A Stage-Structured Prey-Predator Fishery Model In The Presence Of Toxicity With Taxation As A Control Parameter of Harvesting Effort

Abstract

In this paper we have considered stage-structured fishery model in the presence of toxicity, which is diminishing due to the current excessive use of fishing efforts resulting in devastating consequences. The purpose of this study is to propose a bio-economic mathematical model by introducing taxes to the profit per unit biomass of the harvested fish of each species with the intention of controlling fishing efforts in the presence of toxicity. We obtained both boundary and interior equilibrium points along with the conditions ensuring their validity. Local stability for the interior equilibrium point has been found by the trace-determinant criterion and global stability has been analyzed through a suitable Lyapunov function. We have also obtained the optimal harvesting policy with the help of Pontryagins maximum principle. Lastly, numerical simulation with the help of MATLAB have been done and thus, the results of the formulated model have been established.

Sensitivity Analysis of Marine Reserves and Its Implications as Fishery Management Tool

“…But [3] investigated marine reserves and its consequences as a fisheries management tool and indicated that prey-predator interactions do matter when the implementation of reserved is considered. [4] Then proposed a stage-structured prey-predator fishery model in the presence of toxicity with taxation as a control parameter of harvesting effort. Despite the fact that scientists and researcher consider the increasing range of closed areas for conservation of marine biodiversity [5,6].…”