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This paper proposes and analyzes a CTL-mediated HIV infection model. The susceptible CD4+T cells can be infected when they are contacted by one of the following: (i) free HIV particles, (ii) silent infected cells, and (iii) actively infected cells. The effect of saturation infection has been incorporated in the second model. The model is an improvement of an existing HIV infection models which have neglected the infection due to incidence between the silently infected cells and susceptible CD4+T cells. We first show that the models are well-posed. Each of our proposed models has three equilibria, namely: HIV-free equilibrium, Ð0, chronic HIV infection equilibrium with inactive CTL-mediated immune response, Ð1, chronic HIV infection equilibrium with active CTL-mediated immune response, Ð2. We derive two threshold parameters, the basic HIV reproduction number, <0, and the CTL-mediated immunity reproduction number, <1. These parameters determine the existence and global stability of the equilibria of the model. We prove the global asymptotic stability of all equilibria by utilizing the Lyapunov function and LaSalle’s invariance principle. We have proven the following: (i) if <0 6 1, then Ð0 is globally asymptotically stable (G.A.S), (ii) if <1 6 1 < <0, then Ð1 is G.A.S, and (iii) if <1 > 1, then Ð2 is G.A.S. We have illustrated the theoretical results via numerical simulations. We have studied the effects of cell-to-cell (CTC) transmission and saturation on the dynamical behaviour of the system. We have shown that inclusion of CTC transmission decreases the concentration of susceptible CD4+ T cells and increases the concentrations of infected cells and free HIV particles. While the inclusion of saturation increases the concentration of susceptible CD4+ T cells and reduces the concentrations of infected cells and free HIV particles.

Stability of a CTL-mediated immunity HIV infection models with silent infected cells and cellular infection