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具有免疫反应和细胞内时滞的病毒动态模型

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本文研究了一类具有免疫反应和细胞内时滞的病毒动态学模型.通过构造李雅普诺夫函数和应用Lasalle不变原理,得到:模型的全局动力学行为是完全由基本的再生数决定的,并在一定条件下,无病平衡点和地方病平衡点是全局稳定的.我们的结果可以应用到许多发生率函数,如线性发生率函数、标准发生率函数,等等.最后,我们做了数值模拟来验证我们的理论分析并提出了控制病毒感染的方法.
Virus Dynamics Model with Immune Response and Intracellular Delay
In this paper,we study the dynamical behavior of a virus model with immune response and intracellular delay.Through constructing Lyapunov functionals and applying LaSalle invariance principle for delay differential equation,we conclude that the global dynamics are completely determined by the basic reproduction number,and under some assumptions,the disease-free equilibrium and the infection equilibrium are global stable.Our results can be applied to many possible incidence functions,such as linear incidence function,standard incidence function,and so on.Lastly,we perform numerical simulation to favor our theoretic analysis and provide necessary methods to control virus infection.

Virus dynamicsImmune responseIntracellular delayGlobal stabilityLyapunov functional

王晓静、王丹、崔景安、李泽妤

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北京建筑大学理学院,北京100044

北京工商大学嘉华学院,北京101118

病毒动态行为 免疫反应 细胞内时滞 全局稳定 李雅普诺夫函数

Supported by the National Natural Science Foundation of ChinaPlan Project of Science and Technology of Beijing Municipal Education Committeeand the Central Support Local Projects

11371048KM20161001601821147515602

2016

生物数学学报
中国数学会生物数学学会

生物数学学报

ISSN：1001-9626
年,卷(期)：2016.(4)
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