Open Access

ARTICLE

A Structure Preserving Numerical Method for Solution of Stochastic Epidemic Model of Smoking Dynamics

Ali Raza¹, Muhammad Rafiq², Nauman Ahmed³, Ilyas Khan^{4, *}, Kottakkaran Sooppy Nisar⁵, Zafar Iqbal³

1 Department of Mathematics, National College of Business Administration and Economics, Lahore, Pakistan.
2 Faculty of Engineering, University of Central Punjab, Lahore, Pakistan.
3 Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.
4 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
5 Department of Mathematics, College of Arts and Science at Wadi Aldawaser, Prince Sattam Bin Abdulaziz University, Alkharj, Saudi Arabia.

* Corresponding Author: Ilyas Khan. Email: .

Computers, Materials & Continua 2020, 65(1), 263-278. https://doi.org/10.32604/cmc.2020.011289

Received 29 April 2020; Accepted 05 June 2020; Issue published 23 July 2020

Abstract

In this manuscript, we consider a stochastic smoking epidemic model from behavioural sciences. Also, we develop a structure preserving numerical method to describe the dynamics of stochastic smoking epidemic model in a human population. The structural properties of a physical system include positivity, boundedness and dynamical consistency. These properties play a vital role in non-linear dynamics. The solution for nonlinear stochastic models necessitates the conservation of these properties. Unfortunately, the aforementioned properties of the model have not been restored in the existing stochastic methods. Therefore, it is essential to construct a structure preserving numerical method for a reliable analysis of stochastic smoking model. The usual explicit stochastic numerical methods are time-dependent and violate most of the structural properties. In this work, we have developed the implicitly driven explicit method for the solution of stochastic smoking model. It is also proved that the newly developed method sustains all the aforementioned properties of the system. Finally, the convergence analysis of the newly developed method and graphical illustrations are presented.

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