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Numerical Treatment for Stochastic Computer Virus Model

Ali Raza1, Muhammad Shoaib Arif1,*, Muhammad Rafiq2, Mairaj Bibi3, Muhammad Naveed1, Muhammad Usman Iqbal4, Zubair Butt4, Hafiza Anum Naseem4, Javeria Nawaz Abbasi3
Department of Mathematics, Stochastic Analysis & Optimization Research Group, Air University, PAF Complex E-9, Islamabad, Pakistan.
Faculty of Engineering University of Central Punjab, Lahore, Pakistan.
Department of Mathematics, Comsats University, Park Road Chak Shahzad Campus, Islamabad, Pakistan.
Faculty of Computing National College of Business Administration and Economics, Lahore, Pakistan.
* Corresponding Author: Muhammad Shoaib Arif. Email: .

Computer Modeling in Engineering & Sciences 2019, 120(2), 445-465. https://doi.org/10.32604/cmes.2019.06454

Abstract

This writing is an attempt to explain a reliable numerical treatment for stochastic computer virus model. We are comparing the solutions of stochastic and deterministic computer virus models. This paper reveals that a stochastic computer virus paradigm is pragmatic in contrast to the deterministic computer virus model. Outcomes of threshold number C hold in stochastic computer virus model. If C < 1 then in such a condition virus controlled in the computer population while C > 1 shows virus persists in the computer population. Unfortunately, stochastic numerical methods fail to cope with large step sizes of time. The suggested structure of the stochastic non-standard finite difference scheme (SNSFD) maintains all diverse characteristics such as dynamical consistency, boundedness and positivity as defined by Mickens. The numerical treatment for the stochastic computer virus model manifested that increasing the antivirus ability ultimates small virus dominance in a computer community.

Keywords

Computer virus, euler maruyama scheme, stochastic differential equations, stochastic euler scheme, stochastic runge-kutta scheme, stochastic NSFD scheme, stability.

Cite This Article

Raza, A., Arif, M. S., Rafiq, M., Bibi, M., Naveed, M. et al. (2019). Numerical Treatment for Stochastic Computer Virus Model. CMES-Computer Modeling in Engineering & Sciences, 120(2), 445–465.

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This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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