Global threshold dynamics in a five-dimensional virus model with cell-mediated, humoral immune responses and distributed delays
Global threshold dynamics in a five-dimensional virus model with cell-mediated, humoral immune responses and distributed delays
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DOI：
10.1016/j.amc.2014.05.015
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发表时间：
2014-08-15
影响因子：
4
通讯作者：
Enatsu, Yoichi
中科院分区：
文献类型：
--
作者：
Wang, Jinliang;Pang, Jingmei;Enatsu, Yoichi
在本文中，我们研究了一个具有免疫应答和细胞内延迟的五维病毒模型的动力学，该模型描述了HIV病毒、CD4细胞和ctl在宿主内的相互作用，该模型是对现有模型的改进，通过加入(i)两个反映病毒侵入细胞时间方差和被入侵病毒粒子在细胞内繁殖时间方差的分布式核；（ii）病毒感染的非线性发生率函数f，以及（iii）抗体反应，由免疫活性B淋巴细胞的功能实现，在预防和调节感染方面发挥关键作用。通过构建Lyapunov泛函和对这些Lyapunov泛函衍生物的精细估计，我们表明模型的全局动态是由病毒感染R-0、CTL免疫应答R-1、抗体免疫应答R-2、CTL免疫竞争R-3和抗体免疫竞争R-4的繁殖数决定的。模型的全局稳定性排除了长时间内Hopf分岔等复杂动力学行为的存在。为了说明其动力学特性，还进行了数值模拟。(C) 2014爱思唯尔公司版权所有。
In this paper, we investigate the dynamics of a five-dimensional virus model with immune responses and an intracellular delay which describes the interactions of the HIV virus, CD4 cells and CTLs within host, which is an improvement of some existing models by incorporating (i) two distributed kernels reflecting the variance of time for virus to invade into cells and the variance of time for invaded virions to reproduce within cells; (ii) a nonlinear incidence function f for virus infections, and (iii) antibody responses, which are implemented by the functioning of immunocompetent B lymphocytes, play a critical role in preventing and modulating infections. By constructing Lyapunov functionals and subtle estimates of the derivatives of these Lyapunov functionals, we show that the global dynamics of the model is determined by the reproductive numbers for viral infection R-0, for CTL immune response R-1, for antibody immune response R-2, for CTL immune competition R-3 and for antibody immune competition R-4. The global stability of the model precludes the existence of Hopf bifurcation and other complex dynamical behaviors in long time. Numerical simulations are also performed in order to illustrate the dynamical behavior. (C) 2014 Elsevier Inc. All rights reserved.