International Journal of Computer Networks and Applications (IJCNA)

Published By EverScience Publications

ISSN : 2395-0455

International Journal of Computer Networks and Applications (IJCNA)

International Journal of Computer Networks and Applications (IJCNA)

Published By EverScience Publications

ISSN : 2395-0455

Effect of Quarantine & Vaccination on Infectious Nodes in Computer Network

Author NameAuthor Details

Munna Kumar, Bimal Kumar Mishra, T. C. Panda

Munna Kumar[1]

Bimal Kumar Mishra[2]

T. C. Panda[3]

[1]Research Scholar,Department of Mathematics, Utkal University, India.

[2]Department of Mathematics, Birla Institute of Technology, Mesra, Ranchi, India.

[3]Former Principal, Orissa Engineering College, Bhubaneswar Orissa, India.

Abstract

A compartmental epidemic model of viruses in a computer network with vaccination and natural death is formulated. A strong impact of vaccination in the computer network reduces rapidly the spreading behavior of worms and Quarantine plays an important role in the recovery of the infectious nodes. The stability of the result is stated in terms of the Jacobian of the system and the basic reproduction number is also well - defined. The effect of vaccination in the system is also analyzed. Numerical methods and MATLAB are employed to solve and simulate the system of equations developed and analysis of the model gives remarkable exposure.

Index Terms

Epidemic Model

Basic Reproduction Number

Vaccination

Stability

Computer Network

Reference

  1. 1.
    M. Milton Joe and Dr. B. Ramakrishnan, “A Survey of Various Security Issues in Online Social Networks,” International Journal of Computer Networks and Applications”, volume 1, Issue 1, pp. 11–14, November-December (2014).
  2. 2.
    F. Cohen, “Computer viruses. Theory and experiments,” Computers and Security, vol. 6, no. 1, pp. 22–35, 1987.
  3. 3.
    W. H. Murray, “The application of epidemiology to computer viruses,” Computers and Security, vol. 7, no. 2, pp. 139–145, 1988.
  4. 4.
    J. O. Kephart and S. R. White, “Directed-graph epidemiological models of computer viruses,” inProceedings of the IEEE Computer Society Symposium on Research in Security and Privacy, pp. 343–358,May 1991.
  5. 5.
    W.O. Kermack, A.G. McKendrick, “,Contributions of mathematical theory to epidemics, ” Proc. Royal Soc. London – Series A 115(1927) 700–721.
  6. 6.
    W.O. Kermack, A.G. McKendrick, “Contributions of mathematical theory to epidemics, ” Proc. Roy. Soc. London – Series A 138(1932) 55 – 83.
  7. 7.
    W.O. Kermack, A.G. McKendrick, “Contributions of mathematical theory to epidemics, ” Proc. Royal Soc. London – Series A 141 (1933) 94 – 122.
  8. 8.
    J.R.C.Piqueria, “ A modified epidemiological model for computer viruses, ”applied mathematics and computation 213(2009)355-360.
  9. 9.
    J.R.C. Piqueira, F.B. Cesar, “Dynamic models for computer virus propagation,” Math. Prob. Eng., doi:10.1155/2008/940526.
  10. 10.
    J.R.C. Piqueira, B.F. Navarro, L.H.A. Monteiro, “Epidemiological models applied to virus in computer network, ” J.Comput. Sci. 1 (1) (2005) 31 – 34.
  11. 11.
    Y. Wang, C. X. Wang, “Modeling the effect of timing parameters on virus propagation, ” in: 2003 ACM Workshop on Rapid Malcode, ACM, October 2003 pp. 61 – 66.
  12. 12.
    M.J. Keeling, K.T.D. Eames, “Network and epidemic models, ” J. Roy. Soc.Interf. 2 (4) (2005) 295 – 307.
  13. 13.
    Ping Yan, Shengqiang Liu, “SEIR epidemic model with delay,” J. Aust. Math. Soc. Series B – Appl. Math. 48 (1) (2006) 119 – 134.
  14. 14.
    Bimal Kumar Mishra and D. K. Saini, “SEIRS epidemic model with delay for transmission of malicious objects in computer network,” Applied Mathematics and Computation, 188 (2) (2007), 1476-1482.
  15. 15.
    Bimal Kumar Mishra and Navnit Jha, “Fixed period of temporary immunity after run of anti-malicious software on computer nodes,” Applied Mathematics and Computation, 190 (2) (2007) 1207 – 1212.
  16. 16.
    J.O. Kephart, “A biologically inspired immune system for computers,” in: Proceeding of International Joint Conference on Artificial Intelligence, 1995.
  17. 17.
    N. Madar, T. Kalisky, R. Cohen, D. Ben Avraham, S. Havlin, ”Immunization and epidemic dynamics in complex networks,” Eur. Phys. J. B 38 (2004) 269-276.
  18. 18.
    R. Pastor-Satorras, A. Vespignani, “ Epidemics and immunization in scale-free networks, ” Handbook of Graphs and network: From the Genome to the Internet, Willey-VCH, Bsrlin, 2002.
  19. 19.
    R.M. May, A.L. Lloyd, “ Infection dynamics on scale-free networks,” Phys. Rev. E 64 (066112) (2001) 1 – 3.
  20. 20.
    S. Datta, H. Wang, “The effectiveness of vaccinations on the spread of email-borne computer virus,” in: IEEE CCECE/CCGEL, IEEE, May 2005, pp. 219 – 223.
  21. 21.
    Bimal K. Mishra, Samir K. Pandey, “ Dynamic model of worms with vertical transmission in computer network,” Applied Mathematics and Computation, 217 (2011) 8438–8446.
  22. 22.
    C.C. Zou, W. Gong, D. Towsley, “Worm propagation modeling and analysis under dynamic quarantine defense,” in: Proceeding of the ACM CCS Workshop on Rapid Malcode, ACM, 2003, pp. 51 – 60.
  23. 23.
    D. Moore, C. Shannon, G.M. Voelker, S. Savage, “Internet quarantine: requirements for containing self-propagating code,” in: Proceeding of IEEE INFOCOM2003, IEEE, April,2003.
  24. 24.
    T. Chen, N. Jamil, “ Effectiveness of quarantine in worm epidemic,” in: IEEE International Conference on Communications 2006, IEEE, June 2006, pp.2142-2147.
  25. 25.
    Bimal Kumar Mishra, Aditya Kumar Singh, “Two Quarantine Models on the attack of Malicious Objects in Computer Network,” Mathematical problems in Enginering, In Mathematical Problems for Complex Networks, Hindawi Publishing Corporation, Vol. 2012, Article ID 407064, 13 pages, 2012.
  26. 26.
    Bimal K. Mishra, Navnit Jha, “ SEIQRS model for the transmission of malicious objects in computer network, ” Applied Mathematical Modeling, 34 (2010), 710-715.
SCOPUS
SCImago Journal & Country Rank