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Latently infected CD 4 + T cells represent one of the major obstacles to HIV eradication even after receiving prolonged highly active anti-retroviral therapy (HAART). Long-term use of HAART causes the emergence of drug-resistant virus which is then involved in HIV transmission. In this paper, we develop mathematical HIV models with staged disease progression by incorporating entry inhibitor and latently infected cells. We find that entry inhibitor has the same effect as protease inhibitor on the model dynamics and therefore would benefit HIV patients who developed resistance to many of current anti-HIV medications. Numerical simulations illustrate the theoretical results and show that the virus and latently infected cells reach an infected steady state in the absence of treatment and are eliminated under treatment whereas the model including homeostatic proliferation of latently infected cells maintains the virus at low level during suppressive treatment. Therefore, complete cure of HIV needs complete eradication of latent reservoirs. [ABSTRACT FROM AUTHOR]

In this paper, a model of HIV infection taking into account cell-free and cell-to-cell transmissions is investigated under latency. The viral production rate of infectious CD4 T cells and the activation rate of latently infected CD4 T cells play a major role in the evolution of the disease. A system of nonlinear differential equations is derived to capture the dynamics and systematically analyzed thanks to the spectral theory of dynamical systems and a Routh-Hurwitz criterion. In particular, numerical simulations will be performed in order to extract the critical epidemiological features of the solution. [ABSTRACT FROM AUTHOR]

HIV infection is one of the most serious causes of death throughout the world. CD4+ T cells which play an important role in immune protection, are the primary targets for HIV infection. The hallmark of HIV infection is the progressive loss in population of CD4+ T cells. However, the pathway causing this slow T cell decline is poorly understood [16]. This paper studies a discontinuous mathematical model for HIV-1 infection, to investigate the effect of pyroptosis on the disease. For this purpose, we use the theory of discontinuous dynamical systems. In this way, we can better analyze the dynamical behavior of the HIV-1 system. Especially, considering the dynamics of the system on its discontinuity boundary enables us to obtain more comprehensive results rather than the previous researches. A stability region for the system, corresponding to its equilibria on the discontinuity boundary, will be determined. In such a parametric region, the trajectories of the system will be trapped on the discontinuity manifold forever. It is also shown that in the obtained stability region, the disease can lead to a steady state in which the population of uninfected T cells and viruses will preserve at a constant level of cytokines. This means that the pyroptosis will be restricted and the disease cannot progress for a long time. Some numerical simulations based on clinical and experimental data are given which are in good agreement with our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce ordinary and delay differential equations to describe the interactions between a malignant tumour and the immune systemin vivoin the presence of human immunodeficiency virus (HIV) infection of CD4+T-cells. In the delay model, we take into account the time lags required by the healthy effector cell components to recognize the pathogens and tumour cells. The models consist of four populations: tumour cells, healthy effector cells (CD4+T-cells), effector cells infected by HIVs and free viral particles. The presence of delay term in the model leads to a notable increase in the complexity of the observed behaviour. We investigate the qualitative behaviour of the models and find the conditions that guarantee the asymptotic stability of the steady states. Numerical simulations are provided to illustrate and extend the theoretical results. The obtained results are consistent with the real phenomena and give a better understanding of cancer immunity and viral oncogenesis. [ABSTRACT FROM PUBLISHER]

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]

In this paper, neglecting the effects of free virus, we consider a simple model of cell-to-cell spread of HIV-1. We discuss the impact of the CD8+ cell non-cytotoxic anti-viral response (CNAR) and cytotoxic T lymphocyte (CTL) activity on infection by HIV-1. Two types of models are considered: the ordinary differential equation (ODE) model and the discrete time delay differential equation (DDE) system. The steady states of the ODE model are globally asymptotically stable respectively under two threshold criteria. In the DDE model, the global stability of the infected steady state of the ODE model becomes only ultimately stable. Moreover, at a certain interval of the time delay, the DDE model will produce Hopf bifurcation or periodic solutions. The introduction of CTL and CNAR will change the values of these steady states and induce fluctuations in the cell concentration. It also affects the critical value of the time delay and is of utility in the interpretation of typical HIV-dynamics data resulting from clinical trials. The DDE model produces sustained infective oscillations in some real parameter values, which is different from the result of the similar cell-free viral spread model with delay. [ABSTRACT FROM AUTHOR]

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]