具有时滞的SIQR计算机病毒模型的稳定性分析

Stability Analysis of Delayed SIQR Computer Virus Model

建立一类具有非线性发生率和时滞的SIQR计算机病毒模型,得到决定病毒消失或继续存在的基本再生数.通过分析系统对应的特征方程,得到无病平衡点与地方平衡点的局部稳定性.通过构造适当的Lyapunov函数,利用La Salle不变原理,证明当基本再生数小于1时,无病平衡点是全局渐近稳定的。

In this paper, A delayed SIQR computer virus e model is proposed. the basic reproduction number is determining whether the disease dies is found, and the existence of the model is discussed. By analyzing the corresponding characteristic equation.the local stability of a disease-free equilibrium and endemic equilibrium are discussed. According to the suitable Lyapunov function and La Salle invariance principle, it is proved that the disease-free equilibrium is globally asymptotically stable as the basic reproduction number for viral infection is less than unity.