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This paper develops a mathematical model to investigate the Human Immunodeficiency Virus (HIV) infection dynamics. The model includes two transmission modes (cell-to-cell and cell-free), two adaptive immune responses (cytotoxic T-lymphocyte (CTL) and antibody), a saturated CTL immune response, and latent HIV infection. The existence and local stability of equilibria are fully characterized by four reproduction numbers. Through sensitivity analyses, we assess the partial rank correlation coefficients of these reproduction numbers and identify that the infection rate via cell-to-cell transmission, the number of new viruses produced by each infected cell during its life cycle, the clearance rate of free virions, and immune parameters have the greatest impact on the reproduction numbers. Additionally, we compare the effects of immune stimulation and cell-to-cell spread on the model's dynamics. The findings highlight the significance of adaptive immune responses in increasing the population of uninfected cells and reducing the numbers of latent cells, infected cells, and viruses. Furthermore, cell-to-cell transmission is identified as a facilitator of HIV transmission. The analytical and numerical results presented in this study contribute to a better understanding of HIV dynamics and can potentially aid in improving HIV management strategies. [ABSTRACT FROM AUTHOR]

This paper investigates the stochastic HTLV-I infection model with CTL immune response, and the corresponding deterministic model has two basic reproduction numbers. We consider the nonlinear CTL immune response for the interaction between the virus and the CTL immune cells. Firstly, for the theoretical needs of system dynamical behavior, we prove that the stochastic model solution is positive and global. In addition, we obtain the existence of ergodic stationary distribution by stochastic Lyapunov functions. Meanwhile, sufficient condition for the extinction of the stochastic system is acquired. Reasonably, the dynamical behavior of deterministic model is included in our result of stochastic model when the white noise disappears. [ABSTRACT FROM AUTHOR]

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-to-cell 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 () and the CTL immune response activation number (). By using suitable Lyapunov functionals, we show that if , then the infection-free steady state is globally asymptotically stable; if , then the CTL-inactivated infection steady state is globally asymptotically stable; if , then the CTL-activated infection steady state 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. [ABSTRACT FROM AUTHOR]