Open Access

ARTICLE

An Effective Numerical Method for the Solution of a Stochastic Coronavirus (2019-nCovid) Pandemic Model

Wasfi Shatanawi^1,2,3, Ali Raza^4,5,*, Muhammad Shoaib Arif⁴, Kamaledin Abodayeh¹, Muhammad Rafiq⁶, Mairaj Bibi⁷

1 Department of Mathematics and General Courses, Prince Sultan University Riyadh, Riyadh, Saudi Arabia
2 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan
3 Department of Mathematics, Hashemite University, Zarqa, Jordan
4 Stochastic Analysis & Optimization Research Group, Department of Mathematics, Air University, PAF Complex E-9, Islamabad, 44000, Pakistan
5 Department of Mathematics, National College of Business Administration and Economics, Lahore, Pakistan
6 Faculty of Engineering, University of Central Punjab, Lahore, 54500, Pakistan
7 Department of Mathematics, Comsats University, Islamabad, Pakistan

* Corresponding Author: Ali Raza. Email:

(This article belongs to the Special Issue: Mathematical aspects of the Coronavirus Disease 2019 (COVID-19): Analysis and Control)

Computers, Materials & Continua 2021, 66(2), 1121-1137. https://doi.org/10.32604/cmc.2020.012070

Received 12 June 2020; Accepted 07 August 2020; Issue published 26 November 2020

Abstract

Nonlinear stochastic modeling plays a significant role in disciplines such as psychology, finance, physical sciences, engineering, econometrics, and biological sciences. Dynamical consistency, positivity, and boundedness are fundamental properties of stochastic modeling. A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation. Well-known explicit methods such as Euler Maruyama, stochastic Euler, and stochastic Runge–Kutta are investigated for the stochastic model. Regrettably, the above essential properties are not restored by existing methods. Hence, there is a need to construct essential properties preserving the computational method. The non-standard approach of finite difference is examined to maintain the above basic features of the stochastic model. The comparison of the results of deterministic and stochastic models is also presented. Our proposed efficient computational method well preserves the essential properties of the model. Comparison and convergence analyses of the method are presented.

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