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Mathematical Problems in Engineering
Volume 2014, Article ID 784684, 14 pages
http://dx.doi.org/10.1155/2014/784684
Research Article

Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses

1College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China
2Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Hong Kong
3Department of Mathematics, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar

Received 8 January 2014; Accepted 10 May 2014; Published 5 June 2014

Academic Editor: He Huang

Copyright © 2014 Chuandong 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. P. J. Denning, Computers under Attack: Intruders, Worms, and Viruses, Addison-Wesley, Reading, Mass, USA, 1990.
  2. F. Cohen, “A short course on computer viruses,” Computers and Security, vol. 8, pp. 149–160, 1990. View at Google Scholar
  3. L. Billings, W. M. Spears, and I. B. Schwartz, “A unified prediction of computer virus spread in connected networks,” Physics Letters A, vol. 297, no. 3-4, pp. 261–266, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. O. Kephart and S. R. White, “Measuring and modeling computer virus prevalence,” in Proceedings of the IEEE Computer Society Symposium on Research in Security and Privacy, pp. 2–15, Oakland, Calif, USA, May 1993. View at Publisher · View at Google Scholar · View at Scopus
  5. R. Perdisci, A. Lanzi, and W. Lee, “Classification of packed executables for accurate computer virus detection,” Pattern Recognition Letters, vol. 29, no. 14, pp. 1941–1946, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. Y. B. Kafai, “Understanding virtual epidemics: children's folk conceptions of a computer virus,” Journal of Science Education and Technology, vol. 17, no. 6, pp. 523–529, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. X. Han and Q. L. Tan, “Dynamical behavior of computer virus on Internet,” Applied Mathematics and Computation, vol. 217, no. 6, pp. 2520–2526, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. Xu and Z. E. Ma, “Stability of a delayed SIRS epidemic model with a nonlinear incidence rate,” Chaos, Solitons and Fractals, vol. 41, no. 5, pp. 2319–2325, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. W. Ma, M. Song, and Y. Takeuchi, “Global stability of an SIR epidemic model with time delay,” Applied Mathematics Letters, vol. 17, no. 10, pp. 1141–1145, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. C. J. Sun, Y. P. Lin, and M. A. Han, “Stability and Hopf bifurcation for an epidemic disease model with delay,” Chaos, Solitons and Fractals, vol. 30, no. 1, pp. 204–216, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. R. Xu, Z. E. Ma, and Z. P. Wang, “Global stability of a delayed SIRS epidemic model with saturation incidence and temporary immunity,” Computers and Mathematics with Applications, vol. 59, no. 9, pp. 3211–3221, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. S. J. Wang, Q. M. Liu, X. F. Yu, and Y. Ma, “Bifurcation analysis of a model for network worm propagation with time delay,” Mathematical and Computer Modelling, vol. 52, no. 3-4, pp. 435–447, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. X. Y. Shi, J. G. Cui, and X. Y. Zhou, “Stability and Hopf bifurcation analysis of an eco-epidemic model with a stage structure,” Nonlinear Analysis, vol. 74, no. 4, pp. 1088–1106, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. R. C. Piqueira and V. O. Araujo, “A modified epidemiological model for computer viruses,” Applied Mathematics and Computation, vol. 213, no. 2, pp. 355–360, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. J. R. C. Piqueira, B. F. Navarro, and L. H. A. Monteiro, “Epidemiological models applied to viruses in computer networks,” Journal of Computer Science, vol. 1, no. 1, pp. 31–34, 2005. View at Publisher · View at Google Scholar
  16. W. M. Liu, H. W. Hethcote, and S. A. Levin, “Dynamical behavior of epidemiological models with nonlinear incidence rates,” Journal of Mathematical Biology, vol. 25, no. 4, pp. 359–380, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J. Dieudonné, Foundations of Modern Analysis, Academic Press, New York, NY, USA, 1960. View at MathSciNet
  18. S. Ruan and J. Wei, “On the zeros of transcendental functions with applications to stability of delay differential equations with two delays,” Dynamics of Continuous, Discrete and Impulsive Systems A: Mathematical Analysis, vol. 10, no. 6, pp. 863–874, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. B. Hassard, D. Kazarino, and Y. Wan, Theory and Applications of Hopf Bifurcations, Cambridge University Press, Cambridge, UK, 1981.
  20. Z. C. Jiang and J. J. Wei, “Stability and bifurcation analysis in a delayed SIR model,” Chaos, Solitons and Fractals, vol. 35, no. 3, pp. 609–619, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. W. W. Yu and J. D. Cao, “Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with time delays,” Physics Letters A, vol. 351, no. 1-2, pp. 64–78, 2006. View at Publisher · View at Google Scholar · View at Scopus
  22. J. D. Cao and M. Xiao, “Stability and Hopf bifurcation in a simplified BAM neural network with two time delays,” IEEE Transactions on Neural Networks, vol. 18, no. 2, pp. 416–430, 2007. View at Publisher · View at Google Scholar · View at Scopus
  23. J. Q. Lu, J. He, J. D. Cao, and Z. Q. Gao, “Topology influences performance in the associative memory neural networks,” Physics Letters Section A, vol. 354, no. 5-6, pp. 335–343, 2006. View at Publisher · View at Google Scholar · View at Scopus
  24. J. Q. Lu, Z. D. Wang, J. D. Cao, D. C. Ho, and J. Kurths, “Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay,” International Journal of Bifurcation and Chaos, vol. 22, no. 7, Article ID 1250176, 2012. View at Publisher · View at Google Scholar · View at Scopus