Optimal Contraception Control Problems in a Nonlinear Size-Structured Vermin Model

Rong Liu (), Fengqin Zhang () and Yuming Chen ()
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Rong Liu: Shanxi University of Finance and Economics
Fengqin Zhang: Yuncheng University
Yuming Chen: Wilfrid Laurier University

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 3, No 13, 1188-1221

Abstract: Abstract This paper investigates a size-structured vermin contraception control model with nonlinear fertility and mortality, in which the control variable appears in both the state equation and the boundary condition. First, we show that the model has a unique non-negative solution, which has a separable form. Then, some continuity results are established, which are important for the purpose of optimal control. In order to make the final size of vermin as small as possible or as close as possible to the ideal distribution under the condition of the lowest control cost, we consider the least cost-size problem and the least cost-deviation problem. For each of the control problems, the optimality conditions are obtained via the adjoint system and tangent-normal cones. For the first problem, we show the existence of the optimal strategy by compactness and extremal sequence. However, for the second problem, we derive the existence of an optimal control via Ekeland’s variational principle. Some numerical simulations have been performed to demonstrate the feasibility of the obtained theoretical results. Numerical results also suggest that decreasing the reproductive rate instead of increasing the mortality is an effective way of managing the impact of vermin.

Keywords: Contraception control; Size-structure; Least cost-size problem; Least cost-deviation problem; 49K20; 49K15; 92D25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02246-9

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