About this Journal Submit a Manuscript Table of Contents
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.

Linked References

  1. C. C. Zou, D. Towsley, and W. Gong, “Email virus propagation modeling and analysis,” Tech. Rep. TR-CSE-03-04, University of Massachusetts, Amherst, Mass, USA, 2003.
  2. C. Jin, J. Liu, and Q. H. Deng, “Network virus propagation model based on effects of removing time and user vigilance,” International Journal of Network Security, vol. 9, pp. 156–163, 2009.
  3. Virus Bulletin, http://www.virusbtn.com.
  4. National computer virus emergency response center: China's computer virus popular list, http://www.antivirus-china.org.cn/head/liebiao.htm.
  5. L.-P. Song, Z. Jin, G.-Q. Sun, J. Zhang, and X. Han, “Influence of removable devices on computer worms: dynamic analysis and control strategies,” Computers & Mathematics with Applications, vol. 61, no. 7, pp. 1823–1829, 2011. View at Publisher · View at Google Scholar
  6. J. Ren, X. Yang, Q. Zhu, L.-X. Yang, and C. Zhang, “A novel computer virus model and its dynamics,” Nonlinear Analysis, vol. 13, no. 1, pp. 376–384, 2012. View at Publisher · View at Google Scholar
  7. J. R. C. Piqueira, B.F. Navarro, and L.H.A. Monteiro, “Epidemiological models applied to virus in computer networks,” Journal of Computer Science, vol. 1, pp. 31–34, 2005.
  8. M. Draief, A. Ganesh, and L. Massoulié, “Thresholds for virus spread on networks,” Annals of Applied Probability, vol. 18, no. 2, pp. 359–378, 2008. View at Publisher · View at Google Scholar
  9. B. K. Mishra and D. Saini, “Mathematical models on computer viruses,” Applied Mathematics and Computation, vol. 187, no. 2, pp. 929–936, 2007. View at Publisher · View at Google Scholar
  10. J. Liu, Q.H. Deng, P.H. Xu, and X.D. Hu, “Email virus spreading model in the scale-free network,” IEEE Intelligent Computing and Intelligent Systems, vol. 3, pp. 303–306, 2010.
  11. C. C. Zou, D. Towsley, and W. Gong, “Modeling and simulation study of the propagation and defense of internet E-mail worms,” IEEE Transactions on Dependable and Secure Computing, vol. 4, pp. 105–118, 2007.
  12. Y. Hayashi, M. Minoura, and J. Matsukubo, “Oscillatory epidemic prevalence in growing scale-free networks,” Physical Review E, vol. 69, no. 1, Article ID 016112, 8 pages, 2004. View at Scopus
  13. M. E. J. Newman, S. Forrest, and J. Balthrop, “Email networks and the spread of computer viruses,” Physical Review E, vol. 66, no. 3, Article ID 035101, 4 pages, 2002. View at Publisher · View at Google Scholar
  14. J. Xiong, “ACT: attachment chain tracing scheme for eamil virus detection and control,” in Proceedings of the ACM Worhshop on Rapid Malcode, Washington, DC, USA, 2004.
  15. J. Liu, C. Gao, and N. Zhong, “Virus propagation and immunization strategies in email networks,” in Proceedings of the 5th International Conference on Advanced Data Mining and Applications (ADMA '09), vol. 5678 of Lecture Notes in Artificial Intelligence, pp. 222–233, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. C. Gao, J. Liu, and N. Zhong, “Network immunization and virus propagation in email networks: experimental evaluation and analysis,” Knowledge and Information Systems, vol. 27, no. 2, pp. 253–279, 2011. View at Scopus
  17. J. Carr, Applications of Centre Manifold Theory, vol. 35 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1981.
  18. L. Perko, Differential Equations and Dynamical Systems, vol. 7 of Texts in Applied Mathematics, Springer, New York, NY, USA, 3rd edition, 2001.
  19. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, vol. 2 of Texts in Applied Mathematics, Springer, Berlin, Germany, 1990.
  20. A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maĭer, Qualitative Theory of Second-Order Dynamic Systems, John Wiley & Sons, New York, NY, USA, 1973.
  21. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, vol. 42 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1983.
  22. Z. Zhang, J. Wu, Y. Suo, and X. Song, “The domain of attraction for the endemic equilibrium of an SIRS epidemic model,” Mathematics and Computers in Simulation, vol. 81, no. 9, pp. 1697–1706, 2011. View at Publisher · View at Google Scholar
  23. H. K. Khalil, Nonlinear Systems, Macmillan, New York, NY, USA, 1992.
  24. S. Balint, “Considerations concerning the manoeuvring of some physical systems,” Analele Universit tii din Timisoara. Seria Stiinte Matematice, vol. 23, no. 1-2, pp. 8–16, 1985.
  25. L. Hörmander, An Introduction to Complex Analysis in Several Variables, North-Holland, Princeton, NJ, USA, 1973.
  26. S. Balint, A. Balint, and V. Negru, “The optimal Liapunov function in diagonalizable case,” Analele Universit tii din Timisoara. Seria Stiinte Matematice, vol. 24, no. 1-2, pp. 1–7, 1986.
  27. E. Kaslik, A. M. Balint, and St. Balint, “Methods for determination and approximation of the domain of attraction,” Nonlinear Analysis, vol. 60, no. 4, pp. 703–717, 2005. View at Publisher · View at Google Scholar
  28. J. LaSalle and S. Lefschetz, Stability by Liapunov's Direct Method, with Applications, vol. 4 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1961.
  29. O. Hachicho, “A novel LMI-based optimization algorithm for the guaranteed estimation of the domain of attraction using rational Lyapunov functions,” Journal of the Franklin Institute, vol. 344, no. 5, pp. 535–552, 2007. View at Publisher · View at Google Scholar
  30. J. B. Lasserre, “Global optimization with polynomials and the problem of moments,” SIAM Journal on Optimization, vol. 11, no. 3, pp. 796–817, 2001. View at Publisher · View at Google Scholar
  31. J. B. Lasserre, “An explicit equivalent positive semidefinite program for nonlinear 0-1 programs,” SIAM Journal on Optimization, vol. 12, no. 3, pp. 756–769, 2002. View at Publisher · View at Google Scholar
  32. M. Fan, M. Y. Li, and K. Wang, “Global stability of an SEIS epidemic model with recruitment and a varying total population size,” Mathematical Biosciences, vol. 170, no. 2, pp. 199–208, 2001. View at Publisher · View at Google Scholar
  33. H. Wan and H. Zhu, “The backward bifurcation in compartmental models for West Nile virus,” Mathematical Biosciences, vol. 227, no. 1, pp. 20–28, 2010. View at Publisher · View at Google Scholar