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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, a mathematical model is formulated to investigate the dynamics of HIV infection. The model incorporates two routes of infection (namely cell-to-cell transmission and virus-to-cell infection), two types of adaptive immune responses (i.e., cellular and antibody immune response) and two intracellular delays (viz., the eclipse phase and virus production period). By constructing Lyapunov functionals, we show that the global dynamics of the model can be explicitly determined by five reproduction numbers. Using the uncertainty and sensitivity analyses, we obtain the mean values and standard deviation of the five reproduction numbers and find that the reproduction numbers are most sensitive to the death rate of infected cells, viral clearance rate and immune parameters. We further compare four related HIV models and show that cell-to-cell transmission, immune responses and time delays can substantially affect the dynamical behavior of the system. Specifically, cell-to-cell transmission increases the concentration of infected cells. Inclusion of cytotoxic T lymphocyte and virus production delay can significantly reduce the viral load and infected cell concentration, and generate a higher level of uninfected CD4+ T cells. The analytical and numerical results may help to improve the understanding of HIV dynamics. [ABSTRACT FROM AUTHOR]

Virus can disseminate between uninfected target cells via two modes, namely, the diffusion-limited cell-free viral spread and the direct cell-to-cell transfer using virological synapses. To examine how these two viral infection modes impact the viral dynamics, in this paper, we propose and analyze a general viral infection model that incorporates these two viral infection modes. The model also includes nonlinear target-cell dynamics, infinitely distributed intracellular delays, nonlinear incidences, and concentration-dependent clearance rates. It is shown that the numbers of secondly infected cells through the cell-free infection mode and the cell-to-cell infection mode both contribute to the basic reproduction number. Under some reasonable assumptions, the model exhibits a global threshold dynamics: the infection is cleared out if the basic reproduction number is less than one and the infection persists if the basic reproduction number is larger than one. Two specific examples are provided to illustrate that our theoretical results cover and improve some existing ones. When the underlying assumptions are not satisfied, oscillations via global Hopf bifurcation can be observed. A brief simulation of two-parameter bifurcation analysis is given to explore the joint impacts on viral dynamics for the interplay between nonlinear target-cell dynamics and intracellular delays. [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]