Optimal Control of an Eco-Epidemiological Reaction-Diffusion Model

Runmei Du, Xinghua Liang, Yang Na and Fengdan Xu ()
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Runmei Du: School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
Xinghua Liang: School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
Yang Na: School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
Fengdan Xu: Department of Mathematics, Dalian Minzu University, Dalian 116600, China

Mathematics, 2025, vol. 13, issue 13, 1-27

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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