| Abstract: | To protect fishery populations on the verge of extinction and sustain the biodiversity of the marine ecosystem, marine protected areas (MPA) are established to provide a refuge for fishery resource. However, the influence of current harvesting policies on the MPA is still unclear, and precise information of the biological parameters has yet to be conducted. In this paper, we consider a bioeconomic Gompertz population model with interval‐value biological parameters in a 2‐patch environment: a free fishing zone (open‐access) and a protected zone (MPA) where fishing is strictly prohibited. First, the existence of the equilibrium is proved, and by virtue of Bendixson‐dulac Theorem, the global stability of the nontrivial steady state is obtained. Then, the optimal harvesting policy is established by using Pontryagin's maximum principle. Finally, the results are illustrated with the help of some numerical examples. Our results show that the current harvesting policy is advantageous to the protection efficiency of an MPA on local fish populations. |
