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Volume 13
Issue 13
10.3390/math13132069
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Optimal Control of an Eco-Epidemiological Reaction-Diffusion Model

by
Runmei Du
1,
Xinghua Liang
1,
Yang Na
1 and
Fengdan Xu
2,*
1
School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
2
Department of Mathematics, Dalian Minzu University, Dalian 116600, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(13), 2069; https://doi.org/10.3390/math13132069 (registering DOI)
Submission received: 29 May 2025 / Revised: 18 June 2025 / Accepted: 20 June 2025 / Published: 22 June 2025
Versions Notes

Abstract

In this paper, a prey–predator diffusion model with isolation and drug treatment control measures for prey infection is studied. The main objective is to find an optimal control that minimizes the population density of infected prey and the costs of isolation and drug treatment for infected prey. Through analysis, the existence and uniqueness of weak solution, as well as the existence and local uniqueness of optimal controls are proven. The first-order necessary condition is derived, and the feasibility of the theoretical proof is verified through numerical simulations.
Keywords: an eco-epidemiological model; disease in prey; a prey-predator model; reaction-diffusion equation an eco-epidemiological model; disease in prey; a prey-predator model; reaction-diffusion equation

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MDPI and ACS Style

Du, R.; Liang, X.; Na, Y.; Xu, F. Optimal Control of an Eco-Epidemiological Reaction-Diffusion Model. Mathematics 2025, 13, 2069. https://doi.org/10.3390/math13132069

AMA Style

Du R, Liang X, Na Y, Xu F. Optimal Control of an Eco-Epidemiological Reaction-Diffusion Model. Mathematics. 2025; 13(13):2069. https://doi.org/10.3390/math13132069

Chicago/Turabian Style

Du, Runmei, Xinghua Liang, Yang Na, and Fengdan Xu. 2025. "Optimal Control of an Eco-Epidemiological Reaction-Diffusion Model" Mathematics 13, no. 13: 2069. https://doi.org/10.3390/math13132069

APA Style

Du, R., Liang, X., Na, Y., & Xu, F. (2025). Optimal Control of an Eco-Epidemiological Reaction-Diffusion Model. Mathematics, 13(13), 2069. https://doi.org/10.3390/math13132069

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