Optimal Control of Droughts, Diseases and Retaliatory Killing in Prey-Predator Systems
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Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
SCIK Publishing Corporation
Abstract
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.
Description
Abstract. Full text available at: https://doi.org/10.28924/APJM/10-32
Keywords
Prey, predator, optimal control, serengeti ecosystem., predator system
Citation
Charles, R., Makinde, O. D., & Kung’aro, M. (2023). Optimal control of droughts, diseases and retaliatory killing in prey-predator systems. Asia Pacific Journal of Mathematics, 10(32).