We study the optimal harvesting policy for fishery in the marine protected and unreserved areas. In the literature, it is generally assumed that the fish population follows a concrete growth law. In contrast, we consider an abstract model with migration from the reserved area to the unreserved one. Then we examine and analyze the existence and stability of a nontrivial equilibrium point of the model. We also discuss the bionomic equilibrium. After that, we use the Pontryagin maximum principle to obtain the optimal harvest policy, where, instead of the well-known Hamiltonian function, we use the current Hamiltonian function to ease the calculation. Finally, we give some numerical examples to further illustrate our statements, where we also find that in practice the impreciseness of the parameters can influence the existence of the system positive equilibrium.

我们研究了海洋保护区和非保护区的最佳渔业捕捞政策。在文献中，通常假设鱼类种群遵循具体的生长规律。相反，我们考虑一种具有从保留区域到未保留区域的迁移的抽象模型。然后，我们检查并分析了模型的非平凡平衡点的存在性和稳定性。我们还讨论了生物平衡。之后，我们使用Pontryagin最大值原理来获得最佳收获策略，其中，我们使用当前的哈密顿函数代替众所周知的哈密顿函数来简化计算。最后，我们提供一些数字示例以进一步说明我们的陈述，