Computational aspects of an epidemic model involving stochastic partial differential equations

Nauman Ahmed, Muhammad W. Yasin, Syed Mansoor Ali (), Ali Akgül, Ali Raza, Muhammad Rafiq and Muhammad Ali Shar
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Nauman Ahmed: Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
Muhammad W. Yasin: Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan†Department of Mathematics, University of Narowal, Bathanwala, Narowal, Punjab, Pakistan
Syed Mansoor Ali: ��Department of Physics and Astronomy, College of Science, P.O. Box 2455, King Saud University, Riyadh 11451, Saudi Arabia
Ali Akgül: �Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey¶Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon††Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, PC
Ali Raza: ��Department of Mathematics, Govt. Maulana Zafar Ali Khan Graduate College Wazirabad, Punjab Higher Education Department (PHED), Lahore 54000, Pakistan
Muhammad Rafiq: *Department of Mathematics, Faculty of Science and Technology, University of Central Punjab, Lahore, Pakistan††Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, PC
Muhammad Ali Shar: ��‡Department of Mechanical & Energy Systems Engineering, Faculty of Engineering and Informatics, University of Bradford, Bradford BD7 1DP, UK

International Journal of Modern Physics C (IJMPC), 2023, vol. 34, issue 11, 1-27

Abstract: This paper deals with the study of the reaction–diffusion epidemic model perturbed with time noise. It has various applications such as disease in population models of humans, wildlife, and many others. The stochastic SIR model is numerically investigated with the proposed stochastic backward Euler scheme and proposed stochastic implicit finite difference (IFD) scheme. The stability of the proposed methods is shown with Von Neumann criteria and both schemes are unconditionally stable. Both schemes are consistent with systems of the equations in the mean square sense. The numerical solution obtained by the proposed stochastic backward Euler scheme and solutions converges towards an equilibrium but it has negative and divergent behavior for some values. The numerical solution gained by the proposed IFD scheme preserves the positivity and also solutions converge towards endemic and disease-free equilibrium. We have used two problems to check our findings. The graphical behavior of the stochastic SIR model is much adjacent to the classical SIR epidemic model when noise strength approaches zero. The three-dimensional plots of the susceptible and infected individuals are drawn for two cases of endemic equilibrium and disease-free equilibriums. The results show the efficacy of the proposed stochastic IFD scheme.

Keywords: Stochastic SIR model; proposed stochastic finite difference schemes; analysis of the schemes; simulations (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0129183123501462

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