Open Access

ARTICLE

Structure-Preserving Dynamics of Stochastic Epidemic Model with the Saturated Incidence Rate

Wasfi Shatanawi^{1, 2, 3}, Muhammad Shoaib Arif^{4, *}, Ali Raza⁴, Muhammad Rafiq⁵, Mairaj Bibi⁶, Javeria Nawaz Abbasi⁶

1 Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.
2 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan.
3 Department of M-Commerce and Multimedia Applications, Asia University, Taichung, 41354, Taiwan.
4 Stochastic Analysis & Optimization Research Group, Department of Mathematics, Air University, PAF Complex E-9, Islamabad, 44000, Pakistan.
5 Faculty of Engineering, University of Central Punjab, Lahore, Pakistan.
6 Department of Mathematics, Comsats University, Islamabad, Pakistan.

* Corresponding Author: Muhammad Shoaib Arif. Email: .

Computers, Materials & Continua 2020, 64(2), 797-811. https://doi.org/10.32604/cmc.2020.010759

Received 26 March 2020; Accepted 21 April 2020; Issue published 10 June 2020

Abstract

The structure-preserving features of the nonlinear stochastic models are positivity, dynamical consistency and boundedness. These features have a significant role in different fields of computational biology and many more. Unfortunately, the existing stochastic approaches in literature do not restore aforesaid structure-preserving features, particularly for the stochastic models. Therefore, these gaps should be occupied up in literature, by constructing the structure-preserving features preserving numerical approach. This writing aims to describe the structure-preserving dynamics of the stochastic model. We have analysed the effect of reproduction number in stochastic modelling the same as described in the literature for deterministic modelling. The usual explicit stochastic numerical approaches are time-dependent. We have developed the implicitly driven explicit approach for the stochastic epidemic model. We have proved that the newly developed approach is preserving the structural, dynamical properties as positivity, boundedness and dynamical consistency. Finally, convergence analysis of a newly developed approach and graphically illustration is also presented.

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Citations