A New Virus-Antivirus Spreading Model

  • Bei Liu
  • Chuandong Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9377)


Indeed, countermeasures, as well as computer viruses, could spread in the network. This paper aims to investigate the effect of propagation of countermeasures on viral spread. For the purpose, a new virus-antivirus spreading model is proposed. The global asymptotic stability of the virus-free equilibrium is proved when the threshold is below the unity, and the existence of the viral equilibrium is shown when the threshold exceeds the unity. The influences of different model parameters on the threshold are also analyzed. Numerical simulations imply that the propagation of countermeasures contributes to the suppress of viruses, which is consistent with the fact.


computer virus countermeasures virus-antivirus spreading model equilibrium global asymptotic stability 


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  1. 1.
    Kephart, J.O., White, S.R.: Directed-graph epidemiological models of computer viruses. In: 1991 IEEE Computer Society Symposium on Security Privacy, pp. 343–359. IEEE Computer Society, Oakland (1991)CrossRefGoogle Scholar
  2. 2.
    Billings, L., Spears, W.M., Schwartz, I.B.: A unified prediction of computer virus spread in connected networks. Physics Letters A 297, 261–266 (2002)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ren, J., Yang, X., Zhu, Q., et al.: A novel computer virus model and its dynamics. Nonlinear Analysis: Real World Applications 13, 376–384 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Zhu, Q., Yang, X., Ren, J.: Modeling and analysis of the spread of computer virus. Communications in Nonlinear Science and Numerical Simulation 17, 5117–5124 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Gan, C., Yang, X., Liu, W., et al.: Propagation of computer virus under human intervention: a dynamical model. Discrete Dynamics in Nature and Society (2012)Google Scholar
  6. 6.
    Gan, C., Yang, X., Liu, W., et al.: A propagation model of computer virus with nonlinear vaccination probability. Communications in Nonlinear Science and Numerical Simulation 19(1), 92–100 (2014)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Yang, X., Yang, L.-X.: Towards the epidemiological modeling of computer viruses. Discrete Dynamics in Nature and Society (2012)Google Scholar
  8. 8.
    Yang, L.-X., Yang, X.: 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 (2012)Google Scholar
  9. 9.
    Zhu, Q., Yang, X., Yang, L.-X., et al.: A mixing propagation model of computer viruses and countermeasures. Nonlinear Dynamics 73(3), 1433–1441 (2013)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Yang, L.-X., Yang, X.: The effect of infected external computers on the spread of viruses: a compartment modeling study. Physica A: Statistical Mechanics and its Applications 392(24), 6523–6535 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Mishra, B.K., Jha, N.: Fixed period of temporary immunity after run of anti-malicious software on computer nodes. Applied Mathematics and Computation 190(2), 1207–1212 (2007)CrossRefGoogle Scholar
  12. 12.
    Mishra, B.K., Saini, D.K.: SEIRS epidemic model with delay for transmission of malicious objects in computer network. Applied Mathematics and Computation 188(2), 1476–1482 (2007)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Han, X., Tan, Q.: Dynamical behavior of computer virus on Internet. Applied Mathematics and Computation 217(6), 2520–2526 (2010)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Zhang, C., Zhao, Y., Wu, Y.: An impulse model for computer viruses. Discrete Dyn. Nat. Soc. (2012)Google Scholar
  15. 15.
    Zhang, C., Zhao, Y., Wu, Y., Deng, S.: A stochastic dynamic model of computer viruses. Discrete Dyn. Nat. Soc. (2012)Google Scholar
  16. 16.
    Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Physics Review Letters 86(14), 3200–3203 (2001)CrossRefGoogle Scholar
  17. 17.
    Chen, L.C., Carley, K.M.: The impact of countermeasure propagation on the prevalence of computer viruses. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 34(2), 823–833 (2004)CrossRefGoogle Scholar
  18. 18.
    Thieme, H.R.: Asymptotically autonomous differential equations in the plane. Rocky Mt. J. Math. (1994)Google Scholar
  19. 19.
    Robinson, R.C.: An Introduction to Dynamical System: Continuous and Discrete. American Mathematical Soc. (2004)Google Scholar

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© Springer International Publishing Switzerland 2015

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Authors and Affiliations

  • Bei Liu
    • 1
  • Chuandong Li
    • 1
  1. 1.College of Electronic and Information EngineeringSouthwest UniversityChongqingChina

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