CAREER: Dynamics of Hierarchical HouseholdStructured Epidemiological Models

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.