Fishery model influenced by global warming with optimal harvesting policy

Josué Carlos Israël OULAI; Hypolithe OKOU; Albin Tetchi N'GUESSAN

doi:10.61383/ejam.202533113

Authors

Josué Carlos Israël OULAI Email ORCID Research and Formation Unit of Mathematics and Computer Science, Félix Houphouët Boigny University of Abidjan Cocody, Abidjan, Ivory Coast Corresponding Author
Hypolithe OKOU Email ORCID Research and Formation Unit of Mathematics and Computer Science, Félix Houphouët Boigny University of Abidjan Cocody, Abidjan, Ivory Coast
Albin Tetchi N'GUESSAN Email ORCID Research and Formation Unit of Mathematics and Computer Science, Félix Houphouët Boigny University of Abidjan Cocody, Abidjan, Ivory Coast

DOI:

https://doi.org/10.61383/ejam.202533113

Keywords:

equilibrium points, stability, profit, fishing effort, MSY, MEY, temperature

Abstract

In this article, we proposed a modified version of the Gordon-Schaefer model in which harvesting is non-linear and the mortality rate of the fish stock is a function of temperature. We showed that every solution of the system is globally bounded and that there is a single interior equilibrium point that is locally, asymptotically, and globally stable under certain conditions. We then determined the optimal levels of production and profit when the stock evolution is kept constant (MSY and MEY, respectively). Furthermore, using Pontryagin's maximum principle, we characterized the optimal harvesting policy that maximizes net present value. Finally, we performed numerical simulations to validate our theoretical results.

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