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首页> 外文期刊>Discrete dynamics in nature and society >Deterministic and Stochastic Study for an Infected Computer Network Model Powered by a System of Antivirus Programs
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Deterministic and Stochastic Study for an Infected Computer Network Model Powered by a System of Antivirus Programs

机译：由防病毒程序系统提供的受感染计算机网络模型的确定性和随机研究

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摘要

We investigate the various conditions that control the extinction and stability of a nonlinear mathematical spread model with stochastic perturbations. This model describes the spread of viruses into an infected computer network which is powered by a system of antivirus software. The system is analyzed by using the stability theory of stochastic differential equations and the computer simulations. First, we study the global stability of the virus-free equilibrium state and the virus-epidemic equilibrium state. Furthermore, we use the It? formula and some other theoretical theorems of stochastic differential equation to discuss the extinction and the stationary distribution of our system. The analysis gives a sufficient condition for the infection to be extinct (i.e., the number of viruses tends exponentially to zero).The ergodicity of the solution and the stationary distribution can be obtained if the basic reproduction number R_p is bigger than 1, and the intensities of stochastic fluctuations are small enough. Numerical simulations are carried out to illustrate the theoretical results.
机译：我们调查了控制非线性数学展开模型与随机扰动的灭绝和稳定性的各种条件。该模型描述了病毒传播到受感染的计算机网络中，该计算机网络由防病毒软件系统提供支持。通过使用随机微分方程的稳定性理论和计算机模拟来分析该系统。首先，我们研究了无病毒平衡状态和病毒流行均衡状态的全球稳定性。此外，我们使用它吗？随机微分方程的公式与其他理论理学，探讨我们系统的灭绝与静止分布。分析给出了灭绝的感染的充分条件（即，病毒的数量呈指数为零为零）。如果基本再现数R_P大于1，则可以获得溶液的遍历和静止分布，随机波动的强度足够小。进行数值模拟以说明理论结果。

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  • 作者

    Youness El Ansari; Ali El Myr; Lahcen Omari;

  • 作者单位

    Laboratory of Computer Sciences Modeling and Systems Department of Mathematics Faculty of Sciences Sidi Mohamed Ben Abdellah University Dhar-Mahraz BP 1796 Atlas Fez Morocco;

    Laboratory of Computer Sciences Modeling and Systems Department of Mathematics Faculty of Sciences Sidi Mohamed Ben Abdellah University Dhar-Mahraz BP 1796 Atlas Fez Morocco;

    Laboratory of Computer Sciences Modeling and Systems Department of Mathematics Faculty of Sciences Sidi Mohamed Ben Abdellah University Dhar-Mahraz BP 1796 Atlas Fez Morocco;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 数学模拟、近似计算;
  • 关键词

    Deterministic; Stochastic; Antivirus;

    机译：确定性;随机;抗病毒;

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