Optimal control of species augmentation in a competition model

IF 1.9 4区 数学 Q2 BIOLOGY
Munkaila Dasumani , Suzanne Lenhart , Gladys K. Onyambu , Stephen E. Moore
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引用次数: 0

Abstract

Mathematical models of endangered competitive interactions incorporating the Allee effect with augmentation strategies have not been studied extensively. This area is however critical to ecologists since it relates to ways species can become endangered and possibly go extinct due to competition for limited resources. More importantly, the climatic change with its adverse effects has not only affected green forests but has also caused the extinction of some species. Thus, there is a need for critical augmentation strategies to safeguard such species. This paper, therefore, presents an optimal control strategy for a continuous time competition interaction model with strong Allee effects. We seek to maximize the target species at the end of each final time. We consider two objective functionals involving the populations and the cost of the controls. Using Pontryagin’s Maximum Principle, we obtain the optimal control characterizations. We perform numerical simulations using the forward–backward sweep method and the approximate solutions are presented and discussed. Since there is a cost involved in the translocation of the reserve species, we adopt a minimization cost strategy. In addition, we compute the objective functional values for each simulation.
竞争模型中物种扩张的最优控制。
考虑Allee效应和增强策略的濒危竞争相互作用的数学模型尚未得到广泛的研究。然而,这个领域对生态学家来说至关重要,因为它关系到物种可能因争夺有限资源而濒临灭绝甚至可能灭绝的方式。更重要的是,气候变化及其不利影响不仅影响了绿色森林,而且还造成了一些物种的灭绝。因此,有必要采取关键的增加策略来保护这些物种。因此,本文提出了具有强Allee效应的连续时间竞争交互模型的最优控制策略。我们力求在每次最后一次结束时使目标物种最大化。我们考虑涉及人口和控制成本的两个目标函数。利用庞特里亚金极大值原理,得到了最优控制特性。我们使用正向-反向扫描方法进行了数值模拟,并给出了近似解。由于保护区物种的迁移是有成本的,我们采用了成本最小化策略。此外,我们计算了每个模拟的目标函数值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Mathematical Biosciences
Mathematical Biosciences 生物-生物学
CiteScore
7.50
自引率
2.30%
发文量
67
审稿时长
18 days
期刊介绍: Mathematical Biosciences publishes work providing new concepts or new understanding of biological systems using mathematical models, or methodological articles likely to find application to multiple biological systems. Papers are expected to present a major research finding of broad significance for the biological sciences, or mathematical biology. Mathematical Biosciences welcomes original research articles, letters, reviews and perspectives.
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