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

Journal of Applied Sciences ›› 2016, Vol. 34 ›› Issue (3): 329-338.doi: 10.3969/j.issn.0255-8297.2016.03.010

• Computer Science and Applications • Previous Articles Next Articles

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

Abstract

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

CLC Number:

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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Impact of Discontinuous Immunity on SIR Computer Virus Model

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