Journal of Applied Mathematics

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

Charles Raymond, Alfred Hugo, and Monica Kung’aro

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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.

Article information

Source
J. Appl. Math., Volume 2019 (2019), Article ID 2601648, 13 pages.

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

Permanent link to this document
https://projecteuclid.org/euclid.jam/1563933639

Digital Object Identifier
doi:10.1155/2019/2601648

Mathematical Reviews number (MathSciNet)
MR3963596

Citation

Raymond, Charles; Hugo, Alfred; Kung’aro, Monica. Modeling Dynamics of Prey-Predator Fishery Model with Harvesting: A Bioeconomic Model. J. Appl. Math. 2019 (2019), Article ID 2601648, 13 pages. doi:10.1155/2019/2601648. https://projecteuclid.org/euclid.jam/1563933639


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