Mathematical Models of Cell Population Dynamics

Webb9805515 首席研究员研究细胞群体动力学的数学模型。 这些模型由线性和非线性常微分方程和偏微分方程组成，并应用于以下几个方面：（1）造血系统和前体干细胞的连续成熟-增殖的群体模型，（2）HIV感染人体免疫系统的发病机制和艾滋病发展过程中CD_4 ~+ T淋巴细胞的耗竭的群体模型，（3）造血系统和前体干细胞的连续成熟-增殖的群体模型，（4）造血系统和前体干细胞的连续成熟-增殖的群体模型。（3）染色体末端端粒片段长度缩短所指示的细胞系复制历史的群体模型;（4）细胞周期中G1、S、G2、M或G 0位点细胞丢失过程的群体模型。 在这些模型中，主要研究者在群体水平上研究细胞的行为，以及细胞分裂、细胞成熟、细胞死亡、幼稚细胞来源和细胞从静止到静止的转变的动态过程。 主要的解析器利用微分方程理论、算子理论、泛函分析、数值分析和计算机模拟。 研究的意义在于发展数学方法来分析描述细胞群体过程的微分方程解的定性行为。 主要研究者应用这些方法来定性和定量地了解细胞群体问题。 本研究应用群体过程的数学理论分析了正常和异常的血细胞生成系统、HIV向AIDS发展过程中HIV感染免疫系统中CD 4 T细胞的耗竭以及肿瘤的生长。 首席研究员研究这些生物现象，作为人口行为的数学模型描述的动态过程。 本研究结合了理论数学分析和数值计算机模拟的模型。 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.