A hierarchical age-structured model of optimal vermin management by contraception

Rong Liu; Fengqin Zhang; Rong Liu; Fengqin Zhang

doi:10.3934/mbe.2023288

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 4: 6691-6720. doi: 10.3934/mbe.2023288

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A hierarchical age-structured model of optimal vermin management by contraception

Rong Liu ¹,
Fengqin Zhang ^{2
,
,}

1.
School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China
2.
School of Mathematics and Information Technology, Yuncheng University, Yuncheng 044000, China

Received: 08 December 2022 Revised: 11 January 2023 Accepted: 16 January 2023 Published: 03 February 2023

Taking the reproduction law of vermin into consideration, we formulate a hierarchical age-structured model to describe the optimal management of vermin by contraception control. It is shown that the model is well-posed, and the solution has a separable form. The existence of optimal management policy is established via a minimizing sequence and the use of compactness, while the structure of optimal strategy is obtained by using an adjoint system and normal cones. To show the compactness, we use the Fréchet-Kolmogorov theorem and its generalization. To construct the adjoint system, we give some continuity results. Finally, an illustrative example is given.
- hierarchical age-structure,
- optimal vermin management,
- contraception control model,
- encounter mechanism
Citation: Rong Liu, Fengqin Zhang. A hierarchical age-structured model of optimal vermin management by contraception[J]. Mathematical Biosciences and Engineering, 2023, 20(4): 6691-6720. doi: 10.3934/mbe.2023288

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Abstract

Taking the reproduction law of vermin into consideration, we formulate a hierarchical age-structured model to describe the optimal management of vermin by contraception control. It is shown that the model is well-posed, and the solution has a separable form. The existence of optimal management policy is established via a minimizing sequence and the use of compactness, while the structure of optimal strategy is obtained by using an adjoint system and normal cones. To show the compactness, we use the Fréchet-Kolmogorov theorem and its generalization. To construct the adjoint system, we give some continuity results. Finally, an illustrative example is given.

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