Dynamic Modeling and Analysis of the Email Virus Propagation

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 t...

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Bibliographic Details
Published inDiscrete Dynamics in Nature and Society Vol. 2012; no. 2012; pp. 168 - 189-112
Main Authors Li, Yi-Hong, Pan, Jinxiao, Jin, Zhen
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2012
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Computer viruses
Distribution
Dynamic programming
China
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Summary: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.
ISSN:1026-0226
1607-887X
DOI:10.1155/2012/472072