global stability of hiv infection of cd4+ t cells and macrophages with ctl immune response and distributed delays

We study the global stability of a human immunodeficiency virus (HIV) infection model with Cytotoxic T Lymphocytes (CTL) immune response. The model describes the interaction of the HIV with two classes of target cells, CD4+ T cells and macrophages. Two types of distributed time delays are incorporated into the model to describe the time needed for infection of target cell and virus replication. Using the method of Lyapunov functional, we have established that the global stability of the model is determined by two threshold numbers, the basic reproduction number R0 and the immune response reproduction number R0∗. We have proven that, if R0≤1, then the uninfected steady state is globally asymptotically stable (GAS), if R0*≤11, then the infected steady state with CTL immune response is GAS.