The stability of a worm propagation model with time delay on homogeneous networks

There has been a constant barrage of worms over the internet during the recent past. To develop appropriate tools for thwarting quick spread of worms, researchers are trying to understand the behavior of the worm propagation with the aid of epidemiological models. In this study, an improved SIR epidemic model with dynamic input-output and time delay property is proposed. Whereas in the SIR model once a node is cured after infection it becomes permanently immune, we assume this immunity to be temporary, since the cured nodes may again become infected, maybe with a different strain of the same worm. So we obtain a differential system with time delay. Based on homogeneous networks the dynamics of this model are analyzed in detail, where global stability of equilibriums of the model is studied in this paper.

[1]  Y. Moreno,et al.  Epidemic outbreaks in complex heterogeneous networks , 2001, cond-mat/0107267.

[2]  Alessandro Vespignani,et al.  Epidemics and immunization in scale‐free networks , 2002, cond-mat/0205260.

[3]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[4]  Jeffrey O. Kephart,et al.  Directed-graph epidemiological models of computer viruses , 1991, Proceedings. 1991 IEEE Computer Society Symposium on Research in Security and Privacy.

[5]  Alessandro Vespignani,et al.  Epidemic dynamics and endemic states in complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  J. Frauenthal.  Mathematical Modeling in Epidemiology , 1980 .

[7]  Alessandro Vespignani,et al.  Immunization of complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Vern Paxson,et al.  How to Own the Internet in Your Spare Time , 2002, USENIX Security Symposium.

[9]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[10]  David Bawden,et al.  Book Review: Evolution and Structure of the Internet: A Statistical Physics Approach. , 2006 .

[11]  Kevin A. Kwiat,et al.  Modeling the spread of active worms , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[12]  R. May,et al.  How Viruses Spread Among Computers and People , 2001, Science.

[13]  Donald F. Towsley,et al.  Code red worm propagation modeling and analysis , 2002, CCS '02.