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A study on eco-epidemiological model with fractional operators

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  • Kumar, Ajay
  • Kumar, Sunil

Abstract

This paper employs fractional calculus (FC) for modeling three-dimensional prey-predator populations model. This study uses an eco-epidemiological system in which the prey disease is constructed as a susceptible-infected (SI) disease. The Caputo and Caputo-Fabrizio (CF) operators are consolidated into this model and the existence of a solution is explored. The model is evaluated for uniqueness under what conditions it provides a unique solution. Based on the singular kernel of the Caputo operator, we investigate the properties of the proposed model and show it can be stable locally. We developed maximum bifurcation diagrams to analyze the dynamics of the epidemiological model as varying transmission rates β and attack rates b1. To simulate the dynamics of proposed fractional systems, we employed the Toufik-Atangana (TA) numerical technique with the Caputo operator. Moreover, we present another numerical approach based on Adams-Bashforth (AB) technique with CF operators. Results of the numerical analysis show that diverse non-integer operator alternatives to the eco-epidemiological predator-prey model result in a range of dynamical behaviors.

Suggested Citation

  • Kumar, Ajay & Kumar, Sunil, 2022. "A study on eco-epidemiological model with fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077921010511
    DOI: 10.1016/j.chaos.2021.111697
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    References listed on IDEAS

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    1. Owolabi, Kolade M. & Atangana, Abdon, 2017. "Analysis and application of new fractional Adams–Bashforth scheme with Caputo–Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 111-119.
    2. Gashirai, Tinashe B. & Musekwa-Hove, Senelani D. & Lolika, Paride O. & Mushayabasa, Steady, 2020. "Global stability and optimal control analysis of a foot-and-mouth disease model with vaccine failure and environmental transmission," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Kumar, Sunil & Kumar, Ajay & Samet, Bessem & Gómez-Aguilar, J.F. & Osman, M.S., 2020. "A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    4. Iqbal, Muhammad Kashif & Abbas, Muhammad & Wasim, Imtiaz, 2018. "New cubic B-spline approximation for solving third order Emden–Flower type equations," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 319-333.
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    Cited by:

    1. Ajay Kumar & Sara Salem Alzaid & Badr Saad T. Alkahtani & Sunil Kumar, 2022. "Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator," Mathematics, MDPI, vol. 10(10), pages 1-23, May.
    2. Matouk, A.E. & Lahcene, Bachioua, 2023. "Chaotic dynamics in some fractional predator–prey models via a new Caputo operator based on the generalised Gamma function," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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