Optimal Control of a Threatened Wildebeest-lion Prey- predator System Incorporating a Constant Prey Refuge in the Serengeti Ecosystem

Abstract: In this paper a two species prey-predator model is developed in which prey is wildebeest and predator is lion and both are threatened by poaching, drought and diseases.The system is found in the Serengeti ecosystem.The model is constructed based on Holling type II functional response incorporating a constant prey refuge. We apply optimal control theory to investigate optimal strategies for controlling the threats in the system where anti-poaching patrols are used for controlling poaching, construction of dams for mitigating drought and vaccination for diseases control. The possible impact of using combinations of three controls either one at a time or two at a time on the threatened system plus a refuge factor is examined. All control strategies have shown significant increase in prey and predator populations. However, the best result is achieved by controlling all threats together. The effect of variation of prey refuge m to the control of threats is studied and results indicate that increase of m causes more prey individuals to be saved and reduces the number of predator individuals saved