Nonselective harvesting of a prey-predator fishery with Gompertz law of growth

Abstract

This paper develops a mathematical model for the nonselective harvesting of a prey-predator system in which both the prey and the predator obey the Gompertz law of growth and some prey avoid predation by hiding. The steady states of the system are determined, and the dynamical behaviour of both species is examined. The possibility of existence of bionomic equilibria is discussed. The optimal harvest policy is formulated and solved as a control problem with the help of Pontryagin's maximal principle. Finally, the results are illustrated with the help of a numerical example.