CAREER: Dynamics of Hierarchical Household-Structured Epidemiological Models

数学和计算模型将被用来研究按等级划分成称为“家庭”的群体。这些家庭可以代表农田中的斑块、景观中的田地、学校中的宿舍、城市中的学校、区域中的城市，甚至是更大的计算机网络中的子网络。人口模型和流行病学模型将在这一框架内进行探索，作为对格子结构人口的其他工作的补充。在模型中，家庭内部的互动比不同家庭之间的互动发生得更频繁。这些模型的主要目标是更好地了解空间定向和/或集群治疗如何以及为什么影响感染动态，例如，根据农田中虫害的水平改变农田的杀虫剂施用量。模型将包括空间上不同的抗性因素(长期的，由于不同田地的不同作物的花叶种植；以及短期的，例如，杀虫剂的结果)。另一个应用将是通过生物传播策略更好地了解恶意计算机软件在集群异质计算机网络中的传播。昆虫学家和其他研究人员将与首席研究员和他的学生合作，开发该项目的应用程序，如控制缅因州商业蓝莓田的蝇虫、中国稻田的稻飞虱和其他农作物害虫。关于建模和仿真的跨学科课程将结合项目中的各种主题。本科生研究培训将是这项工作的重要组成部分，包括参加一个主要针对代表性不足的少数群体的夏季研究项目。还将包括与高中生和教师的接触，目前正在学习成为K-12教师的本科生也将参与其中。

Mathematical and computational models will be used to study populations hierarchically segregated into groups referred to as "households". These households may represent patches within an agricultural field, fields within a landscape, dorms within a school, schools within a city, cities within a region, or even subnetworks within larger computer networks. Population models and epidemiological models will be explored within this framework, complementing other work with lattice-structured populations. In the models, interactions within a household occur much more often than interactions between different households. Primary goals of the models are to better understand how and why spatially targeted and/or clustered treatments affect dynamics of infections, for example varying the rates of pesticide application to crop fields based on the levels of insect infestations among those fields. Factors such as spatially varying resistance (both long-term, due to e.g. mosaic planting of different crops in different fields; and short-term, e.g. as a result of pesticides) will be included in the models. Another application will be better understanding the spread of malicious computer software ("worms") using biological dispersal strategies in clustered heterogeneous computer networks.Entomologists and other researchers will cooperate with the principal investigator and his students to develop applications of the project such as controlling maggot flies in commercial blueberry fields in Maine, planthoppers in rice fields in China, and other agricultural crop pests. Interdisciplinary courses on modeling and simulation will incorporate various topics from the project. Undergraduate research training will be a significant part of the work, including participation in a summer research program primarily aimed at underrepresented minority groups. Outreach to high school students and teachers will also be included, with the participation of current undergraduates studying to become K-12 teachers.