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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/472072 |
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| _version_ | 1832565169957371904 |
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| author | Yihong Li Jinxiao Pan Zhen Jin |
| author_facet | Yihong Li Jinxiao Pan Zhen Jin |
| author_sort | Yihong Li |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6ee82dc9924848dc92038d65d03a0c70 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-6ee82dc9924848dc92038d65d03a0c702025-02-03T01:08:59ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/472072472072Dynamic Modeling and Analysis of the Email Virus PropagationYihong Li0Jinxiao Pan1Zhen Jin2School of Information and Communication Engineering, North University of China, Taiyuan 030051, ChinaNational Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, ChinaDepartment of Mathematics, North University of China, Shanxi, Taiyuan, 030051, ChinaA 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.http://dx.doi.org/10.1155/2012/472072 |
| spellingShingle | Yihong Li Jinxiao Pan Zhen Jin Dynamic Modeling and Analysis of the Email Virus Propagation Discrete Dynamics in Nature and Society |
| title | Dynamic Modeling and Analysis of the Email Virus Propagation |
| title_full | Dynamic Modeling and Analysis of the Email Virus Propagation |
| title_fullStr | Dynamic Modeling and Analysis of the Email Virus Propagation |
| title_full_unstemmed | Dynamic Modeling and Analysis of the Email Virus Propagation |
| title_short | Dynamic Modeling and Analysis of the Email Virus Propagation |
| title_sort | dynamic modeling and analysis of the email virus propagation |
| url | http://dx.doi.org/10.1155/2012/472072 |
| work_keys_str_mv | AT yihongli dynamicmodelingandanalysisoftheemailviruspropagation AT jinxiaopan dynamicmodelingandanalysisoftheemailviruspropagation AT zhenjin dynamicmodelingandanalysisoftheemailviruspropagation |