数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 49-61.doi: 10.1016/S0252-9602(15)30077-1

• 论文 • 上一篇    下一篇

STABILITY ANALYSIS OF A COMPUTER VIRUS PROPAGATION MODEL WITH ANTIDOTE IN VULNERABLE SYSTEM

Nguyen Huu KHANH   

  1. Department of Mathematics, College of Natural Sciences, Can Tho University, Vietnam
  • 收稿日期:2015-01-21 修回日期:2015-05-13 出版日期:2016-01-30 发布日期:2016-01-30
  • 通讯作者: Nguyen Huu KHANH,E-mail:nhkhanh@ctu.edu.vn E-mail:nhkhanh@ctu.edu.vn

STABILITY ANALYSIS OF A COMPUTER VIRUS PROPAGATION MODEL WITH ANTIDOTE IN VULNERABLE SYSTEM

Nguyen Huu KHANH   

  1. Department of Mathematics, College of Natural Sciences, Can Tho University, Vietnam
  • Received:2015-01-21 Revised:2015-05-13 Online:2016-01-30 Published:2016-01-30
  • Contact: Nguyen Huu KHANH,E-mail:nhkhanh@ctu.edu.vn E-mail:nhkhanh@ctu.edu.vn

摘要:

We study a proposed model describing the propagation of computer virus in the network with antidote in vulnerable system. Mathematical analysis shows that dynamics of the spread of computer viruses is determined by the threshold R0. If R0≤1, the virus-free equilibrium is globally asymptotically stable, and if R0>1, the endemic equilibrium is globally asymptotically stable. Lyapunov functional method as well as geometric approach are used for proving the global stability of equilibria. A numerical investigation is carried out to confirm the analytical results. Through parameter analysis, some effective strategies for eliminating viruses are suggested.

关键词: computer virus, virus-free equilibrium, endemic equilibrium, global stability, antidote

Abstract:

We study a proposed model describing the propagation of computer virus in the network with antidote in vulnerable system. Mathematical analysis shows that dynamics of the spread of computer viruses is determined by the threshold R0. If R0≤1, the virus-free equilibrium is globally asymptotically stable, and if R0>1, the endemic equilibrium is globally asymptotically stable. Lyapunov functional method as well as geometric approach are used for proving the global stability of equilibria. A numerical investigation is carried out to confirm the analytical results. Through parameter analysis, some effective strategies for eliminating viruses are suggested.

Key words: computer virus, virus-free equilibrium, endemic equilibrium, global stability, antidote

中图分类号: 

  • 93C15