Dynamic behaviour of a single-species nonlinear fishery model with infection: the role of fishing tax and time-dependent market price

Abstract

Taxation policy for fishing received global consent to protect fisheries from drastic harvesting. Still, it should be applied sustainably for a greater ecological and economic benefit because over-taxation may impair fishers' earnings and reduce the overall societal revenue. The fish disease may alter the system dynamics and reduce the revenue generation from the fishery. This paper proposes a nonlinear bioeconomic harvesting model of a single-species fishery with infection, variable market price, and nonlinear demand to explore taxation's ecological and economic effects. We provide the stability results of the system's different ecological and economic equilibrium points. The analytical conditions for the existence of transcritical bifurcation are also established. The computational results show that the system exhibits three dynamical regimes depending on the fishing tax. Taxation might control intensive harvesting but augment disease spreading and price hiking. Higher regulatory tax may even cause a regime shift, where the system enters into a non-harvesting regime from the harvesting one, causing an ecological and economic imbalance. Using Pontryagin's maximum principle, we decipher that some optimal fishing tax exists for the maximum societal benefit in a disease-induced fishery.