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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]

The goal of this paper is to investigate the dynamical behavior of a general nonlinear delayed viral infection model with cytotoxic T lymphocyte (CTL) immune response. The intrinsic growth rate of uninfected hepatocytes, incidence rate of infection, removal rate of infected hepatocytes and capsids, production and removal rate of viruses, activation rate of CTLs, and decay rate of CTLs are given by general nonlinear functions with a set of conditions on these general nonlinear functions, which make the analysis of the model more difficult. The global threshold dynamics with respect to the reproduction numbers for viral infection R0 and for CTL immune response R1 have been presented by constructing suitable Lyapunov functionals. Numerical simulations are carried out for a model with specific forms of the general functions to confirm the theoretical results and show that both the numerical and theoretical results are consistent. [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]