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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]

Abstract: In this paper, we consider an HIV pathogenesis model including cure rate and the full logistic proliferation term of CD4+ T cells in healthy and infected populations. Let be the number of virus released by each productive infected CD4+ T cell. The critical number that ensures the existence of the positive equilibrium is obtained. We further show that if , then there exists a unique uninfected equilibrium point that is locally asymptotically stable. If , then the system is persistent and the only infected steady state is globally asymptotically stable in the feasible region. Numerical simulations are presented to illustrate the obtained main results. Moreover, we find that there exist periodic solutions when the infected steady state is unstable. [Copyright &y& Elsevier]

Abstract: It is well-known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with non-linear infection rate. The global dynamics of this model is rigorously established. We prove that, if the basic reproduction number , the HIV infection is cleared from the T-cells population; if , the HIV infection persists. Further, the existence of a non-trivial periodic solution is also studied by means of numerical simulation. [Copyright &y& Elsevier]

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]