On efficient numerical approaches for the study of the interactive dynamics of fractional eco-epidemiological models

Reny George; Shahram Rezapour; Mohammed Shaaf Alharthi; A. F. Aljohani; B. Günay; Reny George; Shahram Rezapour; Mohammed Shaaf Alharthi; A. F. Aljohani; B. Günay

doi:10.3934/math.2023685

AIMS Mathematics

2023, Volume 8, Issue 6: 13503-13524. doi: 10.3934/math.2023685

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On efficient numerical approaches for the study of the interactive dynamics of fractional eco-epidemiological models

1.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
2.
Department of Mathematics and Computer Science, St. Thomas College, Bhilai 49006, India
3.
Department of Mathematics, Kyung Hee University, Kyungheedae-ro 26, Dongdaemun-gu, Seoul, Republic of Korea
4.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
5.
Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
6.
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
7.
Department of Mathematical Sciences, George Mason University, Virginia, USA
8.
Faculty of Engineering and Natural Sciences, Bahçeşehir University, Istanbul 34349, Turkey

Received: 13 January 2023 Revised: 08 March 2023 Accepted: 15 March 2023 Published: 07 April 2023
MSC : 26A33, 37N25, 74S30, 91B50

The present study aims to consider a mathematical eco-epidemiological model involving two fractional operators. To this end, we provide approximate solutions to these fractional systems through the application of a numerical technique that is based on the rule of product integration. This feature contributes greatly to the efficiency and effectiveness of both methods. We have also presented some theoretical discussions related to the equilibrium points of the system. Further, several numerical simulations are presented in order to illustrate the impact of choosing different parameters on the dynamics of the model. It is demonstrated that the obtained numerical results are completely consistent with the expected theoretical results. Moreover, both techniques can be used to solve other problems in epidemiology and describe other problems in the future. The article's model has never been studied via the employed fractional operators, and this is a distinct point for our work and other existing research.
- numerical interactions,
- explicit and implicit schemes,
- extinction,
- sensitivity analysis
Citation: Reny George, Shahram Rezapour, Mohammed Shaaf Alharthi, A. F. Aljohani, B. Günay. On efficient numerical approaches for the study of the interactive dynamics of fractional eco-epidemiological models[J]. AIMS Mathematics, 2023, 8(6): 13503-13524. doi: 10.3934/math.2023685

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Abstract

The present study aims to consider a mathematical eco-epidemiological model involving two fractional operators. To this end, we provide approximate solutions to these fractional systems through the application of a numerical technique that is based on the rule of product integration. This feature contributes greatly to the efficiency and effectiveness of both methods. We have also presented some theoretical discussions related to the equilibrium points of the system. Further, several numerical simulations are presented in order to illustrate the impact of choosing different parameters on the dynamics of the model. It is demonstrated that the obtained numerical results are completely consistent with the expected theoretical results. Moreover, both techniques can be used to solve other problems in epidemiology and describe other problems in the future. The article's model has never been studied via the employed fractional operators, and this is a distinct point for our work and other existing research.

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