Mathematical Sciences: Mathematical Models of Cell Population Dynamics

本项目将对描述细胞种群动力学结构化模型的非线性偏微分方程组进行理论和数值研究。单个细胞通过对应于大小、年龄或其他物理特征的结构变量来区分。种群被划分为通过非线性转移率相互作用的种群子类。主要目标将是了解种群的定性行为、振荡现象的集合以及对外部周期损失函数的响应。主要方法将应用Banach格中的正线性和非线性算子半群理论。主要应用于具有增殖和静止类别的肿瘤细胞群体以及多水平的血细胞生产系统。肿瘤细胞群体研究的目标将是了解静止在肿瘤生长和肿瘤治疗中的作用。血细胞种群研究的目标将是了解正常和异常系统中的调节过程。

This project will make theoretical and numerical investigations of the nonlinear partial differential equations that describe structured models of cell population dynamics. Individual cells are distinguished by structure variables corresponding to size, age, or other physical characteristics. The populations are divided into population subclasses that interact through nonlinear transition rates. The main objective will be to understand the qualitative behavior of the populations, the on- set of oscillatory phenomena, and the response to external periodic loss functions. The main methods will apply the theory of semigroups of positive linear and nonlinear operators in Banach lattices. The main applications will be to tumor cell populations with proliferating and quiescent classes and to multi-level blood cell production systems. The goal in the tumor cell population studies will be to understand the role of quiescence in tumor growth and tumor therapy. The goal in the blood cell population studies will be to understand the regulation processes in normal and abnormal systems.