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Communications in Mathematical Biology and Neuroscience ISSN 2052-2541

Archives › Volume 2019 (2019)

Commun. Math. Biol. Neurosci. 2019 (2019), Article ID 29

Harvesting of a prey-predator model fishery in the presence of competition and toxicity with two effort functions

M. R. Lemnaouar, M. Khalfaoui, Y. Louartassi, I. Tolaimate

PDF (414.9 KB) https://doi.org/10.28919/cmbn/4203

Abstract

In this paper, we propose a predator-prey model with harvesting and reserved area for prey with the presence of competition and toxicity with two effort functions. First, we prove the boundedness of the solutions. Then, the existence is studied, as well as the local and global stability of the equilibria. Lyapunov proved this last with certain conditions. The optimal harvesting policy is discussed using the Maximum Principle of Pantryagin. Finally, we ensure our results by numerical simulations.

Published
12 November 2019
Volume
2019 (2019)
License
CC BY 3.0

Copyright © 2019 M. R. Lemnaouar, M. Khalfaoui, Y. Louartassi, I. Tolaimate. 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

M. R. Lemnaouar, M. Khalfaoui, Y. Louartassi, I. Tolaimate, Harvesting of a prey-predator model fishery in the presence of competition and toxicity with two effort functions, Commun. Math. Biol. Neurosci. 2019 (2019), 29. https://doi.org/10.28919/cmbn/4203

BibTeX
@article{Lemnaouar2019,
  author  = {Lemnaouar, M. R. and Khalfaoui, M. and Louartassi, Y. and Tolaimate, I.},
  title   = {Harvesting of a prey-predator model fishery in the presence of competition and toxicity with two effort functions},
  journal = {Commun. Math. Biol. Neurosci.},
  volume  = {2019},
  year    = {2019},
  pages   = {29},
  doi     = {10.28919/cmbn/4203}
}