Stability and optimal harvesting policy for a stage structured predator-prey system with delay

Due to the fact that many species go through some distinct life stages as they proceed from birth to death. We assume that the predators are divided into two stage groups, juveniles and adult, only adult predators are capable of preying on the prey species, the prey can be modeled by a logistic equation when the predator is absent. With these assumptions, we propose a delayed predator-prey model with linear harvesting rate for adult predator and constant stocking rate for prey. We analyze the dynamical behavior of the system. Under the management objective of the maximum sustainable yield, we give the optimal harvesting policy.