Mathematical Sciences: Models for the Dynamics of InfectiousDiseases and Social Interactions with Applications to AIDS Epidemiology

8906580卡斯蒂略-查韦斯该项目有两个目标。第一是确定可能对确定传染病传播率至关重要的机制，并对可能的干预战略的相对价值进行初步评估。重点将放在艾滋病毒(人类免疫缺陷病毒，艾滋病的病原体)的动态上。第二个目标是为在人口层面的数学流行病学、社会动力学以及它们与理论人口生物学领域的联系方面建立一个坚实的长期研究计划奠定基础。该项目的主要目标是开始系统地研究社会互动的动态及其在性传播和传染病动态中的作用。卡斯蒂略-查韦斯将使用现象学框架来描述人类混合模式，并将开发确定性数学模型(涉及单一或相互作用的人口)，以确定社会混合、可变传染性、长期传染性以及艾滋病毒动态中的辅助因素的作用。次要目标包括升级数学流行病学和人口动力学领域的数学方法，系统地整合不同类型的社会融合，并分析它们对其他传染病传播的影响。

8906580 Castillo-Chavez This project has two objectives. The first is to identify mechanisms that may be crucial in determining the rate of spread of infectious diseases and to make initial evaluations of the relative value of possible intervention strategies. The emphasis will be on the dynamics of HIV (Human Immuno-Deficiency Virus, the etiological agent for AIDS). The second objective is to create the basis for a solid long-term research program in mathematical epidemiology at the population level, on social dynamics, and on their connections to the field of theoretical population biology. This project's principal goal is to begin a systematic study of the dynamics of social interactions and their role in the dynamics of sexually-transmitted and communicable diseases. Castillo-Chavez will use a phenomenological framework to describe human mixing patterns, and deterministic mathematical models (involving single or interacting populations) will be developed to determine the role of social mixing, variable infectivity, long periods of infectiousness and, co-factors in the dynamics of HIV. Secondary goals include upgrading of the mathematical methodology in the areas of mathematical epidemiology and population dynamics by systematically integrating different types of social mixing and analyzing their effect on the transmission of other infectious diseases.