Analysis of optimal harvesting of a prey-predator fishery model with the limited sources of prey and presence of toxicity

Abstract

A model of prey and predator species is discussed to study the effects of the limited prey density and presence of toxicity. The model is studied for sustainable optimal harvesting. The existence of equilibrium points is analyzed to find the stability of coexistence equilibrium, and use Pontryagin’s maximal method to obtain the sustainable optimal harvesting. The results show that the optimal harvesting is obtained from the solution of optimal equilibrium. The toxicity factor decreases the sustainable harvesting.

Keywords

• Prey-predator
• harvesting
• stability
• equilibrium