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Optimal Control of an Eco-Epidemiological Reaction-Diffusion Model

Author

Listed:
  • 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)

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.

Suggested Citation

  • Runmei Du & Xinghua Liang & Yang Na & Fengdan Xu, 2025. "Optimal Control of an Eco-Epidemiological Reaction-Diffusion Model," Mathematics, MDPI, vol. 13(13), pages 1-27, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2069-:d:1684715
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