Global Stability of a Delay-Distributed Human Immunodeficiency Virus Infection Model with Cytotoxic T Lymphocytes Immune Response and Crowley-Martin Functional Response

In this paper, we study the global properties of an human immunodeficiency virus (HIV) infection model with Cytotoxic T Lymphocytes (CTL) immune response. The model is a 6-dimensional that describes the interaction of the HIV with two classes of target cells, CD4⁺ T cells and macrophages. The infection rate is given by Crowley-Martin functional response. 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 R ₀ and the immune response reproduction number R ^* ₀. We have proven that if R ₀ ≤ 1, then the uninfected steady state is globally asymptotically stable (GAS), if R ^* ₀ ≤ 1 < R ₀, then the infected steady state without CTL immune response is GAS, and if R ^* ₀ > 1, then the infected steady state with CTL immune response is GAS.