Optimal contraception control for a size-structured population model with extra mortality

ABSTRACT

This paper investigates the theoretical aspects for an optimal contraception control problem of a linear size-structured population model with extra mortality. The existence of a unique non-negative solution is established by using the Banach fixed-point theorem. The existence of a unique optimal strategy is derived by the Mazur theorem in convex analysis and the optimality conditions are obtained by means of normal cone and adjoint system techniques. Finally, some numerical results demonstrate the effectiveness of the theoretical results in our paper.

COMMUNICATED BY:

• Irena Lasiecka

KEYWORDS:

• Size structure
• contraception control
• extra mortality

AMS SUBJECT CLASSIFICATIONS:

• 49N90
• 92D25

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Nos. 11471197, 11571210, 11501339) and the Natural Science Foundation of Shanxi Province (No. 201601D202002).