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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 472072, 22 pages
http://dx.doi.org/10.1155/2012/472072
Research Article

Dynamic Modeling and Analysis of the Email Virus Propagation

1School of Information and Communication Engineering, North University of China, Taiyuan 030051, China
2National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China
3Department of Mathematics, North University of China, Shanxi, Taiyuan, 030051, China

Received 22 March 2012; Accepted 10 June 2012

Academic Editor: Delfim F. M. Torres

Copyright © 2012 Yihong Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A novel deterministic SEIS model for the transmission of email viruses in growing communication networks is formulated. Interestingly, the model is different from classical SEIS models not only in the form, but also in the dynamical features. We study the equilibria and their stability and analyse the bifurcation dynamics of the model. In particular, we find that the virus-free equilibrium is locally asymptotically stable for any parameter values, which may attribute to the absence of the basic reproduction number. It is shown that the model undergoes a saddle-node bifurcation and admits the bistable phenomenon. Moreover, on the basis of the Lyapunov function, the domains of attraction of equilibria are estimated by solving an LMI optimization problem. Based on the above theoretical results, some effective strategies are also provided to control the propagation of the email viruses. Additionally, our results are confirmed by numerical simulations.