Optimal placement of marine protected areas for a predator–prey fish model

This paper proposes a fishery model with price fluctuations and predators. Under the assumption that the price changes much faster than other variables in the system, the fishery model can be considered as a fast–slow system. Using the approximate aggregation method, a simplified three-dimensional model is used for further research. The results indicate that due to overfishing by fishermen and the presence of predators, fish populations may become extinct, which is also known as catastrophic equilibrium. To avoid this situation, we propose two solutions. The first is to establish marine protected areas (MPAs) that prohibit fishing. We propose a fish population dynamics model with MPA, assuming that fish and predators move freely in protected areas and fishing areas. The results show that it is necessary to establish MPA. The second type is that regulatory agencies can control overfishing by fishermen by increasing taxes, thereby avoiding a catastrophic equilibrium. The ultimate goal is to achieve maximum economic benefits while maintaining balanced development of the ecosystem.