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2019 Modeling Dynamics of Prey-Predator Fishery Model with Harvesting: A Bioeconomic Model
Charles Raymond, Alfred Hugo, Monica Kung’aro
J. Appl. Math. 2019: 1-13 (2019). DOI: 10.1155/2019/2601648

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.

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Charles Raymond. Alfred Hugo. Monica Kung’aro. "Modeling Dynamics of Prey-Predator Fishery Model with Harvesting: A Bioeconomic Model." J. Appl. Math. 2019 1 - 13, 2019. https://doi.org/10.1155/2019/2601648

Information

Received: 7 March 2019; Accepted: 15 May 2019; Published: 2019
First available in Project Euclid: 24 July 2019

zbMATH: 07132114
MathSciNet: MR3963596
Digital Object Identifier: 10.1155/2019/2601648

Rights: Copyright © 2019 Hindawi

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