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Optimal Contraception Control for a Nonlinear Vermin Population Model with Size-Structure

Optimal Contraception Control for a Nonlinear Vermin Population Model with Size-Structure This paper investigates the optimal contraception control for a nonlinear size-structured population model with three kinds of mortality rates: intrinsic, intra-competition and female sterilant. First, we transform the model to a system of two subsystems, and establish the existence of a unique non-negative solution by means of frozen coefficients and fixed point theory, and show the continuous dependence of the population density on control variable. Then, the existence of an optimal control strategy is proved via compactness and extremal sequence. Next, necessary optimality conditions of first order are established in the form of an Euler–Lagrange system by the use of tangent-normal cone technique and adjoint system. Moreover, a numerical result for the optimal control strategy is presented. Our conclusions would be useful for managing the vermin. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Optimal Contraception Control for a Nonlinear Vermin Population Model with Size-Structure

Liu, Rong; Liu, Guirong
Applied Mathematics and Optimization , Volume 79 (2) – Jun 19, 2017
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References (30)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-017-9428-y
Publisher site
See Article on Publisher Site

Abstract

This paper investigates the optimal contraception control for a nonlinear size-structured population model with three kinds of mortality rates: intrinsic, intra-competition and female sterilant. First, we transform the model to a system of two subsystems, and establish the existence of a unique non-negative solution by means of frozen coefficients and fixed point theory, and show the continuous dependence of the population density on control variable. Then, the existence of an optimal control strategy is proved via compactness and extremal sequence. Next, necessary optimality conditions of first order are established in the form of an Euler–Lagrange system by the use of tangent-normal cone technique and adjoint system. Moreover, a numerical result for the optimal control strategy is presented. Our conclusions would be useful for managing the vermin.

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Jun 19, 2017

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