Threshold dynamics of a delayed virus infection model with cellular immunity and general nonlinear incidence

Abstract

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 ℜ 0 and for CTL immune response ℜ 1 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.

Stability of a general adaptive immunity virus dynamics model with multistages of infected cells and two routes of infection

“…The cell‐mediated immunity is based on cytotoxic T lymphocytes (CTLs) that kill the infected cells. Although some viral infection models with two ways of transmissions have been investigated under the effect of either cell‐mediated immune response or humoral immune response . However, in very recent works, both CTL cells and B cells have been incorporated into the viral infection models with two ways of transmissions.…”

“…Although some viral infection models with two ways of transmissions have been investigated under the effect of either cell‐mediated immune response or humoral immune response . However, in very recent works, both CTL cells and B cells have been incorporated into the viral infection models with two ways of transmissions. In the recent works, the production and removal rates of all compartments are given by specific forms as well as the viral and cellular infection rates.…”

“…However, in very recent works, both CTL cells and B cells have been incorporated into the viral infection models with two ways of transmissions. In the recent works, the production and removal rates of all compartments are given by specific forms as well as the viral and cellular infection rates. Besides, they have considered only one class of infected cells (actively infected cells).…”

Global dynamics of a general diffusive HBV infection model with capsids and adaptive immune response

“…However, the spatial mobility of viruses was ignored and the global stability of the equilibria was not analyzed. The production and death rates were given by linear functions which may not describe the real situation during the infection process [32]. The stimulation rates of immune cells and the removal rates were given by bilinear functions.…”

“…Also, the interaction between healthy cells and viruses was given by a bilinear incidence function. In fact, the bilinear incidence rate is not adequate to reflect the actual interaction between uninfected cells and viruses [8,32]. In addition, it indicates that the person with a larger liver is more sensitive to HBV than a person with a smaller liver size, which seems unrealistic [29,33].…”