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Analysis of Computer Virus Propagation Based on Compartmental Model

Received: 25 June 2017     Accepted: 16 August 2017     Published: 6 September 2017
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Abstract

Computer viruses pose a considerable problem for users of personal computers. In order to effectively defend against a virus, this paper proposes a compartmental model SAEIQRS (Susceptible – Antidotal – Exposed - Infected – Quarantine - Recovered - Susceptible) of virus transmission in a computer network. The differential transformation method (DTM) is applied to obtain an improved solution of each compartment. We have achieved an accuracy of order O(h6) and validated the results of DTM with fourth-order Runge-Kutta (RK4) method. Based on the basic reproduction number, we analyzed the local stability of the model for virus free and endemic equilibria. Using a Lyapunov function, we demonstrated the global stability of virus free equilibria. Numerically the eigenvalues are computed using two different sets of parameter values and the corresponding dominant eigenvalues are determined by means of power method. Finally, we simulate the system in MATLAB. Based on the analysis, aspects of different compartments are investigated.

Published in Applied and Computational Mathematics (Volume 7, Issue 1-2)

This article belongs to the Special Issue Recurrent Neural Networks, Bifurcation Analysis and Control Theory of Complex Systems

DOI 10.11648/j.acm.s.2018070102.12
Page(s) 12-21
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Differential Equations, Stability Analysis and Epidemic Models

References
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  • APA Style

    Pabel Shahrear, Amit Kumar Chakraborty, Md. Anowarul Islam, Ummey Habiba. (2017). Analysis of Computer Virus Propagation Based on Compartmental Model. Applied and Computational Mathematics, 7(1-2), 12-21. https://doi.org/10.11648/j.acm.s.2018070102.12

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    ACS Style

    Pabel Shahrear; Amit Kumar Chakraborty; Md. Anowarul Islam; Ummey Habiba. Analysis of Computer Virus Propagation Based on Compartmental Model. Appl. Comput. Math. 2017, 7(1-2), 12-21. doi: 10.11648/j.acm.s.2018070102.12

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    AMA Style

    Pabel Shahrear, Amit Kumar Chakraborty, Md. Anowarul Islam, Ummey Habiba. Analysis of Computer Virus Propagation Based on Compartmental Model. Appl Comput Math. 2017;7(1-2):12-21. doi: 10.11648/j.acm.s.2018070102.12

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  • @article{10.11648/j.acm.s.2018070102.12,
      author = {Pabel Shahrear and Amit Kumar Chakraborty and Md. Anowarul Islam and Ummey Habiba},
      title = {Analysis of Computer Virus Propagation Based on Compartmental Model},
      journal = {Applied and Computational Mathematics},
      volume = {7},
      number = {1-2},
      pages = {12-21},
      doi = {10.11648/j.acm.s.2018070102.12},
      url = {https://doi.org/10.11648/j.acm.s.2018070102.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.s.2018070102.12},
      abstract = {Computer viruses pose a considerable problem for users of personal computers. In order to effectively defend against a virus, this paper proposes a compartmental model SAEIQRS (Susceptible – Antidotal – Exposed - Infected – Quarantine - Recovered - Susceptible) of virus transmission in a computer network. The differential transformation method (DTM) is applied to obtain an improved solution of each compartment. We have achieved an accuracy of order O(h6) and validated the results of DTM with fourth-order Runge-Kutta (RK4) method. Based on the basic reproduction number, we analyzed the local stability of the model for virus free and endemic equilibria. Using a Lyapunov function, we demonstrated the global stability of virus free equilibria. Numerically the eigenvalues are computed using two different sets of parameter values and the corresponding dominant eigenvalues are determined by means of power method. Finally, we simulate the system in MATLAB. Based on the analysis, aspects of different compartments are investigated.},
     year = {2017}
    }
    

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    T1  - Analysis of Computer Virus Propagation Based on Compartmental Model
    AU  - Pabel Shahrear
    AU  - Amit Kumar Chakraborty
    AU  - Md. Anowarul Islam
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    Y1  - 2017/09/06
    PY  - 2017
    N1  - https://doi.org/10.11648/j.acm.s.2018070102.12
    DO  - 10.11648/j.acm.s.2018070102.12
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    JO  - Applied and Computational Mathematics
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    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.s.2018070102.12
    AB  - Computer viruses pose a considerable problem for users of personal computers. In order to effectively defend against a virus, this paper proposes a compartmental model SAEIQRS (Susceptible – Antidotal – Exposed - Infected – Quarantine - Recovered - Susceptible) of virus transmission in a computer network. The differential transformation method (DTM) is applied to obtain an improved solution of each compartment. We have achieved an accuracy of order O(h6) and validated the results of DTM with fourth-order Runge-Kutta (RK4) method. Based on the basic reproduction number, we analyzed the local stability of the model for virus free and endemic equilibria. Using a Lyapunov function, we demonstrated the global stability of virus free equilibria. Numerically the eigenvalues are computed using two different sets of parameter values and the corresponding dominant eigenvalues are determined by means of power method. Finally, we simulate the system in MATLAB. Based on the analysis, aspects of different compartments are investigated.
    VL  - 7
    IS  - 1-2
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Author Information
  • Department of Mathematics, Shahjalal University of Science & Technology, Sylhet, Bangladesh

  • Department of Computer Science and Engineering, Metropolitan University, Sylhet, Bangladesh

  • Department of Mathematics, Shahjalal University of Science & Technology, Sylhet, Bangladesh

  • Government Teachers Training College, Sylhet, Bangladesh

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