Browsing by Author "Charles, Raymond"

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    Optimal Control of Droughts, Diseases and Retaliatory Killing in Prey-Predator Systems
    (SCIK Publishing Corporation, 2023) Charles, Raymond; Makinde, Oluwole Daniel; Kung’aro, Monica
    In this article, we describe an application of optimal control theory to evaluate the success of controls on the dynamics of prey-predator systems of the Serengeti ecosystem, which includes wildebeest, zebra, and lion. This is accomplished by suggesting control variables like education (to prevent retaliatory killing), dam construction (to prevent drought), and treatment (to combat infections). Maximizing population density is the major objective. For this aim, the Pontryagin’s maximum principle has been applied. The optimal control are characterized in terms of optimality system and solved numerically for several scenarios. Results shows that multiple optimal control measures is the most effective strategy in management of wildlife populations. Results also shows that, if the ecosystem management decide to use a single control, the construction of dams is the best control in maximizing the objective function.
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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.