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In the literature, several mathematical models have been formulated and developed to describe the within-host dynamics of either human immunodeficiency virus (HIV) or human T-lymphotropic virus type I (HTLV-I) monoinfections. In this paper, we formulate and analyze a novel within-host dynamics model of HTLV-HIV coinfection taking into consideration the response of cytotoxic T lymphocytes (CTLs). The uninfected CD 4 + T cells can be infected via HIV by two mechanisms, free-to-cell and infected-to-cell. On the other hand, the HTLV-I has two modes for transmission, (i) horizontal, via direct infected-to-cell touch, and (ii) vertical, by mitotic division of active HTLV-infected cells. It is well known that the intracellular time delays play an important role in within-host virus dynamics. In this work, we consider six types of distributed-time delays. We investigate the fundamental properties of solutions. Then, we calculate the steady states of the model in terms of threshold parameters. Moreover, we study the global stability of the steady states by using the Lyapunov method. We conduct numerical simulations to illustrate and support our theoretical results. In addition, we discuss the effect of multiple time delays on stability of the steady states of the system. [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]

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]