Mathematical Sciences: Mathematical Models of Structured Population Dynamics

数学科学：结构化人口动态的数学模型

• 批准号: 9500631
• 负责人: Glenn Webb
• 金额: $ 8万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-15 至 1998-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500631&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Models; Structured; Population

Webb The investigtor studies the qualitative behavior of the linear and nonlinear partial differential equations of structured population dynamics. In these equations structure variables such as age, size, maturity, or other physical attributes of members of the population relate individual population behavior to total population behavior. The methods of the research employ the theory of semigroups of linear operators in Banach spaces, the spectral theory of linear operators in Banach spaces, and the theory of positive linear and nonlinear operators in Banach lattices. The project appliies these researches to (1) models of the blood production system and abnormalities in this system such as aplastic anemia, (2) models of loss of telomeres in ends of chromosomes in proliferating cell lines and the distinction of normal and cancer cells in these loss processes, (3) qualitative models of AZT treatment of AIDS and the development of resistant strains of HIV as a result of treatment, (4) models of periodic chemotherapy of tumor cell populations, and (5) models of epidemics with infection incubation periods and geographical dependence. This project studies the ways in which populations may behave, if the behavior is described by certain kinds of equations that incorporate features of the populations. Such features include the age, size, or maturity of members of the population. The mathematical results are applied to models of populations of cells, of epidemics, and mf treatments. In these various applications the qualitative behaviors of physical and biological phenomena are modelled as dynamical population processes. The significance of this work is in the development of mathematical methods to analyze the qualitative behavior of solutions of the equations that describe structured populations, and to apply these methods to the qualitative understanding of biotechnological processes.

韦伯研究人员研究结构化群体动态的线性和非线性偏微分方程的定性行为。 在这些方程中，人口成员的年龄、体型、成熟度或其他身体属性等结构变量将个体人口行为与总人口行为联系起来。 研究方法采用了Banach空间中线性算子半群理论、Banach空间中线性算子谱理论以及Banach格子中正线性算子和非线性算子理论。 该项目将这些研究应用于（1）造血系统和该系统异常的模型，如再生障碍性贫血；（2）增殖细胞系染色体末端端粒丢失的模型以及这些丢失过程中正常细胞和癌细胞的区别；（3）AZT治疗艾滋病的定性模型以及治疗导致的艾滋病毒耐药株的发展；（4）周期性 肿瘤细胞群的化疗，以及（5）具有感染潜伏期和地理依赖性的流行病模型。 该项目研究群体的行为方式，如果该行为是由某些包含群体特征的方程来描述的话。 这些特征包括人口成员的年龄、体型或成熟度。 数学结果应用于细胞群、流行病和MF治疗的模型。 在这些不同的应用中，物理和生物现象的定性行为被建模为动态群体过程。 这项工作的意义在于开发数学方法来分析描述结构化群体的方程解的定性行为，并将这些方法应用于生物技术过程的定性理解。