Analysis of mathematical model of HIV-1 infection of CD4+ T cells with CTL response and antiretroviral treatment

Abstract

A mathematical model is developed to capture the spread of HIV-1 infection within host cells caused by the contact of cell to cell and CTL response. In this paper, we propose a mathematical model of HIV-1 infection in CD4+T cells taking into account viral transmission from cell to cell and CTL response. The HIV transmission from cell to cell is one of the main factor in the spread of HIV infection and CTL response determines viral set point. We analyse the model to investigate the existence and stability of the equilibria. We analyse the local stability of disease free equilibrium by linearization, while the global stability of endemic equilibrium of the system by constructing Lyapunov function. Numerical simulations are presented to find the effectiveness of antiretroviral treatment in different scenarios and to the implication of CTL response in controlling the progression of HIV-1 infection.