Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 13 (2018), 1 -- 26

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This work is licensed under a Creative Commons Attribution 4.0 International License.


Ali Moussaoui

Abstract. The aim of this work is the formulation and the study of a stock-effort fishing model, in which the fish population is structured by age and is governed by the McKendrick-von Foerster partial differential equation while the fishing effort is described by an ordinary differential equation. In this model, the number of vessels increases when the fishery makes profit, otherwise it decreases. The existence and uniqueness of solutions for the system are proved by using the Banach fixed point theorem. Existence of several stationary solutions is studied: extinction equilibrium where there are no fish and there is no fishing, a Fishery Free Equilibrium (FFE) as well as a Sustainable Fishery Equilibrium (SFE). A relatively simple method is used to arrive at a condition of stability of stationary solutions.

2010 Mathematics Subject Classification: 92A15; 92D25; 93A30.
Keywords: Age-structured model, McKendrick-von Foerster equation, Fisheries management, Steady states, Stability.

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Ali Moussaoui
Département de Mathématiques, Faculté des Sciences, Université de Tlemcen. Algérie.