Skip to main content

Advertisement

SpringerLink
Log in

SIRA Computer Viruses Propagation Model: Mortality and Robustness

  • Technical Note
  • Published:
International Journal of Applied and Computational Mathematics Aims and scope Submit manuscript

Abstract

Among the several works based on the classical Kermack–Mckendrick’s SIR (Susceptible–Infected–Removed) epidemiological model, applied to the context of computer viruses propagation, the introduction of antidotal elements has provided the dynamics of the networks when anti-virus programs are used. The SIRA (Susceptible–Infected–Removed–Antidotal) model has shown good qualitative fitness regarding to real operation of the networks, when the mortality rate is considered zero and all the infected nodes being recovered. Here, the SIRA model is studied, considering the mortality rate as a parameter and the conditions for the existence of a disease-free equilibrium state are derived, helping the design of robust networks.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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

References

  1. Amador, J.: The stochastic SIRA model for computer viruses. Appl. Math. Comput. 232, 1112–1124 (2014)

    MathSciNet  MATH  Google Scholar 

  2. Amador, J., Artalejo, J.R.: Stochastic modeling of computer virus spreading with warning signals. J. Frankl. Inst. 350, 1112–1138 (2013)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  4. Cohen, F.: A short course of computer viruses. Comput. Secur. 8, 149–160 (1990)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  6. Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamic Systems and Bifurcation of Vector Fields. Springer, New York (1983)

    Book  Google Scholar 

  7. Kemar, U.: Stochastic model on computer virus. Int. J. Syst. Signal Control Eng. Appl. 4(4–6), 74–79 (2011)

    Google Scholar 

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

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

  10. Kephart, J.O., White, S.R., Chess, D.M.: Computers and epidemiology. IEEE Spectr. 30, 20–26 (1993)

    Article  Google Scholar 

  11. Kermack, W., Mckendrick, A.: Contributions of mathematical theory to epidemics. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. A115, 700–721 (1927)

    Article  Google Scholar 

  12. Kermack, W., Mckendrick, A.: Contributions of mathematical theory to epidemics. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. A38, 55–83 (1932)

    Article  Google Scholar 

  13. Kermack, W., Mckendrick, A.: Contributions of mathematical theory to epidemics. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. A141, 94–122 (1933)

    Article  Google Scholar 

  14. Mishra, B.K., Jha, N.: SEIQRS model for the transmission of malicious objects in computer network. Appl. Math. Comput. 34, 710–715 (2010)

    MathSciNet  MATH  Google Scholar 

  15. Mishra, B.K., Keshri, N.: Mathematical model on the transmission of worms in wireless sensor network. Appl. Math. Comput. 37, 4103–4111 (2013)

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  17. Mishra, A.K., Verma, M., Sharma, A.: Capturing the interplay between malware and anti-malware in a computer network. Appl. Math. Comput. 229, 340–349 (2014)

    MATH  Google Scholar 

  18. Moler, C.B.: Numerical Computing with MATLAB. SIAM, Philadelphia (2004)

    Book  Google Scholar 

  19. Murray, J.D.: Mathematical Biology, 3rd edn. Springer, New York (2002)

    MATH  Google Scholar 

  20. Peng, S., Yu, S., Yang, A.: Smartphone malware and its propagation modeling: a survey. IEEE Commun. Surv. Tutor. 16(2), 925–941 (2014)

    Article  Google Scholar 

  21. Piqueira, J.R.C., Navarro, B.F., Monteiro, L.H.A.: Epidemiological models applied to viruses in computer networks. J. Comput. Sci. 1(1), 31–34 (2005)

    Article  Google Scholar 

  22. 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), 355–359 (2008)

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  24. Wang, Y., Wen, S., Xiang, Y., Zhou, W.: Modeling the propagation of worms in networks: a survey. IEEE Commun. Surv. Tutor. 16(2), 942–960 (2014)

    Article  Google Scholar 

  25. Weiss, G.H., Dishon, M.: On the asymptotic behavior of the stochastic and deterministic models of an epidemic. Math. Biosci. 11, 261–265 (1971)

    Article  MathSciNet  Google Scholar 

  26. Yang, L.-X., Yang, X., Wu, Y.: The impact of patch forwarding on the prevalence of computer virus: a theoretical assessment approach. Appl. Math. Model. 43, 110–125 (2017)

    Article  MathSciNet  Google Scholar 

  27. Yang, L.-X., Yang, X., Tang, Y.Y.: A bi-virus competing spreading model with generic infection rates. IEEE Trans. Netw. Sci. Eng. 5(1), 2–13 (2018)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Escola Politécnica da Universidade de São Paulo, Av. Prof. Luciano Gualberto, tv. 3-158, São Paulo, SP, Brazil

    Cristiane Mileo Batistela & José Roberto Castilho Piqueira

Authors
  1. Cristiane Mileo Batistela
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. José Roberto Castilho Piqueira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to José Roberto Castilho Piqueira.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this article.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Batistela, C.M., Piqueira, J.R.C. SIRA Computer Viruses Propagation Model: Mortality and Robustness. Int. J. Appl. Comput. Math 4, 128 (2018). https://doi.org/10.1007/s40819-018-0561-3

Download citation

  • Published:

  • DOI: https://doi.org/10.1007/s40819-018-0561-3

Keywords

Mathematics Subject Classification

Search

Navigation