Mathematical Sciences: Analysis and Parameter Estimation of Models with Internal Structure

数学科学：具有内部结构的模型的分析和参数估计

• 批准号: 9112821
• 负责人: Stavros Busenberg
• 金额: $ 7.01万
• 依托单位: Harvey Mudd College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-01 至 1994-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9112821&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analysis; Parameter; Estimation

The dynamics of age-structured epidemic and population problems lead to systems of nonlinear hyperbolic equations that can be studied by the use of semigroup theory. Explicit threshold criteria, the asymptotic behavior of the solutions, and the general forms of the nonlinear force of infection terms have been obtained in certain cases, and these results will be used as the basis for a systematic development of methods for estimating the pertinent model parameters using available data on specific diseases. A second area of biomathematical research that will be pursued involves the study of the triggering of DNA synthesis in eucaryotic cells through the use of compartmental reaction-diffusion models. These models lead to coupled semi-linear parabolic equations with time delays that are due to transcription and translation delays and the movement of biochemicals in the cell. The main methods of analysis here involve the development and use of local and global bifurcation results for such reaction-diffusion equations. Parameter identification and estimation on the basis of available data will be addressed in these models also. This research is concerned with two mathematical problems with biological applications. The first part of this research will develop and study mathematical models that help predict the course of infections and which form the basis for making decisions on how to best use available resources in order to control the spread of diseases. The age structure of the affected population is very important in determining the course and effects of most diseases. Models will be developed and studied that account for the age distribution of the population and that lead to methods for predicting the course of the disease and the effects of proposed control strategies. The results will be applied to the study of optimal control strategies for specific diseases. The second part of this research will seek to shed light on the mechanism that triggers animal cells to start replicating their genetic material and reproducing. This is a fundamental question that has implications in the understanding of growth and development of embryos as well as in disorders such as cancer that result from abnormal cell proliferation. The mathematical models to be studied are designed to allow a detailed analysis of this crucial DNA synthesis triggering mechanism.

年龄结构流行病和人口的动态 问题导致非线性双曲方程组， 可以用半群理论来研究。 显式 阈值准则、解的渐进行为，以及 非线性传染力项的一般形式有 在某些情况下获得，这些结果将被用作 有系统地制定估算方法的基础 使用现有的具体数据， 疾病 生物数学研究的第二个领域是 所进行的研究涉及触发DNA合成的研究， 真核细胞通过使用隔室 反应扩散模型 这些模型导致 耦合半线性时滞抛物方程组 由于转录和翻译的延迟， 细胞中的生化物质。 这里的主要分析方法 涉及发展和利用地方和全球的分歧 这样的反应扩散方程的结果。 参数识别和估计的基础上， 数据也将在这些模型中处理。 本研究涉及两个数学问题 with biological生物application应用. 本研究的第一部分 将开发和研究数学模型，帮助预测 感染的过程，并形成了基础，使 决定如何最好地利用现有资源， 控制疾病的传播。 年龄结构 受影响的人口在决定进程方面非常重要， 和大多数疾病的影响。 将开发模型， 研究了人口的年龄分布 从而产生了预测疾病进程的方法 以及所提出的控制策略的效果。 结果将 应用于最优控制策略的研究， 特定疾病 本研究的第二部分将寻求 以揭示触发动物细胞的机制， 开始复制它们的遗传物质并繁殖。 这 是一个基本的问题， 了解胚胎的生长和发育， 由异常细胞引起的疾病，如癌症 增殖 要研究的数学模型是 旨在详细分析这一关键的DNA 合成触发机制