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In several publications, the dynamical system of HIV and HTLV mono-infections taking into account diffusion, as well as latently infected cells in cellular transmission has been mathematically analyzed. However, no work has been conducted on HTLV/HIV co-infection dynamics taking both factors into consideration. In this paper, a partial differential equations (PDEs) model of HTLV/HIV dual infection was developed and analyzed, considering the cells' and viruses' spatial mobility. CD 4 + T cells are the primary target of both HTLV and HIV. For HIV, there are three routes of transmission: free-to-cell (FTC), latent infected-to-cell (ITC), and active ITC. In contrast, HTLV transmits horizontally through ITC contact and vertically through the mitosis of active HTLV-infected cells. In the beginning, the well-posedness of the model was investigated by proving the existence of global solutions and the boundedness. Eight threshold parameters that determine the existence and stability of the eight equilibria of the model were obtained. Lyapunov functions together with the Lyapunov–LaSalle asymptotic stability theorem were used to investigate the global stability of all equilibria. Finally, the theoretical results were verified utilizing numerical simulations. [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 construct an HIV infection model which includes latent infection, logistic growth for healthy CD4 T-cells, and antiretroviral therapy. We obtain the global asymptotic stability of the uninfected equilibrium by constructing a Lyapunov function, and we give a sufficient condition for the local asymptotic stability of the infected equilibrium. We also use the latin hypercube sampling technique to identify the key parameters in determining the stability of the infected equilibrium. By numerical simulations, we observe that the model without logistic growth would underestimate the number of infectious virions, while the model without latent infection would overestimate the number of infectious virions. [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]

The purpose of this paper is to investigate the qualitative behavior of HIV dynamics models with immune impairment. The HIV particles infect both CD4+ T cells and macrophages. Both latently and actively infected cells are incorporated into the models. The models consider multiple discrete or distributed delays to characterize the time between an HIV contact of an uninfected target cell and the creation of mature HIV. The existence and global stability of the steady states are determined by the basic reproduction number. The global stability analysis of the steady states is performed using Lyapunov method. We solve the system of delay differential equations numerically to support the theoretical results. [ABSTRACT FROM AUTHOR]