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This paper study the dynamical behavior of HIV-1 infection model with saturated virus-target and infected-target incidences. 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. The nonnegativity and boundedness of the solutions of the model as well as global stability of the steady states are studied. The global stability are established using Lyapunov method. 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]

In this paper, we propose and analyze an HIV dynamics model. The model can be seen as a generalization of many HIV dynamics models presented in the literature since it incorporates (i) two classes of target cells, CD4+ T cells and macrophages, (ii) two types of infected cells, short-lived infected cells and the long-lived chronically infected cells, (iii) intracellular discrete delays, (iv) reverse transcriptase inhibitors (RTIs) drugs with different drug efficacies on CD4+T cells and macrophages. The incidence rate of infection is represented by a general function. A bifurcation parameter, known as the basic reproduction number, R0 is derived. We established a set of conditions on the general function which are sufficient to determine the global dynamics of the model. Using Lyapunov functionals and LaSalle's invariance principle, the global asymptotic stability of the two equilibria of the model is obtained. An example is presented and some numerical simulations are conducted in order to illustrate the dynamical behavior. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze an HIV dynamics model. The model can be seen as a generalization of many HIV dynamics models presented in the literature since it incorporates (i) two classes of target cells, CD4+ T cells and macrophages, (ii) two types of infected cells, short-lived infected cells and the long-lived chronically infected cells, (iii) intracellular discrete delays, (iv) reverse transcriptase inhibitors (RTIs) drugs with different drug efficacies on CD4+T cells and macrophages. The incidence rate of infection is represented by a general function. A bifurcation parameter, known as the basic reproduction number, R0 is derived. We established a set of conditions on the general function which are sufficient to determine the global dynamics of the model. Using Lyapunov functionals and LaSalle's invariance principle, the global asymptotic stability of the two equilibria of the model is obtained. An example is presented and some numerical simulations are conducted in order to illustrate the dynamical behavior. [ABSTRACT FROM AUTHOR]

In this paper, we study the global properties of two mathematical models which describe the interaction of the human immunodeficiency virus (HIV) with two classes of target cells, CD4+ T cells and macrophages. The incidence rate of virus infection is given by the Crowley-Martin functional response. The first model has two types of discrete delays while the second one incorporates two types of distributed delays to describe the time needed for infection of cell and virus replication. The basic reproduction number R0 is identified which completely determines the global dynamics of the models. By constructing suitable Lyapunov functionals, we have proven that if R0 ≤ 1 then the uninfected steady state is globally asymptotically stable (GAS), and if R0 > 1 then the infected steady state exists and it is GAS. [ABSTRACT FROM AUTHOR]

In this paper, we study the global analysis of virus dynamics models with discrete delay and with distributed delay. The models describe the interaction of the HIV with two classes of target cells, CD4+ T cells and macrophages. The incidence rate of virus infection is given by the Beddington-DeAngelis functional response. The models have two types of discrete time delay or distributed delay describing the time needed for infection of cell and virus replication. The basic reproduction number R0 is identified which completely determines the global dynamics of the models. By constructing suitable Lyapunov functionals, we have proven that if R0 ≤ 1 then the uninfected steady state is globally asymptotically stable (GAS), and if R0 > 1 then the infected steady state exists and it is GAS. [ABSTRACT FROM AUTHOR]