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Dynamic behavior in a HIV infection model for the delayed immune response

Considering full Logistic proliferation of CD4+ T-cells and retarded immune response, we analyze a HIV model in this paper. Global asymptotic stability of the infection-free equilibrium and immune-absent equilibrium is investigated, and Some conditions for Hopf bifurcation around infected equilibrium to occur are also obtained. Numerical simulating are presented to illustrate the main results, and we can observe the effects of the proliferation rate of CD4+ T-cells for the dynamics of system. This results can explain the complexity of the immune state of AIDS.