IDEAS home Printed from https://ideas.repec.org/a/wly/jijmms/v2025y2025i1n6662455.html

Local Bifurcation and Global Stability of an Eco‐Epidemiological Model Incorporating Fear Effect and Prey Harvesting

Author

Listed:
  • Sozan Fuad Aziz
  • Hanaa Jamal Ahmed
  • Saiwan Majeed Fatah
  • Arkan Nawzad Mustafa

Abstract

In ecological point of view, fears from predator may reduce the reproduction of prey and harvesting and intraspecific competition among predators, may changes the behavior of dynamical interaction between predator and their prey. In this paper, a Holling Type II prey–predator model with SI‐type of disease in prey has been modified and analyzed. Firstly, some properties like positivity and boundedness of the solutions of the model are proved and then the criterion that makes the model equilibrium points persist is determined. The criterion for locally as well as globally asymptotically stable of the each model is investigated. The application of the hypothesis of the Sotomayor theorem for local bifurcation near the equilibrium points is adopted. Finally, further investigations for the global dynamics and confirmation the analytical results of the system are carried out with the help of numerical simulations. It is observed that both fear and harvesting rate may cause extinction in the predator.

Suggested Citation

  • Sozan Fuad Aziz & Hanaa Jamal Ahmed & Saiwan Majeed Fatah & Arkan Nawzad Mustafa, 2025. "Local Bifurcation and Global Stability of an Eco‐Epidemiological Model Incorporating Fear Effect and Prey Harvesting," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jijmms:v:2025:y:2025:i:1:n:6662455
    DOI: 10.1155/ijmm/6662455
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/ijmm/6662455
    Download Restriction: no
    File URL: https://libkey.io/10.1155/ijmm/6662455?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Raid Kamel Naji & Arkan N. Mustafa, 2012. "The Dynamics of an Eco‐Epidemiological Model with Nonlinear Incidence Rate," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Hersh Aziz Mohammed & Arkan Nawzad Mustafa, 2025. "Dynamical Analysis of a Delay Two‐Prey–One‐Predator Model Incorporating Fear Effect in the Growth Rate of Preys," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    4. Hersh Aziz Mohammed & Arkan Nawzad Mustafa, 2025. "Dynamical Analysis of a Delay Two-Prey–One-Predator Model Incorporating Fear Effect in the Growth Rate of Preys," Journal of Applied Mathematics, Hindawi, vol. 2025, pages 1-10, February.
    5. Mortuja, Md Golam & Chaube, Mithilesh Kumar & Kumar, Santosh, 2021. "Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Raid Kamel Naji & Reem Mudar Hussien, 2016. "The Dynamics of Epidemic Model with Two Types of Infectious Diseases and Vertical Transmission," Journal of Applied Mathematics, John Wiley & Sons, vol. 2016(1).
    2. Hanaa Jamal Ahmed & Kawther Yusuf Abdulrahman & Karzan Abdulrahman Hamzah & Arkan Nawzad Mustafa, 2025. "Local Bifurcation and Global Stability of Two‐Prey‐One‐Predator Model," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    3. Hersh Aziz Mohammed & Arkan Nawzad Mustafa, 2025. "Dynamical Analysis of a Delay Two‐Prey–One‐Predator Model Incorporating Fear Effect in the Growth Rate of Preys," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    4. Reem Mudar Hussien & Raid Kamel Naji, 2023. "The Dynamics of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate," Journal of Applied Mathematics, John Wiley & Sons, vol. 2023(1).
    5. Ali, Zeeshan & Rabiei, Faranak & Hosseini, Kamyar, 2023. "A fractal–fractional-order modified Predator–Prey mathematical model with immigrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 466-481.
    6. Yao, Yong, 2025. "Dynamics of a Leslie–Gower type predator–prey system with herd behavior and constant harvesting in prey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 32-49.
    7. Sarif, Nawaj & Kumar, Arjun & Anshu, & Sarwardi, Sahabuddin & Dubey, Balram, 2024. "Spatio-temporal dynamics in a delayed prey–predator model with nonlinear prey refuge and harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    8. Feilong Wang & Min Xiao & Zhengxin Wang & Jing Zhao & Gong Chen & Jinde Cao, 2022. "Spatiotemporal Evolution Characteristics of Time‐Delay Ecological Competition Systems with Food‐Limited and Diffusion," Complexity, John Wiley & Sons, vol. 2022(1).
    9. 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.
    10. Li, Zhenlei & Zhang, Yue, 2024. "Dynamic analysis of a fast slow modified Leslie–Gower predator–prey model with constant harvest and stochastic factor," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 474-499.
    11. Arjun Hasibuan & Asep Kuswandi Supriatna & Endang Rusyaman & Md. Haider Ali Biswas, 2023. "Predator–Prey Model Considering Implicit Marine Reserved Area and Linear Function of Critical Biomass Level," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    12. Huangyu Guo & Jing Han & Guodong Zhang, 2023. "Hopf Bifurcation and Control for the Bioeconomic Predator–Prey Model with Square Root Functional Response and Nonlinear Prey Harvesting," Mathematics, MDPI, vol. 11(24), pages 1-18, December.
    13. Haiyin Li & Xuhua Cheng, 2021. "Dynamics of Stage-Structured Predator–Prey Model with Beddington–DeAngelis Functional Response and Harvesting," Mathematics, MDPI, vol. 9(17), pages 1-15, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jijmms:v:2025:y:2025:i:1:n:6662455. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/6396 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.