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In this paper, the dynamics of stochastic human T‐cell leukemia virus type I (HTLV‐I) infection model with cytotoxic T lymphocyte (CTL) immune response is investigated. First, we show that the stochastic model exists as a unique positive global solution originating from the positive initial value. Second, we demonstrate that the stochastic model is stochastically permanent and stochastically ultimately bounded for any positive initial value. Third, we establish sufficient conditions for the existence of ergodic stationary distribution of the stochastic model. Fourth, the threshold R0∗ between extinction and persistence of the virus is obtained. Finally, numerical simulations are carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a multidelayed in‐host HIV model to represent the interaction between human immunodeficiency virus and immune response. One delay was considered to incorporate the time required by the virus for various intracellular events to make a host cell productively infective, and the second delay was introduced to take into account the time required for adaptive immune system to respond against infection. We extensively analyzed this multidelayed model analytically and numerically. We show that delay may have both destabilizing and stabilizing effects even when the system contains a single immune response delay. It happens when there exists two sequences of critical values of this delay. If the system starts with stable state in absence of delay, then the smallest value of these critical delays causes instability and the next higher value causes stability. The system may also show stability switching for different values of the virus replication factor. These results demonstrate the possible reasons of intrapatients and interpatients variability of CD4+ T cells and virus counts in HIV‐infected patients. [ABSTRACT FROM AUTHOR]

We study a mathematical model of immune response by T cells where the regulatory T cells (Treg) inhibit interleukin 2 (IL‐2) secretion. We model the suppression of the autoimmune line of T cells after a different line of T cells responded to a pathogen infection. In this paper, we show that if the population of the pathogen responding line of T cells becomes large enough, the competition for IL‐2 and the increase in the death rates may lead to a depletion in the concentration of autoimmune T cells. Provided this lasts for a sufficiently long time, the concentration of autoimmune T cells can be brought down to values inside the basin of attraction of the controlled state, and autoimmunity can be suppressed. [ABSTRACT FROM AUTHOR]

In this paper, a humoral and cellular immunity virus dynamics model with the Beddington-DeAngelis incidence rate is set up. We derive the basic reproductive number R0, the cytotoxic T lymphocytes immune response reproductive number R1, the humoral immune response reproductive number R2, humoral immune response competitive reproductive number R3, and cytotoxic T lymphocytes immune response competitive reproductive number R4, and a full description of the relation between the existence of the equilibria and reproductive numbers is given. The global properties of the five equilibria are obtained by constructing Lyapunov functions. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]