Optimal control problem of a discrete spatiotemporal prey–predator three-species fishery model

Abstract

In this work, we discuss a spatiotemporal discrete prey–predator model. It consists of three compartments: prey, predator, and super-predator. The proposed model describes the interaction between prey, predator, and super-predator in a region with a discrete displacement. We also provide research on appropriate regional control strategies. The controls are applied to the predator and the super-predator, respectively; they represent catching these in measured quantities in a space and a time chosen. The aim is to increase the number of prey and reduce the number of predators, restore the food chain system, and ensure its sustainability. Finally, we provide graphical visuals and numerical simulations to support our analytical findings.