Harvesting in a toxicated intraguild predator–prey fishery model with variable carrying capacity

Abstract

Latterly, variable carrying capacity in the predator–prey population models has been widely studied to provide more realistic understanding about population dynamics. In the present paper, we discuss the bio-economic harvesting of an intraguild fishery model where the logistic carrying capacities of both predator and prey fish populations are variable based on the shared biotic resource. Distinct from most fishery models, we incorporate the independent harvesting strategies on the fisheries with different harvesting efforts by assuming them to have different economic values. In our model, the prey fish population is assumed to be infected directly by an anthropogenic toxicant from the environment while the predator is infected indirectly when they feed on prey. We investigate the local stability of trivial equilibria with Routh–Hurwitz criterion and the global stability of non-trivial equilibrium by constructing a Lyapunov function. Bifurcation and numerical analyses are presented to show distinctive result that a Hopf bifurcation occurs with respect to harvesting parameter instead of resource enrichment parameter as in the literature. Bionomic equilibrium is explored with several possibilities and restrictions. The nontrivial bionomic equilibrium is found to depend critically on the resource density. Finally, the optimal harvesting policy of the three dimensional model is derived by utilizing Pontryagin Maximum Principle. From this study, harvesting parameter is a crucial factor for the stability of the intraguild system. The objective is to obtain the optimal sustainable yield that provides maximum monetary profit while conserving the marine ecosystem.