Global stability and periodic solution of a model for HIV infection of CD4+ T cells

It is well-known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with non-linear infection rate. The global dynamics of this model is rigorously established. We prove that, if the basic reproduction number R0⩽1R0⩽1, the HIV infection is cleared from the T-cells population; if R0>1R0>1, the HIV infection persists. Further, the existence of a non-trivial periodic solution is also studied by means of numerical simulation.