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Recent studies demonstrate that resource competition is an essential component of T-cell proliferation in HIV progression, which can contribute instructively to the disease development. In this paper, we formulate an age-structured within-host HIV model, in the form of a hyperbolic partial differential equation (PDE) for infected target cells coupled with two ordinary differential equations for uninfected T-cells and the virions, to explore the effects of both the T-cell competition and viral shedding variations on the viral dynamics. The basic reproduction number is derived for a general viral production rate which determines the local stability of the infection-free equilibrium. Two special forms of viral production rates, which are extensively investigated in previous literature, the delayed exponential distribution and a step function rate, are further investigated, where the original system can be reduced into systems of delay differential equations. It is confirmed that there exists a unique positive equilibrium for two special viral production rates when the basic reproduction number is greater than one. However, the model exhibits the phenomenon of backward bifurcation, where two positive steady states coexist with the infection-free equilibrium when the basic reproduction number is less than one. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce fractional-order into a model of HIV infection of CD4+ T-cells. We show that the model established in this paper possesses non-negative solutions, as desired in any population dynamics. We also carry out a detailed analysis on the stability of equilibrium. Numerical simulations are presented to illustrate the results. [Copyright &y& Elsevier]

Based on some important biological meanings, we propose a class of HIV infection models incorporating both classical cell-free virus diffusion and direct cell-to-cell transmission. According to recent studies, the direct cell-to-cell transfer of HIV is a significantly more efficient mode of retroviral dissemination. In the first part of our analysis, we show that our model possesses non-negative solutions. Then, we derive sufficient conditions for the asymptotic stability of equilibriums. The analytical solutions are verified by simulation results. At the end of the paper, some important conclusions are given. [ABSTRACT FROM AUTHOR]

The mass action infection law, the most frequently used transmission process in the theoretical studies of disease dynamics, has been challenged in various ways. Hill type infection rate is supposed to be a better alternative to mass action law. In the first phase of this paper, we study a basic HIV model with Hill type infection rate. In the second phase, we modify our basic model with intracellular delay τ that measures the time between the first effective contact between a virus and a healthy CD4 + T cell and the latter becomes productively infective. Mathematical results like well-posedness, permanence, local stability and global stability of both the delayed and non-delayed systems are studied. It is observed that the endemic equilibrium is locally and globally asymptotically stable if the virus replication factor is greater than a threshold value and unstable otherwise. In the latter case, the disease-free steady state occurs and is proved to be globally asymptotically stable. Our simulation results shed different insights on drug therapy when various perturbations are given to the system. It is shown that multi-blockers drug therapy is more appropriate in the treatment of HIV patients in comparison to any mono-blocker drug therapy. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study a delayed six-dimensional human immunodeficiency virus (HIV) model with Cytotoxic T Lymphocytes (CTLs) immune response. Our model describes the interaction of HIV with two target cells: CD4+ T cells and macrophages. We derive that the global asymptotic attractivity of the model is completely determined by the basic reproduction number and the immune reproduction number for the viral infection. By constructing Lyapunov functionals, we have shown that the infection-free equilibrium , the immune-free equilibrium and the chronic-infection equilibrium are globally asymptotically attractive when and , respectively. [Copyright &y& Elsevier]

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: In this paper, the homotopy analysis method (HAM) is investigated to give an approximate solution of a model for HIV infection of CD4+ T-cells. This method allows for the solution of the governing differential equation to be calculated in the form of an infinite series with components which can be easily calculated. The HAM utilizes a simple method to adjust and control the convergence region of the infinite series solution by using an auxiliary parameter. The results obtained are presented, and six terms are sufficient to obtain an approximation solution that is very accurate. [Copyright &y& Elsevier]

Abstract: In this paper, a multi-step differential transform method (MsDTM) is performed to give approximate and analytical solutions of nonlinear fractional order ordinary differential equation systems such as a model for HIV infection of CD4+ T cells. The numerical solutions obtained from the proposed method indicate that the approach is easy to implement and accurate when applied to systems of fractional differential equations. Some figures are presented to show the reliability and simplicity of the methods. [Copyright &y& Elsevier]

The major pathway for HIV internalization in CD4+ T cells has been thought to be the direct fusion of virus and cell membranes, because the cell surface is the point of entry of infectious particles. However, the exact contribution of endocytic pathways to the infection of CD4+ T lymphocytes is unknown, and the mechanisms involved in endocytosis of HIV particles are unclear. Recent evidence suggests that endocytosis of cell-free and cell-associated virus particles could lead to effective virus entry and productive infections. Such observations have, in turn, spurred a debate on the relevance of endosomal entry as a mechanism of escape from the immune system and HIV entry inhibitors. In this paper, we review the endocytosis of HIV and discuss its role in HIV infection and pathogenesis. [ABSTRACT FROM AUTHOR]

Abstract: The capability of the HIV to persist latent inside CD4+ T-cells is currently regarded as a barrier to recovery from infection. On the other hand, immune activation, which is a normal immune reaction to pathogens, is now recognized as a key ingredient to sustaining the HIV caused infection. Further, it has been shown that activation of infected memory T-cells indirectly promotes apoptosis (programmed cell death) of bystander CD4+ and CD8+ T-cells. In this paper we use standard modeling techniques to develop a model compliant with the above mentioned mechanisms. Our farthest goal is to study how the long-term depletion of T-cells that characterizes HIV pathogenesis depends on these mechanisms. Consequently, we conduct parameter estimation, and apply standard results of sensitivity analysis and principal component analysis of the state variables with respect to the parameters. [ABSTRACT FROM AUTHOR]

Cortical F-actin plays important roles during HIV-1 infection. A recent paper in Cell highlights the involvement of F-actin in enhancing dendritic cell (DC)-mediated HIV-1 infection of T cells. Such a critical mechanism of HIV-1 trans -enhancement between human DCs and T cells had not been analyzed in molecular detail before this work. [ABSTRACT FROM AUTHOR]

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]

Effector T lymphocyte responses are considered critical for controlling human immunodeficiency virus type-1 (HIV-1) infection. The enzyme-linked immunospot (ELISpot) assay has emerged as a primary means of assessing HIV-specific T cell responses, and the development of objective methods that distinguish positive and negative ELISpot responses while properly controlling the rate of false positives is critical. In this paper, we consider several statistical methods that are helpful in defining such a positive criterion. Simulation results under a variety of scenarios suggest that a permutation-based criterion using a resampling adjustment for multiple comparisons yields the desired false positive rate while remaining competitive with other potential criteria in terms of sensitivity. These results also provide guidance on the effect of the number of experimental and negative control replicate wells on assay sensitivity. Application of different potential positive criteria using ELISpot assay results from IFN-γ-secreting T cells of HIV-1 seropositive and seronegative donors confirmed several of the results obtained under simulation. Our findings support the application of statistically-based positive criteria such as the permutation-based resampling approach in assessing HIV vaccine-induced T cell responses. Moreover, the proposed methods have potential utility in related HIV immunopathogenesis studies and in non-HIV clinical vaccine trials. [Copyright &y& Elsevier]

HIV-1 persistence in long-lived cellular reservoirs remains a major barrier to a cure. In a recent Nature Medicine paper, Buzon et al. identify memory T cells with stem cell-like properties (TSCM) that harbor infectious provirus and that likely contribute to HIV-1 persistence. [ABSTRACT FROM AUTHOR]