具有非线性传染率和时滞的随机SIQR计算机病毒模型的渐近行为  

Asymptotic Behavior of a Stochastic SIQR Computer Virus Model with Nonlinear Incidence Rate and Time Delay

作　　者：王彬 王晓云 WANG Bin;WANG Xiao-yun(College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《数学的实践与认识》2020年第6期171-181,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金青年项目(11801398)。

摘　　要：研究了一类具有非线性发生率和时滞的随机SIQR计算机病毒模型.首先证明了该系统具有唯一的全局正解,然后通过构造适当的Lyapunov函数并利用伊藤公式,分析了该模型的解在无病平衡点附近及地方病平衡点附近的渐近行为,最后通过数值模拟对随机系统解的渐近行为做了进一步的分析并给出了结论.In this paper,a stochastic SIQR computer virus model with nonlinear incidence and time delay is studied.Firstly,it is proved that the system has a unique global positive solution.Then by constructing an appropriate Lyapunov function and using the Ito formula,the asymptotic behavior of the solution of the model near the disease-free equilibrium point and the endemic equilibrium point is analyzed.Finally,the asymptotic behavior of the solution of stochastic system is further analyzed by numerical simulation and the conclusion is given.

关 键 词：非线性发生率 时滞 随机SIQR模型 LYAPUNOV函数 

分 类 号：TP309.5[自动化与计算机技术—计算机系统结构]