Abstract
The mathematical model of the human immunodeficiency virus (HIV) pathogenesis with CTL (cytotoxic T lymphocytes) immune response and cure rate of infected cells is investigated. The model includes four nonlinear differential equations describing the evolution of uninfected cells, infected cells, free HIV viruses, and CTL immune response cells. The positivity and boundedness of solutions are established. The local stability for the disease-free steady state and for the infection steady states is studied. Finally, numerical simulations are performed to support our theoretical findings and to show the effectiveness of the cure rate in reducing the severity of the disease.
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