[1]李 迅,王星星,张道祥.非连续免疫对非线性计算机病毒模型的影响[J].南京师范大学学报(工程技术版),2016,16(04):061.[doi:10.3969/j.issn.1672-1292.2016.04.011]
 Li Xun,Wang Xingxing,Zhang Daoxiang.Impact of Discontinuous Immune on Computer Virus Modelwith Nonlinear Vaccination Probability[J].Journal of Nanjing Normal University(Engineering and Technology),2016,16(04):061.[doi:10.3969/j.issn.1672-1292.2016.04.011]
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非连续免疫对非线性计算机病毒模型的影响
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南京师范大学学报(工程技术版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
16卷
期数:
2016年04期
页码:
061
栏目:
计算机与信息工程
出版日期:
2016-12-31

文章信息/Info

Title:
Impact of Discontinuous Immune on Computer Virus Modelwith Nonlinear Vaccination Probability
文章编号:
1672-1292(2016)04-0061-08
作者:
李 迅1王星星2张道祥3
(1.南京卫生学校,江苏 南京 210038)(2.合肥师范学院生命科学学院,安徽 合肥 230009)(3.安徽师范大学数学计算机科学学院,安徽 芜湖 241002)
Author(s):
Li Xun1Wang Xingxing2Zhang Daoxiang3
(1.Nanjing Health School,Nanjing 210038,China)(2.College of Life Science,Hefei Normal University,Hefei 230009,China)(3.Department of Mathematics and Computer Science,Anhui Normal University,Wuhu 241002,China)
关键词:
非连续免疫计算机病毒有限时间全局稳定
Keywords:
discontinuous immunecomputer virusglobal stability in finite time
分类号:
TP309.5; O175.15
DOI:
10.3969/j.issn.1672-1292.2016.04.011
文献标志码:
A
摘要:
研究了一类具有非连续免疫策略的非线性传染SIR计算机病毒模型. 运用右端不连续函数性质及微分包含相关知识,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. 通过计算得到模型的基本再生数R0,通过构造合适的Lyapunov函数及运用Lasalle不变集原理,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收敛于有病平衡点; 当R0<1时,相同的方法可证明模型的解都在有限时间内收敛于无病平衡点. 运用Matlab软件进行了数值模拟,验证了理论结果的正确性.
Abstract:
This paper mainly studies the impact of discontinuous immunity on global dynamics of nonlinear vaccination computer virus model. By using the right hang discontinuity and the knowledge of differential inclusion,we define the solution of Filippov,and prove the existence and uniqueness of equilibrium. We obtain the basic reproduction number R0 by calculation. By constructing Lyapunov function and using LaSalle invariant set principle,we show that solutions are all convergence to the disease equilibrium infinite time when R0>1. Similarly,we can also demonstrate that solutions are all convergence to the free disease equilibrium in finite time when R0<1. Numerical simulations are carried out to illustrate and expand the theoretical results.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2015-11-16.
基金项目:国家自然科学基金(11302002).
通讯联系人:张道祥,博士研究生,副教授,研究方向:应用数学,计算数学. E-mail:1123676642@qq.com
更新日期/Last Update: 2016-12-31