Impact of Harvesting on a Bioeconomic Predator–Prey Fishery Model Subject to Environmental Toxicant
- 9 Downloads
The present paper studies a predator–prey fishery model which incorporates the independent harvesting strategies and nonlinear impact of an anthropogenic toxicant. Both fish populations are harvested with different harvesting efforts, and the cases for the presence and non-presence of harvesting effort are discussed. The prey fish population is assumed to be infected by the toxicant directly which causes indirect infection to predator fish population through the feeding process. Each equilibrium of the proposed system is examined by analyzing the respective local stability properties. Dynamical behavior and bifurcations are studied with the assistance of threshold conditions influencing the persistence and extinction of both predator and prey. Bionomic equilibrium solutions for three possible cases are investigated with certain restrictions. Optimal harvesting policy is explored by utilizing the Pontryagin’s Maximum Principle to optimize the profit while maintaining the sustainability of the marine ecosystem. Bifurcation analysis showed that the harvesting parameters are the key elements causing fishery extinction. Numerical simulations of bionomic and optimal equilibrium solutions showed that the presence of toxicant has a detrimental effect on the fish populations.
KeywordsPredator–prey Harvesting Toxicant Biotechnical productivity Bionomic equilibrium Optimal harvesting policy
Authors thank the anonymous reviewers for their critical comments and helpful suggestions to improve the quality and presentation of this work. The present research is supported by Research Management Centre (RMC) University Tun Hussein Onn Malaysia (Postgraduate Research Grant Code: U992) and Incentive Grant Scheme For Publication (U677).
- Arrow KJ, Kurz M (1970) Public investment, the rate of return and optimal fiscal policy. John Hopfkins, BaltimoreGoogle Scholar
- Ermentrout B (2010) XPPAUT 6:00Google Scholar
- FAO (2016) The State of World Fisheries and Aquaculture 2016 (SOFIA): contributing to food security and nutrition for all, 200. Food and Agriculture Organization, RomeGoogle Scholar
- Maplesoft (2008) Maplesoft v. 16, Maplesoft, Waterloo, Ontario, CanadaGoogle Scholar
- MathWorks (2014) MATLAB v. R2015a, The MathWorks, USAGoogle Scholar