The effects of CTL immune response on HIV infection model with potent therapy, latently infected cells and cell-to-cell viral transmission

Abstract

In this paper, a mathematical model is formulated to investigate the effect of cytotoxic T lymphocyte (CTL) immune response on human immunodeficiency virus (HIV) infection dynamics. The model includes latently infected cells, antiretroviral therapy, cell-free virus infection and cell-tocell viral transmission. By constructing Lyapunov functionals, the global stability of three equilibria is obtained. More specifically, the infection-free equilibrium Ef is globally asymptotically stable when the basic reproductive numbers R0 < 1, implying that the virus can be eventually cleared; the infected equilibrium without immune response Ew is globally asymptotically stable when the CTL immune response reproduction number R1 is less than one and R0 is greater than one, implying that the infection becomes chronic, but CTL immune response has not been established; the infected equilibrium with immune response Ec is globally asymptotically stable when R1 > 1, implying that the infection becomes chronic with persistent CTL immune response. Numerical simulations confirm the above theoretical results. Moreover, the inclusion of CTL immune response can generate a higher level of uninfected CD4+ T cells, and significantly reduce infected cells and viral load. These results may help to improve the understanding of HIV infection dynamics.