Fuzzy VEISV Epidemic Propagation Modeling for Network Worm Attack

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 246)


An epidemic vulnerable—exposed—infectious—secured—vulnerable (VEISV) model for the fuzzy propagation of worms in computer network is formulated. In this paper, the comparison between classical basic reproduction number and fuzzy basic reproduction number is analyzed. Epidemic control strategies of worms in the computer network—low, medium, and high—are analyzed. Numerical illustration is provided to simulate and solve the set of equations.


Epidemic threshold Reproduction number Fuzzy logic Worm propagation 


  1. 1.
    Bimal Kumar Mishra, D.K. Saini, SEIRS epidemic model with delay for transmission of malicious objects in computer network, Appl. Math. Comput. 188 (2) (2007) 1476–1482.Google Scholar
  2. 2.
    Bimal Kumar Mishra, Dinesh Saini, Mathematical models on computer viruses, Appl. Math. Comput. 187 (2) (2007) 929–936.Google Scholar
  3. 3.
    Bimal Kumar Mishra, Navnit Jha, Fixed period of temporary immunity after run of anti-malicious software on computer nodes, Appl. Math. Comput.190 (2) (2007) 1207–1212.Google Scholar
  4. 4.
    E. Gelenbe, Dealing with software viruses: a biological paradigm, Inform. Secur. Tech. Rep. 12 (4) (2007) 242–250.Google Scholar
  5. 5.
    W.O. Kermack, A.G. McKendrick, Contributions of mathematical theory to epidemics, Proc. R. Soc. Lond. Ser. A 115 (1927) 700–721.Google Scholar
  6. 6.
    W.O. Kermack, A.G. McKendrick, Contributions of mathematical theory to epidemics, Proc. R. Soc. Lond. Ser. A 138 (1932) 55–83.Google Scholar
  7. 7.
    W.O. Kermack, A.G. McKendrick, Contributions of mathematical theory to epidemics, Proc. R. Soc. Lond. Ser. A 141 (1933) 94–122.Google Scholar
  8. 8.
    J. Kim, S. Radhakrishana, J. Jang, Cost optimization in SIS model of worm infection, ETRI J. 28 (5) (2006) 692–695.Google Scholar
  9. 9.
    H. Zhou, Y. Wen, H. Zhao, Modeling and analysis of active benign worms and hybrid benign worms containing the spread of worms, in: Proceedings of the IEEE International Conference on Networking (ICN07), 2007.Google Scholar
  10. 10.
    M.H.R. Khouzani, S. Sarkar, E. Altman, Maximum damage malware attack in mobile wireless networks, in: IEEE Proceedings, INFOCOM10, 1419 Mar.2010, pp. 1–9.Google Scholar
  11. 11.
    X.Z. Li, L.L. Zhou, Global stability of an SEIR epidemic model with vertical transmission and saturating contact rate, Chaos Soliton. Fract. 40 (2007) 874–884.Google Scholar
  12. 12.
    G. Li, J. Zhen, Global stability of an SEI epidemic model with general contact rate, Chaos Soliton. Fract. 23 (2004) 997–1004.Google Scholar
  13. 13.
    B.K. Mishra, N. Jha, SEIQRS model for the transmission of malicious objects in computer network, Appl. Math. Modell. 34 (2009) 1207–1212.Google Scholar
  14. 14.
    N. Yi, Q. Zhang, K. Mao, D. Yang, Q. Li, Analysis and control of an SEIR epidemic system with nonlinear transmission rate, Math. Comput. Modell. 50(2009) 1498–1513.Google Scholar
  15. 15.
    Y. Jin, W. Wang, S. Xiao, An SIRS model with a nonlinear incidence rate, Chaos Soliton. Fract. 34 (2007) 1482–1497.Google Scholar
  16. 16.
    Q. Liu, R. Xu, S. Wang, Modelling and analysis of an SIRS model for worm propagation, in: Proceedings of the International Conference Computational Intelligence and Security, CIS 09, vol. 2, 1114 Dec. 2009, pp. 361–365.Google Scholar
  17. 17.
    F. Wang, Y. Zhang, C. Wang, J. Ma, S. Moon, stability analysis of SEIQV epidemic model for rapid spreading worms, Comput. Secur. 29 (2010) 410–418.Google Scholar
  18. 18.
    Ossama A. Toutonji, Seong-Moo Yoo, Moongyu Park, Stability analysis of VEISV propagation modeling for network worm attack, Appl. Math. Model. 36 (2012) 2751–2761.Google Scholar
  19. 19.
    E. Massad, M.N. Burattini, N.R.S. Ortega, Fuzzy logic and measles vaccination: designing a control strategy, Int. J. Epidemiol. 28 (3) (1999) 550–557.Google Scholar
  20. 20.
    N.R.S. Ortega, P.C. Sallum, E. Massad, Fuzzy dynamical systems in epidemic modelling, Kybernetes 29 (12) (2000) 201–218.Google Scholar
  21. 21.
    E. Massad, et al., Fuzzy Logic in Action: Applications and Epidemiology and Beyond, in: STUDFUZZ, vol. 232, Springer-Verlag, Berlin, Heidelberg, 2008.Google Scholar
  22. 22.
    L.C. Barros, R.C. Bassanezi, M.B.F. Leite, The epidemiological models SI with a fuzzy transmission, Comput. Math. Appl. 45 (2003) 1619–1628.Google Scholar
  23. 23.
    B K Mishra and S K Pandey, Fuzzy epidemic model for the transmission of worms in computer network,Nonlinear Analysis: Real World Applications 11 (2010) 4335–4341.Google Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Computational SciencesPSG College of TechnologyCoimbatoreIndia

Personalised recommendations