Allee and fear effects in prey-predator dynamics: stability analysis and optimal harvesting
Abstract
This study incorporates the Allee effect and the fear effect into a predator-prey model. We investigate how these factors, along with fishing pressure, influence the population dynamics of both predator and prey. The analysis begins by establishing the positivity and boundedness of solutions, ensuring the populations remain within realistic ranges. Stability analysis of the interior equilibrium point, where both populations coexist, reveals the system’s resilience to disturbances. Furthermore, we explore optimal fishing strategies that balance maximizing long-term profit with maintaining sustainable populations. Finally, numerical simulations conducted validate the theoretical predictions.
- Published
- 17 July 2025
- Volume
- 2025 (2025)
- License
- CC BY 3.0
Copyright © 2025 Asmaa Idmbarek, Mohamed Hafdane, Nossaiba Baba, Youssef El Foutayeni, Naceur Achtaich. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
A. Idmbarek, M. Hafdane, N. Baba, Y. El Foutayeni, N. Achtaich, Allee and fear effects in prey-predator dynamics: stability analysis and optimal harvesting, Commun. Math. Biol. Neurosci. 2025 (2025), 87. https://doi.org/10.28919/cmbn/9353
BibTeX
@article{Idmbarek2025,
author = {Idmbarek, Asmaa and Hafdane, Mohamed and Baba, Nossaiba and El Foutayeni, Youssef and Achtaich, Naceur},
title = {Allee and fear effects in prey-predator dynamics: stability analysis and optimal harvesting},
journal = {Commun. Math. Biol. Neurosci.},
volume = {2025},
year = {2025},
pages = {87},
doi = {10.28919/cmbn/9353}
}