A hierarchical age-structured model of optimal vermin management by contraception

Taking the reproduction law of vermin into consideration, we formulate a hierarchical age-structured model to describe the optimal management of vermin by contraception control. It is shown that the model is well-posed, and the solution has a separable form. The existence of optimal management policy is established via a minimizing sequence and the use of compactness, while the structure of optimal strategy is obtained by using an adjoint system and normal cones. To show the compactness, we use the Fréchet-Kolmogorov theorem and its generalization. To construct the adjoint system, we give some continuity results. Finally, an illustrative example is given.