Optimal harvesting for periodic age-dependent population dynamics

Here we investigate the optimal harvesting problem for some periodic age-dependent population dynamics; namely, we consider the linear Lotka-McKendrick model with periodic vital rates and a periodic forcing term that sustains oscillations. Existence and uniqueness of a positive periodic solution are demonstrated and the existence and uniqueness of the optimal control are established. We also state necessary optimality conditions. A numerical algorithm is developed to approximate the optimal control and the optimal harvest. Some numerical results are presented.