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.
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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 |
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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. |
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Copyright © The Author(s), 2017. Published by Science Publishing Group |
Differential Equations, Stability Analysis and Epidemic Models
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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
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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Download@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}
}
TY - JOUR T1 - Analysis of Computer Virus Propagation Based on Compartmental Model AU - Pabel Shahrear AU - Amit Kumar Chakraborty AU - Md. Anowarul Islam AU - Ummey Habiba 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 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 12 EP - 21 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 ER -
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