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Stochastic Analysis for the Dynamics of a Poliovirus Epidemic Model

Ali Raza1, Dumitru Baleanu2,3,4, Zafar Ullah Khan5, Muhammad Mohsin6,*, Nauman Ahmed7, Muhammad Rafiq8, Pervez Anwar9
1 Department of Mathematics, Government Maulana Zafar Ali Khan Graduate College Wazirabad, Punjab Higher Education Department (PHED), Lahore, 54000, Pakistan
2 Department of Mathematics, Cankaya University, Balgat, Ankara, 06530, Turkey
3 Department of Medical Research, China Medical University, Taichung, 40402, Taiwan
4 Institute of Space Sciences, Magurele-Bucharest, 077125, Romania
5 Department of Dermatology, Rashid Latif Medical College Lahore, Lahore, 54000, Pakistan
6 Department of Mathematics, Technische Universitat Chemnitz, Chemnitz, 6209111, Germany
7 Department of Mathematics and Statistics, The University of Lahore, Lahore, 54590, Pakistan
8 Department of Mathematics, Faculty of Science and Technology, University of Central Punjab, Lahore, 54000, Pakistan
9 Department of Biochemistry, University of Sialkot, Sialkot, 51311, Pakistan
* Corresponding Author: Muhammad Mohsin. Email: muhammadmohsincheema@gmail.com
(This article belongs to this Special Issue: Bio-inspired Computer Modelling: Theories and Applications in Engineering and Sciences)

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2023.023231

Received 15 April 2022; Accepted 30 August 2022; Published online 18 October 2022

Abstract

Most developing countries such as Afghanistan, Pakistan, India, Bangladesh, and many more are still fighting against poliovirus. According to the World Health Organization, approximately eighteen million people have been infected with poliovirus in the last two decades. In Asia, still, some countries are suffering from the virus. The stochastic behavior of the poliovirus through the transition probabilities and non-parametric perturbation with fundamental properties are studied. Some basic properties of the deterministic model are studied, equilibria, local stability around the stead states, and reproduction number. Euler Maruyama, stochastic Euler, and stochastic Runge-Kutta study the behavior of complex stochastic differential equations. The main target of this study is to develop a nonstandard computational method that restores dynamical features like positivity, boundedness, and dynamical consistency. Unfortunately, the existing methods failed to fix the actual behavior of the disease. The comparison of the proposed approach with existing methods is investigated.

Keywords

Poliovirus model; differential equations; methods; analysis
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