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The Impact of Fear on a Harvested Prey–Predator System with Disease in a Prey

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  • Hiba Abdullah Ibrahim

    (Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq)

  • Raid Kamel Naji

    (Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq)

Abstract

A mathematical eco-epidemiological model consisting of harvested prey–predator system involving fear and disease in the prey population is formulated and studied. The prey population is supposed to be separated into two groups: susceptible and infected. The susceptible prey grows logistically, whereas the infected prey cannot reproduce and instead competes for the environment’s carrying capacity. Furthermore, the disease is transferred through contact from infected to susceptible individuals, and there is no inherited transmission. The existence, positivity, and boundedness of the model’s solution are discussed. The local stability analysis is carried out. The persistence requirements are established. The global behavior of the system is investigated with the use of the Lyapunov method. An application to the Sotomoyar theorem of local bifurcation is performed around the equilibrium points. In the end, the system is numerically simulated to confirm our obtained analytical results and specify the control set of parameters. Bifurcation diagrams are used to show the dynamical behavior as a function of some parameters. It is obtained that the prey’s fear stabilizes the system, while the disease and harvest cause extinction in one or more species.

Suggested Citation

  • Hiba Abdullah Ibrahim & Raid Kamel Naji, 2023. "The Impact of Fear on a Harvested Prey–Predator System with Disease in a Prey," Mathematics, MDPI, vol. 11(13), pages 1-28, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2909-:d:1182183
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    References listed on IDEAS

    as
    1. Raid Kamel Naji & Arkan N. Mustafa, 2012. "The Dynamics of an Eco-Epidemiological Model with Nonlinear Incidence Rate," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-24, October.
    2. Zhang, Huisen & Cai, Yongli & Fu, Shengmao & Wang, Weiming, 2019. "Impact of the fear effect in a prey-predator model incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 328-337.
    3. Charles Raymond & Alfred Hugo & Monica Kung’aro, 2019. "Modeling Dynamics of Prey-Predator Fishery Model with Harvesting: A Bioeconomic Model," Journal of Applied Mathematics, Hindawi, vol. 2019, pages 1-13, June.
    4. Naji, R.K. & Balasim, A.T., 2007. "On the dynamical behavior of three species food web model," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1636-1648.
    5. Zainab Saeed Abbas & Raid Kamel Naji, 2022. "Modeling and Analysis of the Influence of Fear on a Harvested Food Web System," Mathematics, MDPI, vol. 10(18), pages 1-37, September.
    6. Abayneh Fentie Bezabih & Geremew Kenassa Edessa & Koya Purnachandra Rao, 2021. "Ecoepidemiological Model and Analysis of Prey-Predator System," Journal of Applied Mathematics, Hindawi, vol. 2021, pages 1-17, February.
    7. Firas Hussean Maghool & Raid Kamel Naji, 2021. "The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear," Journal of Applied Mathematics, Hindawi, vol. 2021, pages 1-21, September.
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