Optimal Harvesting of Wildebeest-Lion Interactions in Serengeti Ecosystem with Prey Refuge

Abstract

This paper describes an optimal harvesting policy for a wildebeest-lion prey-predator system in the Serengeti ecosystem with prey refuge. A Holling Type II prey-predator model with a nonlinear harvesting aspect was developed. Theoretical and numerical analyses were performed, and the dynamic behaviour of the system was found to be mathematically well-posed. Data on lion population density from the Serengeti ecosystem were used to fit the model using the maximum-likelihood method. The optimal harvesting policy was numerically determined using Pontryagin’s maximum principle. Furthermore, the impact of prey refuge on the predator population was numerically evaluated. The results of this study highlight the importance of managing the lion population in the ecosystem, specifically in terms of harvesting criteria, to ensure that the threshold for wildebeest-lion coexistence is not exceeded. Based on the findings, this paper argues that the lion population should be given special attention in terms of managerial harvesting criteria so that the threshold for the wildebeest-lion coexistence in the ecosystem is not exceeded.