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Modeling Dynamics of Prey-Predator Fishery Model with Harvesting: A Bioeconomic Model

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  • Charles Raymond
  • Alfred Hugo
  • Monica Kung’aro

Abstract

A mathematical model is proposed and analysed to study the dynamics of two-prey one predator system of fishery model with Holling type II function response. The effect of harvesting was incorporated to both populations and thoroughly analysed. We study the ecological dynamics of the Nile perch, cichlid, and tilapia fishes as prey-predator system of lake Victoria fishery in Tanzania. In both cases, by nondimensionalization of the system, the equilibrium points are computed and conditions for local and global stability of the system are obtained. Condition for local stability was obtained by eigenvalue approach and Routh-Hurwitz Criterion. Moreover, the global stability of the coexistence equilibrium point is proved by defining appropriate Lyapunov function. Bioeconomic equilibrium is analysed and numerical simulations are also carried out to verify the analytical results. The numerical results indicate that the three species would coexist if cichlid and tilapia fishes will not be overharvested as these populations contribute to the growth rates of Nile perch population. The fishery control management should be exercised to avoid overharvesting of cichlid and tilapia fishes.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnljam:2601648
    DOI: 10.1155/2019/2601648
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    Cited by:

    1. 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.
    2. Bairagi, Nandadulal & Bhattacharya, Santanu & Auger, Pierre & Sarkar, Biswajit, 2021. "Bioeconomics fishery model in presence of infection: Sustainability and demand-price perspectives," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    3. Dian Savitri & Agus Suryanto & Wuryansari Muharini Kusumawinahyu & Abadi, 2020. "Dynamical Behavior of a Modified Leslie–Gower One Prey–Two Predators with Competition," Mathematics, MDPI, vol. 8(5), pages 1-16, April.

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