Global dynamics of a novel multi-group model for computer worms

doi:10.1088/1674-1056/22/4/040204

Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (4): 40204-040204.doi: 10.1088/1674-1056/22/4/040204

Global dynamics of a novel multi-group model for computer worms

巩永旺^{a b}, 宋玉蓉^a, 蒋国平^a

a College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
b School of Information Engineering, Yancheng Institute of Technology, Yancheng 224051, China

收稿日期:2012-09-04 修回日期:2012-10-16 出版日期:2013-03-01 发布日期:2013-03-01
基金资助:
Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010526), the Six Projects Sponsoring Talent Summits of Jiangsu Province, China (Grant No. SJ209006), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103223110003), the Ministry of Education Research in the Humanities and Social Sciences Planning Fund of China (Grant No. 12YJAZH120), and the Graduate Student Innovation Research Project of Jiangsu Province, China (Grant Nos. CXLX11_-0417 and CXLX11_-0404).

Global dynamics of a novel multi-group model for computer worms

Gong Yong-Wang (巩永旺)^{a b}, Song Yu-Rong (宋玉蓉)^a, Jiang Guo-Ping (蒋国平)^a

a College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
b School of Information Engineering, Yancheng Institute of Technology, Yancheng 224051, China

Received:2012-09-04 Revised:2012-10-16 Online:2013-03-01 Published:2013-03-01
Contact: Gong Yong-Wang E-mail:gong_yw@126.com
Supported by:
Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010526), the Six Projects Sponsoring Talent Summits of Jiangsu Province, China (Grant No. SJ209006), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103223110003), the Ministry of Education Research in the Humanities and Social Sciences Planning Fund of China (Grant No. 12YJAZH120), and the Graduate Student Innovation Research Project of Jiangsu Province, China (Grant Nos. CXLX11_-0417 and CXLX11_-0404).

摘要/Abstract

摘要： In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multi-group SIQR (susceptible-infected-quarantined-removed) model is proposed for computer worms by explicitly considering anti-virus measures and the network infrastructure. Then, the basic reproduction number of worm R₀ is derived and the global dynamics of the model is established. It is shown that if R₀ is less than or equal to 1, the disease-free equilibrium is globally asymptotically stable and the worm dies out eventually, whereas, if R₀ is greater than 1, there exists one unique endemic equilibrium and it is globally asymptotically stable, thus the worm persists in the network. Finally, numerical simulations are given to illustrate the theoretical results.

关键词: computer worm, multi-group model, Lyapunov function, global dynamics

Abstract: In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multi-group SIQR (susceptible-infected-quarantined-removed) model is proposed for computer worms by explicitly considering anti-virus measures and the network infrastructure. Then, the basic reproduction number of worm R₀ is derived and the global dynamics of the model is established. It is shown that if R₀ is less than or equal to 1, the disease-free equilibrium is globally asymptotically stable and the worm dies out eventually, whereas, if R₀ is greater than 1, there exists one unique endemic equilibrium and it is globally asymptotically stable, thus the worm persists in the network. Finally, numerical simulations are given to illustrate the theoretical results.

Key words: computer worm, multi-group model, Lyapunov function, global dynamics

中图分类号: (Global analysis and analysis on manifolds)

02.40.Vh

89.20.Ff (Computer science and technology) 02.60.Lj (Ordinary and partial differential equations; boundary value problems)

巩永旺, 宋玉蓉, 蒋国平. Global dynamics of a novel multi-group model for computer worms[J]. Chin. Phys. B, 2013, 22(4): 40204-040204.

Gong Yong-Wang (巩永旺), Song Yu-Rong (宋玉蓉), Jiang Guo-Ping (蒋国平). Global dynamics of a novel multi-group model for computer worms[J]. Chin. Phys. B, 2013, 22(4): 40204-040204.

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Global dynamics of a novel multi-group model for computer worms

Global dynamics of a novel multi-group model for computer worms

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