An age-dependent hybrid system for optimal contraception control of vermin

This paper discusses the optimal contraception control problem for vermin. The novel model consists of a first-order partial differential equation for the age-dependent density of vermin and two ordinary differential equations for the amounts of female sterilant in the environment and in an individual. We first show that the hybrid system is well-posed by applying the fixed-point theorem. Then the structure of an optimal contraception policy is established by considering the normal cone and adjoint system. Moreover, there is a unique optimal policy by employing Ekeland's variational principle and fixed-point theory. The optimal policy that we have derived offers a rational deployment strategy for the use of sterilants as a means of efficacious pest control. These criteria guarantee that during the application of sterilants, the predetermined objectives are attained while simultaneously minimizing expenditure and environmental implications. Utilizing these optimality criteria facilitates the development of streamlined and economically viable pest management protocols.