| 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 |
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| 引用本文： | 王彬,王晓云.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[J].数学的实践与认识,2020(6):171-181. |
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| 作者姓名： | 王彬 王晓云 |
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| 作者单位： | 太原理工大学数学学院 |
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| 基金项目： | 国家自然科学基金青年项目(11801398)。 |
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| 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.
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| 关 键 词： | 非线性发生率 时滞 随机SIQR模型 LYAPUNOV函数 |
Asymptotic Behavior of a Stochastic SIQR Computer Virus Model with Nonlinear Incidence Rate and Time Delay |
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| WANG Bin,WANG Xiao-yun.Asymptotic Behavior of a Stochastic SIQR Computer Virus Model with Nonlinear Incidence Rate and Time Delay[J].Mathematics in Practice and Theory,2020(6):171-181. |
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| Authors: | WANG Bin WANG Xiao-yun |
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| Institution: | (College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China) |
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| Abstract: | 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. |
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| Keywords: | nonlinear incidence rate time delay stochastic SIQR model Lyapunov function |
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