Global Stability of a Predator-Prey Fishery Model With Non-Selective Harvesting: A Study of Linear Optimal Control

Abstract

A proposed two-dimensional modified Lotka-Volterra fishery model in terms of predator-prey aims to explore the effect of non-selective harvesting on the predator and the prey populations. The study delves into various essential aspects of the dynamical system, comprising positivity, uniform boundedness and persistence. Points of equilibrium are identified. The system’s local and global stability are thoroughly examined and discussed. Moreover, the research explores the concept of bionomic equilibrium, a scenario where economic rent is entirely dissipated. Extending the bioeconomic model, the study investigates a linear optimal control problem to determine the most effective harvesting strategy. Utilising Pontryagin’s maximum principle, the optimal control is characterised. The findings indicate that maximum allowable effort should be exerted whenever the net revenue per unit effort surpasses the total net marginal revenue of predator and prey stocks. Numerical simulations, with data on the marine artisanal fishery in Ghana, are conducted to validate the theoretical discoveries. The outcomes reveal that the fishery can support sustainable harvesting of both predator (tuna) and prey (sardinella) populations, so far as the optimal harvesting effort is set at 100,000 fishing trips annually.