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Communications in Mathematical Biology and Neuroscience ISSN 2052-2541

Archives › Volume 2020 (2020)

Commun. Math. Biol. Neurosci. 2020 (2020), Article ID 12

Optimal control analysis of a predator-prey model with harvesting and variable carrying capacity

Ibrahim M. ELmojtaba, Amina Al-Sawaii, Mariam Al-Moqbali

PDF (340.6 KB) https://doi.org/10.28919/cmbn/4505

Abstract

In this paper, we developed and fully analysed a mathematical model for the dynamics of predator and prey where the carrying capacity is considered to be a logistically increasing function of time, and both populations are under harvesting. Our results showed that if the harvesting rate is high then both populations could go to extinction. We also showed that the system undergoes Hopf bifurcation when the harvesting rate of the prey crosses a critical value; in fact the stability of the system changes with the change of the values of the prey harvesting rate. Optimal harvesting is shown to give a high yield and keep both population away from extension.

Published
23 March 2020
Volume
2020 (2020)
License
CC BY 3.0

Copyright © 2020 Ibrahim M. ELmojtaba, Amina Al-Sawaii, Mariam Al-Moqbali. 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

I. M. ELmojtaba, A. Al-Sawaii, M. Al-Moqbali, Optimal control analysis of a predator-prey model with harvesting and variable carrying capacity, Commun. Math. Biol. Neurosci. 2020 (2020), 12. https://doi.org/10.28919/cmbn/4505

BibTeX
@article{ELmojtaba2020,
  author  = {ELmojtaba, Ibrahim M. and Al-Sawaii, Amina and Al-Moqbali, Mariam},
  title   = {Optimal control analysis of a predator-prey model with harvesting and variable carrying capacity},
  journal = {Commun. Math. Biol. Neurosci.},
  volume  = {2020},
  year    = {2020},
  pages   = {12},
  doi     = {10.28919/cmbn/4505}
}