Construction and numerical analysis of a fuzzy non-standard computational method for the solution of an SEIQR model of COVID-19 dynamics

Fazal Dayan; Nauman Ahmed; Muhammad Rafiq; Ali Akgül; Ali Raza; Muhammad Ozair Ahmad; Fahd Jarad; Fazal Dayan; Nauman Ahmed; Muhammad Rafiq; Ali Akgül; Ali Raza; Muhammad Ozair Ahmad; Fahd Jarad

doi:10.3934/math.2022471

AIMS Mathematics

2022, Volume 7, Issue 5: 8449-8470. doi: 10.3934/math.2022471

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Research article Special Issues

Construction and numerical analysis of a fuzzy non-standard computational method for the solution of an SEIQR model of COVID-19 dynamics

1.
Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan
2.
Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan
3.
Department of Mathematics, Faculty of Science, University of Central Punjab, Lahore, Pakistan
4.
Department of Mathematics, Art and Science Faculty, Siirt University, TR 56100, Siirt, Turkey
5.
Department of Mathematics, Govt. Maulana Zafar Ali Khan Graduate College Wazirabad, 52000, Punjab Higher Education Department (PHED), Lahore, 54000, Pakistan
6.
Department of Mathematics, Çankaya University, Etimesgut 06790, Ankara, Turkey
7.
Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
8.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Received: 17 December 2021 Revised: 15 February 2022 Accepted: 17 February 2022 Published: 28 February 2022
MSC : 65L12, 34A07

This current work presents an SEIQR model with fuzzy parameters. The use of fuzzy theory helps us to solve the problems of quantifying uncertainty in the mathematical modeling of diseases. The fuzzy reproduction number and fuzzy equilibrium points have been derived focusing on a model in a specific group of people having a triangular membership function. Moreover, a fuzzy non-standard finite difference (FNSFD) method for the model is developed. The stability of the proposed method is discussed in a fuzzy sense. A numerical verification for the proposed model is presented. The developed FNSFD scheme is a reliable method and preserves all the essential features of a continuous dynamical system.
- Covid-19 model,
- fuzzy parameters,
- fuzzy nonstandard finite difference technique,
- convergence analysis,
- stability analysis
Citation: Fazal Dayan, Nauman Ahmed, Muhammad Rafiq, Ali Akgül, Ali Raza, Muhammad Ozair Ahmad, Fahd Jarad. Construction and numerical analysis of a fuzzy non-standard computational method for the solution of an SEIQR model of COVID-19 dynamics[J]. AIMS Mathematics, 2022, 7(5): 8449-8470. doi: 10.3934/math.2022471

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Abstract

This current work presents an SEIQR model with fuzzy parameters. The use of fuzzy theory helps us to solve the problems of quantifying uncertainty in the mathematical modeling of diseases. The fuzzy reproduction number and fuzzy equilibrium points have been derived focusing on a model in a specific group of people having a triangular membership function. Moreover, a fuzzy non-standard finite difference (FNSFD) method for the model is developed. The stability of the proposed method is discussed in a fuzzy sense. A numerical verification for the proposed model is presented. The developed FNSFD scheme is a reliable method and preserves all the essential features of a continuous dynamical system.

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