收稿日期: 2015-06-23
修回日期: 2015-10-24
网络出版日期: 2016-05-30
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
Received date: 2015-06-23
Revised date: 2015-10-24
Online published: 2016-05-30
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 . DOI: 10.3969/j.issn.0255-8297.2016.03.010
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.
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