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

该项目研究是否包括人口结构可以改变生态或流行病学系统的非结构化模型，这些模型收敛于平衡状态，进入经历阻尼振荡的模型。从数学上讲，这相当于将常微分方程系统转换为具有非线性边界条件和泛函项的非线性偏微分方程。将这些方程作为演化方程在适当的巴拿赫空间中进行研究。具体的例子有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和水蚤种群的尺寸结构模型（水蚤是一种重要的实验动物）。结构种群的动态和传染病的传播比简单模型预测的要复杂得多。理解振荡在数学模型中发生的方式可能对公共卫生很重要，因为它有助于预测流行病或地方性感染的进程

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.***