Mathematical Sciences: Stability, Oscillations, and Persistence in Differential Equation Models for Structured Populations.

数学科学：结构化总体微分方程模型的稳定性、振荡和持久性。

• 批准号: 9101979
• 负责人: Horst Thieme
• 金额: $ 10.23万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-01 至 1995-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101979&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Stability; Oscillations; Persistence

This project studies whether including population structures can change unstructured models of ecological or epidemiological systems that converge to equilibrium states into models that undergo damped oscillations. Mathematically this amounts to converting systems of ordinary differential equations into nonlinear partial differential equations with nonlinear boundary conditions and functional terms. These equations are studied as evolution equations in an appropriate Banach space. Specific examples are age-structured models of childhood diseases, infection-age-structured models of fatal infectious diseases, and size-structured models of waterflea populations (waterfleas are an important laboratory animal). The dynamics of structured populations and the spread of infectious diseases are more complicated than simple models predict. An understanding of the ways oscillations occur in mathematical models may well be important to public health, by helping to predict the course of epidemic or endemic infections.***

这个项目研究是否包括人口结构 可以改变生态学或流行病学的非结构化模型 系统收敛到平衡状态， 经历阻尼振荡。 从数学上讲，这相当于 将常微分方程组转化为 非线性边界偏微分方程 条件和功能术语。 这些方程被研究为 在适当的Banach空间中的演化方程。 具体 例子是儿童疾病的年龄结构模型， 致命传染病的感染年龄结构模型，以及 水蚤种群的大小结构模型（水蚤是 重要的实验动物）。 结构化人口的动态和 传染病比简单的模型更复杂 预测。 了解振荡发生的方式， 数学模型可能对公共卫生很重要， 有助于预测流行病或地方病的进程 感染。*