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  3. Volume 11, Number 2, 2024
  4. Optimal control problem of a discrete spatiotemporal prey–predator three-species fishery model

Optimal control problem of a discrete spatiotemporal prey–predator three-species fishery model

MMC.
2024;
Volume 11, Number 2
: pp. 528–538
https://doi.org/10.23939/mmc2024.02.528
Received: December 31, 2023
Revised: June 23, 2024
Accepted: June 27, 2024

Sakkoum A., Toufga H., Hizazi H., Lhous M., Magri E. M.  Optimal control problem of a discrete spatiotemporal prey–predator three-species fishery model.  Mathematical Modeling and Computing. Vol. 11, No. 2, pp. 528–538 (2024)

Authors:
  1. A. Sakkoum
  2. H. Toufga
  3. H. Hizazi
  4. M. Lhous
  5. E. M. Magri
1
Fundamental and Applied Mathematics Laboratory, Faculty of Sciences Ain Chock, Hassan II University of Casablanca
2
Fundamental and Applied Mathematics Laboratory, Faculty of Sciences Ain Chock, Hassan II University of Casablanca
3
Fundamental and Applied Mathematics Laboratory, Faculty of Sciences Ain Chock, Hassan II University of Casablanca
4
Fundamental and Applied Mathematics Laboratory, Faculty of Sciences Ain Chock, Hassan II University of Casablanca
5
Fundamental and Applied Mathematics Laboratory, Faculty of Sciences Ain Chock, Hassan II University of Casablanca

In this work, we discuss a spatiotemporal discrete prey–predator model.  It consists of three compartments: prey, predator, and super-predator.  The proposed model describes the interaction between prey, predator, and super-predator in a region with a discrete displacement.  We also provide research on appropriate regional control strategies.  The controls are applied to the predator and the super-predator, respectively; they represent catching these in measured quantities in a space and a time chosen.  The aim is to increase the number of prey and reduce the number of predators, restore the food chain system, and ensure its sustainability.  Finally, we provide graphical visuals and numerical simulations to support our analytical findings.

prey–predator
spatiotemporal discrete model
optimal control
Pontryagin's maximum principle
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