Skip to main content
SpringerLink
Log in

Effect of Vaccination in the Computer Network for Distributed Attacks – A Dynamic Model

  • Conference paper
  • First Online:
Book cover Advances in Computing and Data Sciences (ICACDS 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1046))

Included in the following conference series:

Abstract

In this reviewed endeavour, a mathematical model is formulated to assess the spread of a distributed attack over a computer network for critical targeted resources. In this paper a mathematical model is formulated, the two sources susceptible, vaccinated, infected, recovered nanonodes in the target population (e-\( S_{t} V_{t} I_{t} R_{t} \)) and susceptible, infected, susceptible nanonodes in the attacking population (e-SIS) epidemic model generated in order to propagate malicious object in the network. Further the analysis of the model has been concentrated upon the basic reproduction number. Where threshold value has effectively examined the stability of the network system. This work is verified for both asymptotical stable, that is the basic reproduction number less than on when the infection free equilibrium express the stability and basic reproduction number is more than one when endemic equilibrium is stable. A very general recognized control mechanism is regarded as vaccination strategy, which is deployed in order to defend the malicious object in the computer network. Finally we examine the effect of vaccination on performance of the controlling strategy of malicious objects in the network. The simulated result produced has become compatible with the overall theoretical analysis.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Gan, C., Xiaofan, Y., Qingyi, Z., Li, H.: The spread of computer virus under external computers. Nonlinear Dyn. 73(3), 1615–1620 (2013)

    Article  MathSciNet  Google Scholar 

  2. Gelenbe, E., Gellman, M., Loukas, G.: Defending networks against denial-of-service attacks. In: Unmanned/Unattended Sensors and Sensor Networks, vol. 5611, pp. 233–244. International Society for Optics and Photonics (2004)

    Google Scholar 

  3. Li, M.Y., Graef, J.R., Wang, L., Karsai, J.: Global dynamics of an SEIR model with a varying total population size. Math. Biosci. 160, 191–213 (1999)

    Article  MathSciNet  Google Scholar 

  4. Kermac, W.O., McKendrick, A.G.: Contribution of mathematical theory to epidemic. Proc. R. Soc. Lond. Ser. Contain. Pap. Math. Phys. Character 14(843), 94–122 (1933)

    Article  Google Scholar 

  5. Haldar, K., Mishra, B.K.: A mathematical model for the distributed attack on the target resources in the computer network. Commun. Nonlinear Sci. Simul. 19, 3149–3160 (2014)

    Article  MathSciNet  Google Scholar 

  6. Mishra, B.K., Haldar, K.: e-epidemic models on attack and defence of malicious objects in networks, theories and simulations of complex social system. In: Dabbaghian, V., Mago, V. (eds.) Theories and Simulations of Complex Social Systems. Intelligent System Reference Library, vol. 52, pp. 117–143. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-39149-1_9

    Chapter  Google Scholar 

  7. Song, X., Chen, L.: Optimal harvesting and stability for two species competitive system with stage structure. Math. Biosci. 170, 173–186 (2001)

    Article  MathSciNet  Google Scholar 

  8. Toutonji, O., Yoo, S.M.: Passive benign worm propagation modelling with dynamic quarantine defence. KSII Trans. Internet Inf. Syst. 3(1), 96–107 (2009)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  10. Wang, L., Li, M.Y.: A criteria for stability of matrices. Math. Anal. Appl. 225, 249–264 (1998)

    Article  MathSciNet  Google Scholar 

  11. Dagon, D., Zou, C., Lee, W.: Modelling bonnet propagation using time zones. In: Proceedings of 13th Network and Distributed System Security Symposium NDSS, vol. 6, pp. 2–13 (2006)

    Google Scholar 

  12. Bailey, N.: The mathematical theory of epidemic. Wiley, New York (1957)

    Google Scholar 

  13. LaSalle, J.: The Stability of Dynamical Systems. Regional to Conference Series in Applied Mathematics. SIAM, Philadelphia (1976)

    Book  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  15. Rao, Y.S., Rauta, A.K., Saini, H., Panda, T.C.: Mathematical model for the cyber attack in the computer network. Int. J. Bus. Data Commun. Netw. 13(1), 58–65 (2017). https://doi.org/10.4018/ijbdcn.2017010105

    Article  Google Scholar 

  16. Nayak, P.K., Rao, Y.S., Panda, T.C.: Calculation of basic reproduction number by graph reduction method and stability analysis in SEIQRS E epidemic model in computer network. J. Eng. Appl. Sci. 12(23), 7332–7338 (2017)

    Google Scholar 

  17. Rauta, A.K., Rao, Y.S., Panda, T.C., Saini, H.: A probabilistic approach using poisson process for detecting the existence of unknown computer virus in real time. Int. J. Eng. Sci. 4, 47–51 (2015)

    Google Scholar 

  18. Rao, Y.S., Rauta, A.K., Saini, H., Panda, T.C.: Influence of educational qualification on different types of cyber crime: a statistical interpretation. Indian J. Sci. Technol. 9(32), 1–7 (2016)

    Google Scholar 

  19. Saini, H., Rao, Y.S., Panda, T.C.: Cyber-crimes and their impacts: a review. Int. J. Eng. Res. Appl. 2, 202–209 (2012)

    Google Scholar 

  20. Liu, X., Takeuchi, Y.: SVIR epidemic model with vaccination strategies. J. Theor. Biol. 253, 1–11 (2008)

    Article  MathSciNet  Google Scholar 

  21. Driessche, P.V.D., Watmough, J.: Reproduction numbers and sub threshold endemic equilibria for compartmental models of diseases transmission. Math. Biosci. 180, 29–48 (2002)

    Article  MathSciNet  Google Scholar 

  22. Routh-Hurwitz Criterion. http://web.abo.fi/fak/mnf/mate/kurser/dynsyst/2009/R-hcriteria.pdf

  23. Kribs-Zaleta, C., Velasco-Hernandez, J.: A simple vaccination model with multiple endemic states. Math. Biosci. 164, 183–201 (2000)

    Article  Google Scholar 

  24. 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, 265–274 (2013)

    MathSciNet  MATH  Google Scholar 

  25. Anwar, S.: Wireless nanosensor networks: a basic review. Int. J. Emerg. Technol. Adv. Eng. 5(12), 151–154 (2015)

    Google Scholar 

  26. Mishra, B.K., Tyagi, I.: Defending against malicious threats in wireless sensor network: a mathematical model. Int. J. Inf. Technol. Comput. Sci. 6, 12–19 (2014)

    Google Scholar 

  27. Peng, M., Mou, H.: A novel computer virus model and its stability. J. Netw. 9, 367–374 (2014)

    Google Scholar 

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

    Article  Google Scholar 

  29. Zheng, R., Lu, W., Xu, S.: Preventive and reactive cyber defense dynamics is globally stable. IEEE Trans. Netw. Sci. Eng. 5, 156–170 (2018)

    Article  MathSciNet  Google Scholar 

  30. Yang, L.X., Li, P., Yang, X., Wu, Y., Tang, Y.Y.: On the competition of two conflicting messages. Nonlinear Dyn. 91, 1853–1869 (2018)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Gandhi Institute of Excellent Technocrats, Bhubaneswar, 752054, Odisha, India

    Yerra Shankar Rao

  2. Department of Computer Science and Engineering, Jaypee University of Information Technology, Wakanghat, 173234, Himachal Pradesh, India

    Hemraj Saini & Geetanjali Rathee

  3. Department of Mathematics, Revenshaw University, Cuttack, 753003, Odisha, India

    Tarini Charan Panda

Authors
  1. Yerra Shankar Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hemraj Saini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Geetanjali Rathee
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tarini Charan Panda
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Hemraj Saini or Geetanjali Rathee .

Editor information

Editors and Affiliations

  1. University of KwaZulu-Natal, Durban, South Africa

    Mayank Singh

  2. Computer Science and Engineering, Jaypee Institute of Information Technology, Waknaghat, Himachal Pradesh, India

    P.K. Gupta

  3. Department of Computer Science and Engineering, Jaypee University of Engineering and Technology, Guna, Madhya Pradesh, India

    Vipin Tyagi

  4. ÚTIA AV ČR, Institute of Information Theory and Automation, Prague 8, Praha, Czech Republic

    Jan Flusser

  5. School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, ON, Canada

    Tuncer Ören

  6. CSE Department, Inderprastha Engineering College, Ghaziabad, Uttar Pradesh, India

    Rekha Kashyap

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Rao, Y.S., Saini, H., Rathee, G., Panda, T.C. (2019). Effect of Vaccination in the Computer Network for Distributed Attacks – A Dynamic Model. In: Singh, M., Gupta, P., Tyagi, V., Flusser, J., Ören, T., Kashyap, R. (eds) Advances in Computing and Data Sciences. ICACDS 2019. Communications in Computer and Information Science, vol 1046. Springer, Singapore. https://doi.org/10.1007/978-981-13-9942-8_17

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-9942-8_17

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-9941-1

  • Online ISBN: 978-981-13-9942-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation