CAREER: Dynamics of Hierarchical Household-Structured Epidemiological Models

数学和计算模型将用于研究按等级划分为“家庭”的群体。这些家庭可以代表农田中的小块、景观中的田地、学校中的宿舍、城市中的学校、地区中的城市，甚至是大型计算机网络中的子网。人口模型和流行病学模型将在这一框架内进行探索，补充其他晶格结构人口的工作。在这些模型中，一个家庭内部的互动比不同家庭之间的互动要频繁得多。这些模型的主要目标是更好地理解空间定向和/或集群处理如何以及为什么会影响感染的动态，例如，根据这些田地的虫害水平改变作物的农药施用量。模型将包括空间上不同的抗性等因素（包括长期因素，如在不同的田地种植不同的作物，以及短期因素，如杀虫剂）。另一个应用将是更好地理解恶意计算机软件（“蠕虫”）在集群异构计算机网络中使用生物扩散策略的传播。昆虫学家和其他研究人员将与首席研究员及其学生合作开发该项目的应用，例如控制缅因州商业蓝莓田的蛆蝇，中国稻田的飞虱以及其他农作物害虫。关于建模和仿真的跨学科课程将纳入该项目的各个主题。本科生研究培训将是工作的重要组成部分，包括参与主要针对代表性不足的少数群体的暑期研究项目。此外，还将包括面向高中学生和教师的推广，目前正在学习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.