Mathematical Sciences: Analysis of Models with Time Delays and Spatial Dependence

8902712 布森贝格 该项目将研究生物和物理模型 根据功能和部分功能制定的系统 非局部微分方程 的主要领域 这项工作是：a）。具有空间扩散的房室模型 和时间延迟及其对理解 尺寸、时间延迟和其他因素对 细胞中某些生化过程的稳定性; B）.模型 基于实际疾病动态的流行病 特别强调纵向传播和 年龄结构和其他内部变量的影响 人口对这些模型的动力学行为的影响;以及c）. 振动周期的锐界的推导 连续和离散动力系统的解， 排除下列可能性的条件的推导 周期性和更复杂的动力学。 该项目将 采用分析研究和数值方法 旨在将数学结果与 观察数据。 所有这些问题都需要发展 新的分析技术，可以应用于广泛的 在模拟某些类型的 生物和物理现象。

8902712 Busenberg This project will study models of biological and physical systems which are formulated in terms of functional and partial differential equations with nonlocal terms. The main areas of this work are: a). Compartmental models with spatial diffusion and time delays and their application to the understanding of the effects of size, time delays, and other factors on the stability of certain biochemical processes in cells; b). models of epidemics which are based on the dynamics of actual diseases with particular emphasis on vertical transmission and on the effects of age-structure and other internal variables of a population on the dynamics behavior of these models; and c). the derivation of sharp bounds on the periods of oscillatory solutions of continuous and discrete dynamical systems and the derivation of conditions which rule out the possibility of periodic and more complicated dynamics. The project will employ both analytical investigations and numerical methods that will be aimed at fitting the mathematical results to observed data. All of these problems require the development of new techniques of analysis that can be applied to broad classes of equations that occur in modelling certain types of biological and physical phenomena.