| Summary: | 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-to-cell viral transmission. By constructing Lyapunov functionals, the global stability of three equilibria is obtained. More specifically, the infection-free equilibrium $E_{f}$ is globally asymptotically stable when the basic reproductive numbers $\mathcal{R}_{0} < 1$, implying that the virus can be eventually cleared; the infected equilibrium without immune response $E_{w}$ is globally asymptotically stable when the CTL immune response reproduction number $\mathcal{R}_{1}$ is less than one and $\mathcal{R}_{0}$ is greater than one, implying that the infection becomes chronic, but CTL immune response has not been established; the infected equilibrium with immune response $E_{c}$ is globally asymptotically stable when $\mathcal{R}_{1}>1$, 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.
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