@article{fdi:010085866,
  title = {{O}ptimal placement of marine protected areas to avoid the extinction of the fish stock},
  author = {{G}houali, {A}. and {M}oussaoui, {A}. and {A}uger, {P}ierre and {N}guyen-{H}uu, {T}ri},
  editor = {},
  language = {{ENG}},
  abstract = {{I}n this paper, we propose to study a fishery model with variable price. {W}e assume that the price evolves much faster than the rest of the system. {U}nder certain assumptions, this makes it possible to consider the fishery system as a slow-fast system, on two time scales, and to study it with a reduced model of dimension two. {T}wo main cases can occur. {T}he first one which we called catastrophic equilibrium corresponds to over-exploitation leading to fish extinction and a booming price. {T}he second case corresponds to a sustainable fishery equilibrium which is stable. {T}he possible effects of the creation of marine protected areas ({MPA}s), sites where fishing is prohibited, on the fish stock and fishery are evaluated. {W}e show that {MPA}s can have a positive effect on the restoration of depleted fish stocks by destabilizing the catastrophic equilibrium and keeping only one positive equilibrium which will be globally asymptotically stable. {T}his problem is addressed by proposing a model with {MPA} for the fish dynamics. {F}ish are assumed to move between {MPA} and fishing area and are subject to harvesting through fishing. {W}e show that to avoid the extinction of the stock and stabilize the fishery in the long term, it is necessary to define a fishing zone such that the ratio of its carrying capacity to its surface is small enough. {W}e further show that with a judicious choice of the surface area of the {MPA}, it is possible to optimize the total capture.},
  keywords = {{S}tock-{E}ffort {M}odel ; {V}arying {P}rice ; {N}onlinear {D}emand ; {A}ggregation of {V}ariables ; {M}arine {R}eserve ; {M}aximum {S}ustainable {Y}ield},
  booktitle = {},
  journal = {{J}ournal of {B}iological {S}ystems},
  volume = {30},
  numero = {02},
  pages = {323--337},
  ISSN = {0218-3390},
  year = {2022},
  DOI = {10.1142/s0218339022500115},
  URL = {https://www.documentation.ird.fr/hor/fdi:010085866},
}