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In this paper, we propose an optimal control problem for an HIV infection model with cellular and humoral immune responses, logistic growth of uninfected cells, cell-to-cell spread, saturated infection, and cure rate. The model describes the interaction between uninfected cells, infected cells, free viruses, and cellular and humoral immune responses. We use two control functions in our model to show the effectiveness of drug therapy on inhibiting virus production and preventing new infections. We apply Pontryagin maximum principle to study these two control functions. Next, we simulate the role of optimal therapy in the control of the infection by numerical simulations and AMPL software. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes a CTL-mediated HIV infection model. The model describes the interaction between healthy CD4+T cells, silent infected cells, active infected cells, free HIV particles, and cytotoxic T lymphocytes (CTLs). The healthy CD4+T cells can be infected when contacted by one of the following: (i) free HIV particles, (ii) silent infected cells, and (iii) active infected cells. The incidence rates of the healthy CD4+T cells with free HIV particles, silent infected cells, and active infected cells are given by general functions. Moreover, the production/proliferation and removal/death rates of all compartments are represented by general functions. The model is an improvement of the existing HIV infection models which have neglected the incidence between the silent infected cells and healthy CD4+T cells. We first show that the model is well posed. The proposed model has three equilibria and their existence is governed by derived two threshold parameters: the basic HIV reproduction number ℜ 0 and the HIV-specific CTL-mediated immunity reproduction number ℜ 1 . Under a set of conditions on the general functions and the parameters ℜ 0 and ℜ 1 , we have proven the global asymptotic stability of all equilibria by using Lyapunov method. We have illustrated the theoretical results via numerical simulations. We have studied the effect of cell-to-cell (CTC) transmission on the dynamical behavior of the system. We have shown that inclusion of CTC transmission decreases the concentration of healthy CD4+T cells and increases the concentrations of infected cells and free HIV particles. [ABSTRACT FROM AUTHOR]

Abstract This paper studies a stochastic HIV-1 infection model with degenerate diffusion. The asymptotic dynamics of the stochastic model are shown to be governed by a threshold parameter. When the parameter is negative, the infection is predicted to go extinct exponentially while the level of healthy cells converges weakly to a unique invariant measure. When the threshold parameter is positive, the solution of the stochastic model converges polynomially to a unique invariant probability measure, indicating that the system admits a unique ergodic stationary distribution. Numerical simulations are conducted to show the analytical results. These results highlight the role of environmental noise in the spread of HIV-1. The method can also be applied to the non-degenerate systems. [ABSTRACT FROM AUTHOR]

Abstract: We develop and analyze a model for the interactions of T-cells, antigen presenting cells (APCs), and HIV-1. Our model consists of five components: APCs, resting helper T-cells, activated uninfected helper T-cells, activated and infected helper T-cells, and the free virus. We emphasize the impact of APCs during HIV infection and the cell-to-cell contact manner in the transference of HIV-1 in vivo. The existence and stability of the uninfected steady state and those of the infected steady states are discussed. The uniform persistence of the system is also obtained. As a novel approach, multiple exposures of HIV-1 are illustrated and discussed in the paper. Through numerical stimulations, we check the sensitivity of APCs and helper T-cells in impacting the infection outcome and obtain some relevant results. We also give the lowest infectioe dose for certain individuals. [Copyright &y& Elsevier]