Modelling optimal control of harvested prey predator system incorporating a prey refuge

Abstract

prey-predator interactions have been an important role in the dynamics of species populations. This work presents mathematical model for Modelling Optimal control of Harvested prey- predator system incorporating a prey refuge using deterministic differential equations. This study, develops two harvested prey-predator species, in which both species are affected by over-harvesting, furthermore the predator is affected by prey refuge. The intention is to in- vestigate the impacts of over-harvesting to prey-predator species and suggest control strategies to alleviate the problem of loss of prey-predator species. The analysis of stability of equilib- rium points were done by Jacobian matrix, Global stability analysis is done using Lyapunov function while the analysis of optimal control was done using Pontrygians maximum principle (PMP) and Hamiltonian principle. The control strategy suggested is the creation of reserve ar- eas with restrictions of harvesting. The results obtained from theoretical and numerical analysis of the prey-predator with harvesting without control strategies showed that, harvesting affect the prey-predator species negatively. However, the results obtained from numerical analysis of the prey-predator model with control strategies showed that, the use of control strategy encourage the survival of both species