Skip to main content
Log in

Propagation of computer virus under the influences of infected external computers and removable storage media

Modeling and analysis

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In reality, a portion of infected external computers could enter the Internet, and removable storage media could carry virus. To our knowledge, nearly all previous models describing the spread of computer virus ignore the combined impact of these two factors. In this paper, a new dynamical model is established based on these facts. A systematic analysis of the model is performed, and it is found that the unique (viral) equilibrium is globally asymptotically stable. Some simulation experiments are also made to justify the model. Finally, a result and some applicable measures for suppressing viral spread are suggested.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Kephart J.O., White S.R.: Directed-graph epidemiological models of computer viruses. In: Proceedings of the 1991 IEEE Symposium on Research in Security and Privacy, pp. 343–359 (1991)

  2. Cohen, F.: Computer viruses: theory and experiments. Comput. Secur. 6(1), 22–35 (1987)

    Article  Google Scholar 

  3. Murray, W.H.: The application of epidemiology to computer viruses. Comput. Secur. 7(2), 130–150 (1988)

    Article  Google Scholar 

  4. Billings, L., Spears, W.M., Schwartz, I.B.: A unified prediction of computer virus spread in connected networks. Phys. Lett. A 297(3–4), 261–266 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ren, J., Yang, X., Zhu, Q., Yang, L.X., Zhang, C.: A novel computer virus model and its dynamics. Nonlinear Anal. Real World Appl. 13, 376–384 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Zhu, Q., Yang, X., Ren, J.: Modeling and analysis of the spread of computer virus. Commun. Nonlinear Sci. Numer. Simul. 17(12), 5117–5124 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Mishra, B.K., Jha, N.: Fixed period of temporary immunity after run of anti-malicious software on computer nodes. Appl. Math. Comput. 190(2), 1207–1212 (2007)

    Article  MATH  Google Scholar 

  8. Han, X., Tan, Q.: Dynamical behavior of computer virus on Internet. Appl. Math. Comput. 217(6), 2520–2526 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ren, J., Yang, X., Yang, L.-X., Xu, Y., Yang, F.: A delayed computer virus propagation model and its dynamics. Chaos Solitons Fractals 45(1), 74–79 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Feng, L., Liao, X., Li, H., Han, Q.: Hopf bifurcation analysis of a delayed viral infection model in computer networks. Math. Comput. Model. 56(7–8), 167–179 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhu, Q., Yang, X., Yang, L.-X., Zhang, C.: Optimal control of computer virus under a delayed model. Appl. Math. Comput. 218(23), 11613–11619 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Gan C., Yang X., Liu W., Zhu Q., Zhang X.: Propagation of computer virus under human intervention: a dynamical model. Discret. Dyn. Nat. Soc. Article ID 106950 (2012)

  13. Gan, C., Yang, X., Liu, W., Zhu, Q., Zhang, X.: An epidemic model of computer viruses with vaccination and generalized nonlinear incidence rate. Appl. Math. Comput. 222(1), 265–274 (2013)

    Article  MathSciNet  Google Scholar 

  14. Gan, C., Yang, X., Liu, W., Zhu, Q.: A propagation model of computer virus with nonlinear vaccination probability. Commun. Nonlinear Sci. Numer. Simul. 19(1), 92–100 (2014)

    Article  MathSciNet  Google Scholar 

  15. Gan C., Yang X., Zhu Q.: Global stability of a computer virus propagation model with two kinds of generic nonlinear probabilities. Abstr. Appl. Anal. Article ID 735327 (2014)

  16. Yuan, H., Chen, G.: Network virus-epidemic model with the point-to-group information propagation. Appl. Math. Comput. 206(1), 357–367 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Yuan, H., Chen, G., Wu, J., Xiong, H.: Towards controlling virus propagation in information systems with point-to-group information sharing. Decis. Supp. Syst. 48(1), 57–68 (2009)

    Article  Google Scholar 

  18. Dong T., Liao X., Li H.: Stability and Hopf bifurcation in a computer virus model with multistate antivirus. Abstr. Appl. Anal. Article ID 841987 (2012)

  19. Mishra, B.K., Saini, D.K.: SEIRS epidemic model with delay for transmission of malicious objects in computer network. Appl. Math. Comput. 188(2), 1476–1482 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Mishra, B.K., Pandey, S.K.: Dynamic model of worms with vertical transmission in computer network. Appl. Math. Comput. 217(21), 8438–8446 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Mishra, B.K., Saini, D.K.: SEIQRS model for the transmission of malicious objects in computer network. Appl. Math. Model. 34(3), 710–715 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. Yang X., Yang L.-X.: Towards the epidemiological modeling of computer viruses. Discret. Dyn. Nat. Soc. Article ID 259671 (2012)

  23. Yang L.-X., Yang X., Wen L., Liu J.: Propagation behavior of virus codes in the situation that infected computers are connected to the Internet with positive probability. Discret. Dyn. Nat. Soc. Article ID 693695 (2012)

  24. Yang, L.-X., Yang, X., Wen, L., Liu, J.: A novel computer virus propagation model and its dynamics. Int. J. Comput. Math. 89(17), 2307–2314 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  25. Yang, L.-X., Yang, X.: The spread of computer viruses under the influence of removable storage devices. Appl. Math. Comput. 219(8), 3914–3922 (2012)

    Article  MathSciNet  Google Scholar 

  26. Yang, L.-X., Yang, X., Zhu, Q., Wen, L.: A computer virus model with graded cure rates. Nonlinear Anal. Real World Appl. 14(1), 414–422 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  27. Yang, L.-X., Yang, X., Liu, J., Zhu, Q., Gan, C.: Epidemics of computer viruses: a complex-network approach. Appl. Math. Comput. 219(16), 8705–8717 (2013)

  28. Gan, C., Yang, X., Liu, W., Zhu, Q., Jin, J., He, L.: The spread of computer virus under the effect of external computers. Nonlinear Dyn. 73(3), 1615–1620 (2013)

    Article  MATH  Google Scholar 

  29. Gan, C., Yang, X., Liu, W., Zhu, Q., Jin, J., He, L.: Propagation of computer virus both across the Internet and external computers: a complex-network approach. Commun. Nonlinear Sci. Numer. Simul. 19(1), 2785–2792 (2014)

    Article  MathSciNet  Google Scholar 

  30. Gan C., Yang X., Zhu Q., Jin J.: The combined impact of external computers and network topology on the spread of computer viruses. Int. J. Comput. Math. (2014) doi:10.1080/00207160.2014.888421

  31. Yang, L.-X., Yang, X.: The effect of infected external computers on the spread of viruses: a compartment modeling study. Phys. A 392(24), 6523–6535 (2013)

    Article  MathSciNet  Google Scholar 

  32. Zhu, Q., Yang, X., Yang, L.-X., Zhang, X.: A mixing propagation model of computer viruses and countermeasures. Nonlinear Dyn. 73(3), 1433–1441 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  33. Yang X., Mishra B.K., Liu Y.: Computer viruses: theory, model, and methods. Discret. Dyn. Nat. Soc. Article ID 473508 (2012)

  34. Zhang C., Zhao Y., Wu Y., Deng S.: A stochastic dynamic model of computer viruses. Discret. Dyn. Nat. Soc. Article ID 264874 (2012)

  35. Kephart J.O., White S.R.: Measuring and modeling computer virus prevalence. In: Proceedings of 1993 IEEE Symposium on Security and Privacy, pp. 2–15 (1993)

  36. Piqueira, J.R.C., de Vasconcelos, A.A., Gabriel, C.E.C.J., Araujo, V.O.: Dynamic models for computer viruses. Comput. Secur. 27(7–8), 355–359 (2008)

    Article  Google Scholar 

  37. Piqueira, J.R.C., Araujo, V.O.: A modified epidemiological model for computer viruses. Appl. Math. Comput. 213(2), 355–360 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  38. Toutonji, O.A., Yoo, S.-M., Park, M.: Stability analysis of VEISV propagation modeling for network worm attack. Appl. Math. Model. 36(6), 2751–2761 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  39. Thieme, H.R.: Asymptotically autonomous differential equations in the plane. Rocky Mt. J. Math. 24(1), 351–380 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  40. Robinson, R.C.: An Introduction to Dynamical System: Continuous and Discrete. Prentice Hall, Englewood Cliffs (2004)

    Google Scholar 

  41. http://green.wangminjie.cn/newsinfo-136730.html

  42. http://pcedu.pconline.com.cn/pingce/pingcesystem/1109/2527365_all.html

Download references

Acknowledgments

The authors are grateful to the anonymous reviewers for their valuable suggestions that have greatly improved the quality of this paper. This work is supported by Natural Science Foundation of China (Grant No. 10771227) and Doctorate Foundation of Educational Ministry of China (Grant No. 20110191110022).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiaofan Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gan, C., Yang, X. & Zhu, Q. Propagation of computer virus under the influences of infected external computers and removable storage media. Nonlinear Dyn 78, 1349–1356 (2014). https://doi.org/10.1007/s11071-014-1521-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1521-z

Keywords

Navigation