JCP 2014 Vol.9(10): 2420-2427 ISSN: 1796-203X
doi: 10.4304/jcp.9.10.2420-2427
doi: 10.4304/jcp.9.10.2420-2427
Stability Analysis of a SEIQRS Model with Graded Infection Rates for Internet Worms
Fangwei Wang1, Fang Yang2, Yunkai Zhang3, Jianfeng Ma1
1School of Telecommunications Engineering, Xidian University, Xi’an, China
2Department of science and technology, Hebei Vocational College of Public Security Police, Shijiazhuang, China
3Department of Information Engineering, Shijiazhuang Institute of Railway Technology, Shijiazhuang, China
Abstract—Internet worms have drawn a significant attention owing to their enormous threats to the Internet infrastructure and services. In order to effectively defend against them, this paper proposes a novel epidemic SEIQRS model with graded infection rates for Internet worms. Using this SEIQRS model, we obtain the basic reproduction number for determining whether the worm dies out completely. The global stabilities of worm-free equilibrium and endemic equilibrium are proved, and determined by the basic reproduction number. The impact of different parameters of this model is studied. Simulation results show that the number of susceptible and infected hosts are consistent with theoretical analysis. The model provides a theoretical foundation for control and forecasting for Internet worms.
Index Terms—network security, Internet worm, stability analysis, endemic equilibrium, basic reproduction number
2Department of science and technology, Hebei Vocational College of Public Security Police, Shijiazhuang, China
3Department of Information Engineering, Shijiazhuang Institute of Railway Technology, Shijiazhuang, China
Abstract—Internet worms have drawn a significant attention owing to their enormous threats to the Internet infrastructure and services. In order to effectively defend against them, this paper proposes a novel epidemic SEIQRS model with graded infection rates for Internet worms. Using this SEIQRS model, we obtain the basic reproduction number for determining whether the worm dies out completely. The global stabilities of worm-free equilibrium and endemic equilibrium are proved, and determined by the basic reproduction number. The impact of different parameters of this model is studied. Simulation results show that the number of susceptible and infected hosts are consistent with theoretical analysis. The model provides a theoretical foundation for control and forecasting for Internet worms.
Index Terms—network security, Internet worm, stability analysis, endemic equilibrium, basic reproduction number
Cite: Fangwei Wang, Fang Yang, Yunkai Zhang, Jianfeng Ma, "Stability Analysis of a SEIQRS Model with Graded Infection Rates for Internet Worms," Journal of Computers vol. 9, no. 10, pp. 2420-2427, 2014.
General Information
ISSN: 1796-203X
Abbreviated Title: J.Comput.
Frequency: Bimonthly
Abbreviated Title: J.Comput.
Frequency: Bimonthly
Editor-in-Chief: Prof. Liansheng Tan
Executive Editor: Ms. Nina Lee
Abstracting/ Indexing: DBLP, EBSCO, ProQuest, INSPEC, ULRICH's Periodicals Directory, WorldCat,etc
E-mail: jcp@iap.org
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