Spatial dynamics of a pest population with stage-structure and control.

IF 2.3 4区 数学 Q2 BIOLOGY
Stephen Becklin, Yu Jin, Richard Rebarber, Brigitte Tenhumberg
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引用次数: 0

Abstract

We study an integro-difference model for a pest population that is divided into four life stages. In the model, spatial spread of the population is described by an integral convolution and pest control is applied to each population stage. When the spatial domain is infinite, we establish the spreading speeds and existence of traveling waves; when the spatial domain is finite, we first establish threshold conditions in terms of the principal eigenvalue of an associated eigenvalue problem to determine population persistence and extinction, and then define the net reproductive rate and use it to develop equivalent threshold conditions for persistence and extinction. The cases where the reproduction function is monotone and where it is nonmonotone are both investigated. Numerical simulations show that the larger the control effectiveness is the easier to eradicate the pest population and that the same control effectiveness on different stages may yield different population dynamics in the long-term.

害虫种群的空间动态、阶段结构和控制。
我们研究了一个划分为四个生命阶段的害虫种群的积分-差分模型。在该模型中,种群的空间扩散用积分卷积来描述,并对每个种群阶段进行害虫控制。当空间范围无限时,我们建立了行波的传播速度和存在性;当空间域有限时,我们首先根据相关特征值问题的主特征值建立阈值条件来确定种群的持续和灭绝,然后定义净繁殖率,并利用它来建立种群持续和灭绝的等效阈值条件。研究了繁殖函数为单调和非单调的情况。数值模拟表明,控制效果越大越容易消灭害虫种群,不同阶段相同的控制效果可能产生不同的长期种群动态。
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
CiteScore
3.30
自引率
5.30%
发文量
120
审稿时长
6 months
期刊介绍: The Journal of Mathematical Biology focuses on mathematical biology - work that uses mathematical approaches to gain biological understanding or explain biological phenomena. Areas of biology covered include, but are not restricted to, cell biology, physiology, development, neurobiology, genetics and population genetics, population biology, ecology, behavioural biology, evolution, epidemiology, immunology, molecular biology, biofluids, DNA and protein structure and function. All mathematical approaches including computational and visualization approaches are appropriate.
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