Applied and Computational Mathematics
Volume 7, Issue 1-2, January 2018, Pages: 12-21
Received: Jun. 25, 2017;
Accepted: Aug. 16, 2017;
Published: Sep. 6, 2017
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Pabel Shahrear, Department of Mathematics, Shahjalal University of Science & Technology, Sylhet, Bangladesh
Amit Kumar Chakraborty, Department of Computer Science and Engineering, Metropolitan University, Sylhet, Bangladesh
Md. Anowarul Islam, Department of Mathematics, Shahjalal University of Science & Technology, Sylhet, Bangladesh
Ummey Habiba, Government Teachers Training College, Sylhet, Bangladesh
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.
Amit Kumar Chakraborty,
Md. Anowarul Islam,
Analysis of Computer Virus Propagation Based on Compartmental Model, Applied and Computational Mathematics. Special Issue:Recurrent Neural Networks, Bifurcation Analysis and Control Theory of Complex Systems.
Vol. 7, No. 1-2,
2018, pp. 12-21.
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