Abstract
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 R 0 ⩽ 1 , the HIV infection is cleared from the T-cells population; if R 0 > 1 , the HIV infection persists. Further, the existence of a non-trivial periodic solution is also studied by means of numerical simulation.
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