Stability of HIV-1 infection with saturated virus-target and infected-target incidences and CTL immune response

This paper studies the dynamical behavior of an HIV-1 infection model with saturated virus-target and infected-target incidences with Cytotoxic T Lymphocyte (CTL) immune response. The model is incorporated by two types of intracellular distributed time delays. The model generalizes all the existing HIV-1 infection models with cell-tocell transmission presented in the literature by considering saturated incidence rate and the effect of CTL immune response. The existence and global stability of all steady states of the model are determined by two parameters, the basic reproduction number (R-0) and the CTL immune response activation number (R-1). By using suitable Lyapunov functionals, we show that if R-0 <= 1, then the infection-free steady state S-0 is globally asymptotically stable; if R-1 <= 1 < R-0, then the CTL-inactivated infection steady state S-1 is globally asymptotically stable; if R-1 > 1, then the CTL-activated infection steady state S-2 is globally asymptotically stable. Using MATLAB we conduct some numerical simulations to confirm our results. The effect of the saturated incidence of the HIV-1 dynamics is shown.