About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 531781, 13 pages
http://dx.doi.org/10.1155/2013/531781
Research Article

The Influence of User Protection Behaviors on the Control of Internet Worm Propagation

1National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China
2Department of Mathematics, North University of China, Taiyuan 030051, China
3Department of Computer Science and Technology, North University of China, Taiyuan 030051, China

Received 6 May 2013; Revised 21 July 2013; Accepted 21 July 2013

Academic Editor: Yanni Xiao

Copyright © 2013 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. D. M. Kienzle and M. C. Elder, “Recent worms: a survey and trends,” in Proceedings of the 2003 ACM Workshop on Rapid Malcode (WORM '03), pp. 1–10, ACM, New York, NY, USA, October 2003. View at Scopus
  2. O. A. Toutonji, S.-M. Yoo, and M. Park, “Stability analysis of VEISV propagation modeling for network worm attack,” Applied Mathematical Modelling, vol. 36, no. 6, pp. 2751–2761, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. X. Fan and Y. Xiang, “Modeling the propagation of Peer-to-Peer worms,” Future Generation Computer Systems, vol. 26, no. 8, pp. 1433–1443, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. X. Yang and L.-X. Yang, “Towards the epidemiological modeling of computer viruses,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 259671, 11 pages, 2012. View at Publisher · View at Google Scholar
  5. L.-X. Yang, X. Yang, J. Liu, Q. Zhu, and C. Gan, “Epidemics of computer viruses: s complex-network approach,” Applied Mathematics and Computation, vol. 219, no. 16, pp. 8705–8717, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  6. Q. Zhu, X. Yang, L.-X. Yang, and C. Zhang, “Optimal control of computer virus under a delayed model,” Applied Mathematics and Computation, vol. 218, no. 23, pp. 11613–11619, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  7. C. C. Zou, W. Gong, and D. Towsley, “Code red worm propagation modeling and analysis,” in Proceedings of the 9th ACM Conference on Computer and Communications Security, pp. 138–147, ACM, New York, NY, USA, November 2002. View at Scopus
  8. X. Yang, B. K. Mishra, and Y. Liu, “Theory, model, and methods,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 473508, 2 pages, 2012. View at Publisher · View at Google Scholar
  9. W. Yu, X. Wang, A. Champion, D. Xuan, and D. Lee, “On detecting active worms with varying scan rate,” Computer Communications, vol. 34, no. 11, pp. 1269–1282, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. Y.-H. Choi, L. Li, P. Liu, and G. Kesidis, “Worm virulence estimation for the containment of local worm outbreak,” Computers and Security, vol. 29, no. 1, pp. 104–123, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. L.-X. Yang and X. Yang, “Propagation behavior of virus codes in the situation that infected computers are connected to the internet with positive probability,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 693695, 13 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. X. Zheng, T. Li, and Y. Fang, “Strategy of fast and light-load cloud-based proactive benign worm countermeasure technology to contain worm propagation,” The Journal of Supercomputing, vol. 62, pp. 1451–1479, 2012.
  13. M. E. J. Newman, “Spread of epidemic disease on networks,” Physical Review E, vol. 66, no. 1, Article ID 016128, 11 pages, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  14. L.-X. Yang and X. Yang, “The spread of computer viruses under the influence of removable storage devices,” Applied Mathematics and Computation, vol. 219, no. 8, pp. 3914–3922, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  15. C. C. Zou, D. Towsley, and W. Gong, “Email virus propagation modeling and analysis,” Tech. Rep. TR-CSE-03-04, University of Massachusettes, Amherst, Mass, USA, 2003.
  16. G. Chen and R. S. Gray, “Simulating non-scanning worms on peer-to-peer networks,” in Proceedings of the 1st International Conference on Scalable Information Systems (InfoScale '06), pp. 1–13, Hong Kong, June 2006. View at Publisher · View at Google Scholar · View at Scopus
  17. 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, no. 2, pp. 106–118, 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. C. Gan, X. Yang, W. Liu, Q. Zhu, and X. Zhang, “Propagation of computer virus under human intervention: a dynamical model,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 106950, 8 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  19. X. Sun, Y.-H. Liu, J.-Q. Zhu, and F.-P. Li, “Research on simulation and modeling of social network worm propagation,” Chinese Journal of Computers, vol. 34, no. 7, pp. 1252–1261, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. H. Yuan and G. Chen, “Network virus-epidemic model with the point-to-group information propagation,” Applied Mathematics and Computation, vol. 206, no. 1, pp. 357–367, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. L. Feng, X. Liao, Q. Han, and L. Song, “Modeling and analysis of peer-to-peer botnets,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 865075, 18 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. L.-P. Song, X. Han, D.-M. Liu, and Z. Jin, “Adaptive human behavior in a two-worm interaction model,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 828246, 13 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. O. Diekmann, J. A. P. Heesterbeek, and J. A. J. Metz, “On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations,” Journal of Mathematical Biology, vol. 28, no. 4, pp. 365–382, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. R. M. Anderson and R. M. May, Infectious Diseases of Humans, Oxford University, Oxford, UK, 1991.
  25. J. Carr, Applications of Center Manifold Theory, Springer, New York, NY, USA, 1981.
  26. L. Perko, Differential Equations and Dynamical Systems, vol. 7 of Texts in Applied Mathematics, Springer, New York, NY, USA, 3rd edition, 2001. View at MathSciNet
  27. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, vol. 2 of Texts in Applied Mathematics, Springer, New York, NY, USA, 1990. View at MathSciNet
  28. L. Arriola and J. Hyman, Forward and Adjoint Sensitivity Analysis: With Applications in Dynamical Systems, Lecture Notes in Linear Algebra and Optimisation, Mathematical and Theoretical Biology Institute, 2005.
  29. A. Zeitoun and S. Jamin, “Rapid Exploration of Internet Live Address Space Using Optimal Discovery Path,” in Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '03), pp. 2885–2890, San Francisco, Calif, USA, December 2003. View at Scopus
  30. 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 · View at MathSciNet
  31. Q. Zhu, X. Yang, and J. Ren, “Modeling and analysis of the spread of computer virus,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 12, pp. 5117–5124, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. B. K. Mishra and S. K. Pandey, “Effect of anti-virus software on infectious nodes in computer network: a mathematical model,” Physics Letters A, vol. 376, pp. 2389–2393, 2012.
  33. L.-X. Yang, X. Yang, L. Wen, and J. Liu, “A novel computer virus propagation model and its dynamics,” International Journal of Computer Mathematics, vol. 89, no. 17, pp. 2307–2314, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. C. Gan, X. Yang, W. Liu, and Q. Zhu, “A propagation model of computer virus with nonlinear vaccination probability,” Communications in Nonlinear Science and Numerical Simulation. View at Publisher · View at Google Scholar
  35. L.-X. Yang, X. Yang, Q. Zhu, and L. Wen, “A computer virus model with graded cure rates,” Nonlinear Analysis: Real World Applications, vol. 14, no. 1, pp. 414–422, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  36. A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier, Qualitative Theory of Second-Order Dynamical Systems, John Wiley & Sons, New York, NY, USA, 1973.
  37. 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. View at MathSciNet