STRUCTURE PRESERVING SPLITTING TECHNIQUES FOR EBOLA REACTION–DIFFUSION EPIDEMIC SYSTEM

Nauman Ahmed, Tahira Sumbal Shaikh, Muhammad Rafiq, Sayed M. Eldin, Abdul Hamid Ganie, Mubasher Ali, Ali Raza, Ilyas Khan and M. I. Khan
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Nauman Ahmed: Department of Mathematics and Statistics, The University of Lahore, Lahore 53700, Pakistan2Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
Tahira Sumbal Shaikh: Department of Mathematics, Lahore College for Women University, Lahore 5400, Pakistan
Muhammad Rafiq: Department of Mathematics, Faculty of Sciences and Technology, University of the Central Punjab, Lahore, Pakistan5Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC
Sayed M. Eldin: Center of Research, Faculty of Engineering, Future University in Egypt, New Cairo 11835, Egypt
Abdul Hamid Ganie: Basic Sciences Department, College of Science and Theoretical Studies, Saudi Electronic University, Abha Male 61421, Saudi Arabia
Mubasher Ali: School of Engineering and Digital Arts, University of Kent, Canterbury Kent, UK
Ali Raza: Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon9Department of Mathematics, Government Maulana Zafar Ali Khan Graduate College Wazirabad, Punjab Higher Education Department (PHED), Lahore 54000, Pakistan
Ilyas Khan: 0Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
M. I. Khan: 1School of Mechanics and Engineering Science, Peking University, Beijing, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 02, 1-12

Abstract: In this paper, we deal with the numerical solution of the reaction–diffusion Ebola epidemic model. The diffusion which is an important phenomenon for the epidemic model is included in the model. This inclusion has made the model more comprehensive for studying the disease dynamics in the human population. The quantities linked with the model indicate the population sizes which are taken as absolute, therefore, the numerical schemes utilized to solve the underlying Ebola epidemic system should sustain the positivity. The numerical approaches used to solve the underlying epidemic models are explicit nonstandard finite difference operator splitting (ENSFD-OS) and implicit nonstandard finite difference operator splitting (INSFD-OS) techniques. These schemes preserve all the physical features of the state variables, i.e. projected schemes hold the positive solution acquired by the Ebola diffusive epidemic model. The underlying epidemic model illustrates two stable steady states, a virus-free state, and a virus existence state. The suggested approaches retain the stability of each of the steady states possessed by the assumed epidemic model. A numerical example and simulations for validation of all the characteristics of suggested techniques are also investigated.

Keywords: Ebola Infection; Reaction–diffusion System; Splitting Techniques; Nonstandard Finite Differences; Simulations (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400418

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