PDF(Pubmed)
Abstract：
We consider an age-structured density-dependent population model on several temporally variable patches. There are two key assumptions on which we base model setup and analysis. First, intraspecific competition is limited to competition between individuals of the same age (pure intra-cohort competition) and it affects density-dependent mortality. Second, dispersal between patches ensures that each patch can be reached from every other patch, directly or through several intermediary patches, within individual reproductive age. Using strong monotonicity we prove existence and uniqueness of solution and analyze its large-time behavior in cases of constant, periodically variable and irregularly variable environment. In analogy to the next generation operator, we introduce the net reproductive operator and the basic reproduction number [Formula: see text] for time-independent and periodical models and establish the permanence dichotomy: if [Formula: see text], extinction on all patches is imminent, and if [Formula: see text], permanence on all patches is guaranteed. We show that a solution for the general time-dependent problem can be bounded by above and below by solutions to the associated periodic problems. Using two-side estimates, we establish uniform boundedness and uniform persistence of a solution for the general time-dependent problem and describe its asymptotic behaviour.
摘要：
我们在几个时间可变的补丁上考虑年龄结构化的密度相关人口模型。我们基于两个关键假设建立和分析模型。首先,种内竞争仅限于同龄个体之间的竞争(纯队列内竞争),并且影响密度依赖性死亡率.第二,补丁之间的分散确保每个补丁可以从每个其他补丁到达，直接或通过几个中间补丁，在个体生育年龄内。使用强单调性，我们证明了解的存在性和唯一性，并分析了其在常数情况下的大时间行为，周期性变化和不规则变化的环境。类似于下一代运营商，我们为时间无关和周期性模型引入净繁殖算子和基本繁殖数[公式：见文本]，并建立持久性二分法：如果[公式：见文本]，所有补丁的灭绝迫在眉睫，如果[公式：见文本]，保证所有补丁的持久性。我们证明了一般的时间相关问题的解决方案可以通过相关的周期问题的解决方案上下限制。使用双方估计，我们建立了一般时间相关问题的解的一致有界性和一致持久性，并描述了其渐近行为。
