Browsing by Author "Makinde, Oluwole Daniel"

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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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    A review of the mathematical models for the impact of seasonal weather variation and infections on prey predator interactions in Serengeti ecosystem
    (Scientific Research Publishing, 2022) Charles, Raymond; Makinde, Oluwole Daniel; Kung’aro, Monica
    Interaction between prey and predator species is a complex and non-linear process. Understanding various phenomena in the dynamics of prey-predator systems is vital to both mathematical ecology and conservation biology. Mathematical models on prey-predator systems have been the hot sport providing important information regarding the interactions of prey and predator species in various ecosystems. In this paper, a review of the available mathematical models on prey-predator systems was done. Our aim was to assess their structure, behaviour, available control strategies, population involved and their ability in predicting the future behaviour of the ecosystems. We observed diversities in the reviewed mathematical models, some model incorporated factors such as drought, harvesting and prey refuge as the factors that affect ecosystems, some ignored the contribution of environmental variations while others considered the variable carrying capacity. Most of the models reviewed have not considered the contribution of diseases and seasonal weather variation in the dynamics of prey predator systems. Some of the reviewed models do not match the real situation in most modelled ecosystems. Thus, to avoid unreliable results, this review reveals the need to incorporate seasonal weather variations and diseases in the dynamics of prey predator systems of Serengeti ecosystem.