Abstract
In this paper, we propose and study a diffusive HIV infection model with infected cells delay, virus mature delay, abstract function incidence rate and a virus diffusion term. By introducing the reproductive numbers for viral infection R0 and for CTL immune response number R1, we show that R0 and R1 act as threshold parameter for the existence and stability of equilibria. If R0≤1, the infection-free equilibrium E0 is globally asymptotically stable, and the viruses are cleared; if R1≤1<R0, the CTL-inactivated equilibrium E1 is globally asymptotically stable, and the infection becomes chronic but without persistent CTL response; if R1>1, the CTL-activated equilibrium E2 is globally asymptotically stable, and the infection is chronic with persistent CTL response. Next, we study the dynamic of the discreted system of our model by using non-standard finite difference scheme. We find that the global stability of the equilibria of the continuous model and the discrete model is not always consistent. That is, if R0≤1, or R1≤1<R0, the global stability of the two kinds model is consistent. However, if R1>1, the global stability of the two kinds model is not consistent. Finally, numerical simulations are carried out to illustrate the theoretical results and show the effects of diffusion factors on the time-delay virus model.
Highlights
IntroductionPublisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
In the past few years, host-virus dynamics models have been developed to explain the interactions between virus and target T cells, much attention has been given to the role of the immune response to human immunodeficiency virus (HIV) infection
Inspired by [16,23], in this paper, we extend the classic model of virus dynamics to a diffusive infection model with intracellular delay and cell-mediated immune response, with two delays and general nonlinear incidence rate, as follows
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. To help the body heal, cytotoxic T-lymphocyte effectors (CTLe) of the immune system will remove the infected cells to prevent further viral replications To model these extra dynamics, researchers have studied the model of viral interaction with CTL response [10,17]. In [18,19], researchers studied a mathematical model for HIV-1 infection with both intracellular delay and cell-mediated immune response: dx (t) dt = λ − dx ( t ) − βxv, dy(t). Inspired by [16,23] , in this paper, we extend the classic model of virus dynamics to a diffusive infection model with intracellular delay and cell-mediated immune response, with two delays and general nonlinear incidence rate, as follows.
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