Mathematical Sciences: Models for the Spread of HIV; Equations with Piecewise Continuous Argument; Dynamics of Discretizations

数学科学：艾滋病毒传播模型；

• 批准号: 8807478
• 负责人: Kenneth Cooke
• 金额: $ 13.55万
• 依托单位: Pomona College
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8807478&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Models; Spread; HIV

This project will focus on three scientific areas. The first concerns mathematical analysis of epidemiological models for the spread of HIV (human immunodeficiency virus). Mathematical models for the spread of the virus will be developed and evaluated. The models will be based on dividing the population into groups according to criteria such as sex, sexual behavior and socioeconomic categories. They will be represented in terms of ordinary and delay-differential equations. Stability and bifurcation phenomenon will be analyzed, simulations performed and comparisons made among the predictions of the different models. A second line of investigation concerns differential equations with piecewise continuous delays. Such equations arise in a number of physical contexts governed by memory effects. An objective of this work is to develop theory and applications of initial and boundary-value problems. Conditions for stability will be sought; periodic and oscillation phenomena will be studied for equations with bounded and unbounded delay. General functional differential equations of alternating type will also be considered. Work will also be done investigating Liapunov functions and the qualitative behavior of discretizations. This research will focus on stability questions related to nonlinear difference equations using an extension of Liapunov's direct method and the invariance principle. The relation between the asymptotic dynamics of classes of differential equations and the dynamics of discretized and semidiscretized versions of these equations will be explored. Applications to population dynamics and chemical kinetics will be sought.

该项目将集中在三个科学领域。 第一个涉及艾滋病毒传播的流行病学模型的数学分析（人类免疫缺陷病毒）。 将开发和评估病毒传播的数学模型。 这些模型将基于根据性，性行为和社会经济类别等标准将人口分为群体。 它们将以普通和差异方程式表示。 将分析稳定性和分叉现象，进行模拟，并在不同模型的预测中进行比较。 第二条调查涉及分段连续延迟的微分方程。 这种方程式在许多由内存效应控制的物理环境中产生。 这项工作的一个目的是开发初始和边界值问题的理论和应用。 将寻求稳定条件；将研究定期和振荡现象的方程式，并具有有界延迟和无界延迟的方程式。 还将考虑一般的功能微分方程。 还将完成研究Liapunov功能和离散性的定性行为。 这项研究将使用Liapunov的直接方法和不变性原理扩展与非线性差异方程相关的稳定问题。 将探讨这些方程式的分散方程类别的渐近动力学与离散和半差异版本的动力学之间的关系。 将寻求对种群动态和化学动力学的应用。