A dynamic reaction model of a prey-predator system with stage-structure for predator

Abstract

In this paper, we have considered a prey-predator model with stage-structure for predator and selective harvesting of prey species. A regulatory agency controls exploitation by imposing a tax per unit biomass of the prey species. The existence of steady states and their stability are studied. The problem of optimal harvesting policy is solved by using Pontryagin's  maximal principle. It is also shown that time delay may cause a stable equilibrium to become unstable. Finally, some numerical simulations are carried out.