Dynamical and computational analysis of a fractional predator-prey model with an infectious disease and harvesting policy

Devendra Kumar; Jogendra Singh; Dumitru Baleanu; Devendra Kumar; Jogendra Singh; Dumitru Baleanu

doi:10.3934/math.20241712

AIMS Mathematics

2024, Volume 9, Issue 12: 36082-36101. doi: 10.3934/math.20241712

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Dynamical and computational analysis of a fractional predator-prey model with an infectious disease and harvesting policy

1.
Department of Mathematics, University of Rajasthan, Jaipur-302004, India
2.
Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, 02447, Korea
3.
Department of Mathematics, Raj Rishi Govt. College, Alwar-301001, India
4.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
5.
Institute of Space Sciences-Subsidiary of INFLPR, Magurele-Bucharest, Romania

Received: 11 August 2024 Revised: 27 October 2024 Accepted: 05 November 2024 Published: 26 December 2024
MSC : 34A08, 34D20, 37N25

This paper examined the features of an infection therapy for fractional-order quarry-hunter systems in order to control sickness. It focused especially on how illnesses and several populations combine to affect how well harvesting policies work. We created a new dynamic model full of such ideas by examining systems with fractional-order non-integer systems and introducing fractional-order systems that can remember in order to comprehend that specific system. These thresholds are essential for directing management strategies, according to research on the presence, uniqueness, and stability of solutions to these models. Additionally, we presented particular MATLAB-based numerical methods for fractional-order model. Through a series of numerical application experiments, we validated the method's efficacy and its value in guiding strategy modifications regarding harvesting rates in the face of epidemic infections. This demonstrates the necessity of using a fractional approach in ecosystem research in order to improve the methods used for resource management. This paper primarily focused on the unique insight brought into the quarry-hunter models with infectious diseases by the fractional-order dynamics in ecology. The results are meaningful especially since they can be utilized to come up with effective measures to control diseases and even promote the sustainability of ecological systems.
- fractional-order quarry-hunter models,
- specialized MATLAB routines,
- harvesting policies,
- disease dynamics
Citation: Devendra Kumar, Jogendra Singh, Dumitru Baleanu. Dynamical and computational analysis of a fractional predator-prey model with an infectious disease and harvesting policy[J]. AIMS Mathematics, 2024, 9(12): 36082-36101. doi: 10.3934/math.20241712

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Abstract

This paper examined the features of an infection therapy for fractional-order quarry-hunter systems in order to control sickness. It focused especially on how illnesses and several populations combine to affect how well harvesting policies work. We created a new dynamic model full of such ideas by examining systems with fractional-order non-integer systems and introducing fractional-order systems that can remember in order to comprehend that specific system. These thresholds are essential for directing management strategies, according to research on the presence, uniqueness, and stability of solutions to these models. Additionally, we presented particular MATLAB-based numerical methods for fractional-order model. Through a series of numerical application experiments, we validated the method's efficacy and its value in guiding strategy modifications regarding harvesting rates in the face of epidemic infections. This demonstrates the necessity of using a fractional approach in ecosystem research in order to improve the methods used for resource management. This paper primarily focused on the unique insight brought into the quarry-hunter models with infectious diseases by the fractional-order dynamics in ecology. The results are meaningful especially since they can be utilized to come up with effective measures to control diseases and even promote the sustainability of ecological systems.

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