Browsing by Author "Sagamiko, Thadei Damas"

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    Optimal control of a threatened wildebeest-lion prey-predator system incorporating a constant prey refuge in the Serengeti ecosystem
    (Science Publishing Group, 2015) Sagamiko, Thadei Damas; Shaban, Nyimvua; Nahonyo, Cuthbert Leonard; Makinde, Oluwole Daniel
    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 to the control of threats is studied and results indicate that increase of causes more prey individuals to be saved and reduces the number of predator individuals saved. This behaviour agrees with theoretical results obtained in co-existence equilibrium point.
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    Optimal harvesting of wildebeest-lion interactions in Serengeti ecosystem with prey refuge
    (African Journals Online (AJOL), 2023) Hugo, Alfred Kisuda; Sagamiko, Thadei Damas; Mbalawata, Isambi Sailon
    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.