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

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

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.

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Published: 2020-03-23

How to Cite this Article:

Ibrahim M. ELmojtaba, Amina Al-Sawaii, Mariam Al-Moqbali, Optimal control analysis of a predator-prey model with harvesting and variable carrying capacity, Commun. Math. Biol. Neurosci., 2020 (2020), Article ID 12

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.

Commun. Math. Biol. Neurosci.

ISSN 2052-2541

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