficiency virus (HIV) models. The basic model is a 5-dimensional nonlinear ODEs that describes the interaction of the HIV with two target cells, CD4+ T cells and macrophages. An HIV model with exposed state and a model with nonlinear incidence rate are also analyzed. Lyapunov functions are constructed to establish the global asymptotic stability of the uninfected and infected steady states. We have proven that if the basic reproduction number R 0 is less than unity, then the uninfected steady state is globally asymptotically stable. If R 0 > 1 (or if the infected steady state exists), then the infected steady state is globally asymptotically stable. In a control system framework, we have shown that the HIV model incorporating the effect of Highly Active AntiRetroviral Therapy (HAART) is globally asymptotically controllable to the uninfected steady state.

Global properties of a class of HIV models

Global properties for virus dynamics model with Beddington–DeAngelis functional response

An HBV model with diffusion and time delay.

Global stability of an HIV-1 infection model with saturation infection and intracellular delay

The rate of infection in many virus dynamics models is assumed to be bilinear in the virus and uninfected target cells. In this paper, the dynamical behavior of a virus dynamics model with general incidence rate and cure rate is studied. Global dynamics of the model is established. We prove that the virus is cleared and the disease dies out if the basic reproduction number R 0 ≤ 1 while the virus persists in the host and the infection becomes endemic if R 0 > 1 .

Xinyu Song

Papers

Global stability and periodic solution of the viral dynamics