Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review

Abstract

The United Nations has predicted the growth of the human population to reach 8.405 billion by mid-2023, which is a 70% increase in global food demand. This growth will significantly affect global food security, mainly marine resources. Most marine resources exist within complex biological food webs, including predator–prey interactions. These interactions have been researched for decades by mathematicians, who have spent their efforts developing realistic and applicable models. Therefore, this paper systematically reviews articles related to predator–prey models considering the harvesting of resources in marine protected areas. The review identifies future remodeling problems using several mathematical tools. It also proposes the use of feedback linearization consisting of both the approximation and exact methods as an alternative to Jacobian linearization. The results show that in an optimal control analysis, adding a constraint in the form of population density greater than or equal to the positive threshold value should be considered to ensure an ecologically sustainable policy. This research and future developments in this area can significantly contribute to achieving the Sustainable Development Goals (SDGs) set for 2030.