Global properties of a delayed HIV infection model with CTL immune response

In this paper, we study a delayed six-dimensional human immunodeficiency virus (HIV) model with Cytotoxic T Lymphocytes (CTLs) immune response. Our model describes the interaction of HIV with two target cells: CD4+ T cells and macrophages. We derive that the global asymptotic attractivity of the model is completely determined by the basic reproduction number R0R0 and the immune reproduction number R0∗ for the viral infection. By constructing Lyapunov functionals, we have shown that the infection-free equilibrium E0E0, the immune-free equilibrium E1E1 and the chronic-infection equilibrium E2E2 are globally asymptotically attractive when R0⩽1,R0∗⩽1R0∗>1, respectively.