1. Community dynamics of infectious disease. Simple compartmental models of infectious disease provide a theoretical basis for understanding of how epidemic and endemic diseases spread through host populations. Extending these models to accommodate more complicated biological realities is challenging. In particular, progressing from models with one host species and/or one pathogen to scenarios with multiple hosts and multiple pathogens requires a fundamentally different mathematical approach. I am excited to be part of a collaborative research effort to use the model system of barley yellow dwarf virus in grasses to build an understanding of community disease dynamics. The website here provides more information about this project.
2. Transgenic pest control. Genetic technologies offer new promises for regulating abundances of unwanted pest species. Mathematical modeling will be a key component of the design of successful pest-control strategies using transgenic methods. NCSU has recently been awared an NSF IGERT grant to train graduate students in the social, biological, and technical aspects of genetic pest management. The website here provides more information about this project.
3. Time-series analysis of coral-reef dynamics. Coral-reef ecosystems are both spectacular and spectacularly diverse, yet reef ecosystems as we know them are imperiled by rapid environmental change. My collaborator Peter Edmunds has studied coral communities in St. John, USVI since 1987. Together, we are using vector autoregressive models (statistical models for time-series data) to estimate metrics of ecosystem stability from these monitoring data. These metrics will capture how various environmental changes (such as ocean warming, ocean acidification, hurricane activity) impact different coral taxa in different habitats around St. John, and will help us to understand what continued environmental change portends for these ecosystems.