TY  - JOUR
AU  - Yi, Xin
AU  - Liu, Rong
PY  - 2025
TI  - An age-dependent hybrid system for optimal contraception control of vermin
JO  - AIMS Mathematics
SP  - 2619
EP  - 2633
VL  - 10
IS  - 2
AB  - 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.
UR  - https://doi.org/10.3934/math.2025122
DO  - 10.3934/math.2025122