Optimal birth control problems for a nonlinear vermin population model with size-structure

In this paper we investigate theoretically the least cost-size problem and the least cost-deviation problem for a nonlinear size-structured vermin population model with separable mortality, which takes fertility rate as the control variable. We obtain the existence of a unique non-negative solution by considering the separable solution of the model, which is crucial to obtain the optimal control strategy. We also illustrate the continuous dependence of the population density on initial value and control parameter. Finally, we study the least cost-size problem and the least cost-deviation problem. Our conclusion would be useful for managing the vermin.