Mathematical Models of Cell Population Dynamics

首席研究员Webb9805515研究细胞种群动力学的数学模型。这些模型由线性和非线性的常微分方程组和偏微分方程组组成。这些研究应用于以下项目：(1)血液生产系统和前体干细胞的持续成熟-增殖的种群模型；(2)人类免疫系统感染HIV的发病机制和艾滋病进展阶段CD4T淋巴细胞耗尽的种群模型；(3)以染色体末端端粒片段长度缩短表示的细胞系复制历史的种群模型；(4)细胞周期中G1、S、G2、M或G0位置特有的细胞丢失过程的种群模型。在这些模型中，主要研究人员在种群水平上研究细胞的行为，以及细胞分裂、细胞成熟、细胞死亡、原始细胞来源以及细胞从静止状态转换到静止状态的动态过程。主要研究人员运用了微分方程组理论、算子理论、泛函分析、数值分析和计算模拟。这项研究的意义在于发展数学方法来分析描述细胞种群过程的微分方程解的定性行为。首席研究员将这些方法应用于对细胞种群问题的定性和定量理解。在这项研究中，应用种群过程的数学理论来分析正常和异常的血细胞生产系统，HIV感染的免疫系统中CD4T细胞在HIV进展为AIDS的过程中的耗尽，以及肿瘤的生长。主要研究者将这些生物现象作为种群行为的数学模型所描述的动态过程来研究。研究采用理论数学分析和计算机数值模拟相结合的方法。这项研究的目的是促进对正常和异常细胞增殖过程的理解。

Webb9805515 The principal investigator studies mathematical models ofcell population dynamics. The models consist of linear andnonlinear ordinary and partial differential equations.Applications of the research are made to the following projects:(1) population models of the blood production system and thecontinuous maturation-proliferation of precursor stem cells; (2)population models of the pathogenesis of HIV infection of thehuman immune system and the depletion of CD4 T lymphocytes duringthe stages of AIDS progression; (3) population models ofreplicative histories of cell lines as indicated by shortening oftelomere fragment lengths on the ends of chromosomes; and (4)population models of cell loss processes specific to the positionG1, S, G2, M, or G0 in the cell cycle. In these models theprincipal investigator studies the behavior of cells at thepopulation level and the dynamic processes of cell division, cellmaturation, cell mortality, naive cell sources, and celltransition to and from quiescence. The principal investigatorutilizes differential equations theory, operator theory,functional analysis, numerical analysis, and computationalsimulation. The significance of the research is in the development ofmathematical methods to analyze the qualitative behavior ofsolutions to the differential equations that describe cellpopulation processes. The principal investigator applies thesemethods to the qualitative and quantitative understanding of cellpopulation problems. In this research the mathematical theory ofpopulation processes is applied to analyze normal and abnormalblood cell production systems, the depletion of CD4 T cells inthe HIV infected immune system during HIV progression to AIDS,and the growth of tumors. The principal investigator studiesthese biological phenomena as dynamic processes described bymathematical models of population behavior. The research combinestheoretical mathematical analysis and numerical computersimulations of the models. The goal of the research is to advanceunderstanding of normal and abnormal cell proliferationprocesses.