非连续免疫策略对计算机病毒SIR模型的影响

doi:10.3969/j.issn.0255-8297.2016.03.010

应用科学学报 ›› 2016, Vol. 34 ›› Issue (3): 329-338.doi: 10.3969/j.issn.0255-8297.2016.03.010

非连续免疫策略对计算机病毒SIR模型的影响

张道祥, 李迅

安徽师范大学数学计算机科学学院, 安徽芜湖 241002

收稿日期:2015-06-23 修回日期:2015-10-24 出版日期:2016-05-30 发布日期:2016-05-30
作者简介:张道祥,博士,副教授,研究方向应用数学及计算数学,E-mailzdxiang1012@sina.com
基金资助:
国家自然科学基金青年项目基金(No.11302002)资助

Impact of Discontinuous Immunity on SIR Computer Virus Model

ZHANG Dao-xiang, LI Xun

School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241002, Anhui Province, China

Received:2015-06-23 Revised:2015-10-24 Online:2016-05-30 Published:2016-05-30

摘要/Abstract

摘要：

研究一类具有非连续免疫策略的计算机病毒模型.运用微分包含的相关知识,给出了该模型的Filippov解的定义,证明了该非连续模型的平衡点存在唯一性.通过计算得到了模型基本再生数R₀,通过构造合适的Lyapunov函数,证明了当R₀>1时,满足初始条件的每一个解都在有限时间内全局收敛于地方平衡点;当R₀<1时,同样的方法可以证明模型的解在有限时间内收敛于无病平衡点.利用MATLAB软件进行数值模拟,验证了理论结果的正确性.

关键词: 计算机病毒, 非连续免疫策略, 有限时间全局收敛

Abstract:

This paper studies the impact of discontinuous immunity on global dynamics of a computer virus model. Using differential inclusion, we define the solution of Filippov, and study existence and uniqueness of equilibrium. We get the basic reproduction number R₀ by calculation. By constructing a Lyapunov function, we show that all solutions converge to disease equilibrium in a finite time when R₀ > 1. Similarly, all solutions converge to free disease equilibrium in a finite time when R₀ < 1. Numerical simulations are carried out to illustrate and expand the theoretical results.

Key words: computer virus, global convergence in finite time, discontinuous immune strategy

中图分类号:

张道祥, 李迅. 非连续免疫策略对计算机病毒SIR模型的影响[J]. 应用科学学报, 2016, 34(3): 329-338.

ZHANG Dao-xiang, LI Xun. Impact of Discontinuous Immunity on SIR Computer Virus Model[J]. Journal of Applied Sciences, 2016, 34(3): 329-338.

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非连续免疫策略对计算机病毒SIR模型的影响

Impact of Discontinuous Immunity on SIR Computer Virus Model

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