具有免疫反应和细胞内时滞的病毒动态模型（英文）

Virus Dynamics Model with Immune Response and Intracellular Delay

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.

In this paper, we study the dynamical behavior of a virus model with immune response and intracellular delay. Through constructing Lyapunov funetionals 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.