Fishery model influenced by pollution with optimal harvesting policy

Josué Carlos Israël OULAI; Hypolithe OKOU; David Paul TUO

doi:10.61383/ejam.202534114

Authors

Josué Carlos Israël OULAI Research and Formation Unit of Mathematics and Computer Science, Félix Houphouët-Boigny University of Abidjan Cocody, Abidjan, Ivory Coast Corresponding Author https://orcid.org/0009-0003-1739-8780
Hypolithe OKOU Research and Formation Unit of Mathematics and Computer Science, Félix Houphouët-Boigny University of Abidjan Cocody, Abidjan, Ivory Coast https://orcid.org/0000-0001-5504-9387
David Paul TUO Research and Formation Unit of Mathematics and Computer Science, Félix Houphouët-Boigny University of Abidjan Cocody, Abidjan, Ivory Coast https://orcid.org/0009-0008-9896-4946

DOI:

https://doi.org/10.61383/ejam.202534114

Keywords:

Equilibrium points, stability, profit, fishing effort, MSY, MEY, pollution

Abstract

In this work, we proposed a simplified version of the Gordon-Schaefer model in which the mortality rate of the fish stock biomass and the unit cost of effort are due to aquatic pollution, and harvesting is non-linear. Our dynamic study shows that our system is globally bounded and asymptotically and globally stable under certain conditions around the single interior equilibrium point. We then performed a numerical simulation to validate our theoretical results. Next, we determined the maximum sustainable yield (MSY) and maximum equilibrium yield (MEY), and presented numerical results. Finally, using Pontryagin's maximum principle, we determined the optimal control and performed a numerical simulation.

References

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