Affiliations 

  • 1 Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, University Tun Hussein Onn Malaysia, 86400, Batu Pahat, Johor, Malaysia
  • 2 Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, University Tun Hussein Onn Malaysia, 86400, Batu Pahat, Johor, Malaysia. hamizahs@uthm.edu.my
  • 3 Applied and Industrial Mathematics Research Group, School of Physical, Environmental and Mathematical Sciences, UNSW Canberra, Canberra, ACT, 2600, Australia
Bull. Math. Biol., 2019 Jul;81(7):2748-2767.
PMID: 31201660 DOI: 10.1007/s11538-019-00627-8

Abstract

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.

* Title and MeSH Headings from MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine.