Over the past several years, we have been developing new network-based mathematical approaches for predicting the spread of infectious diseases. In collaboration with public health officials in the United States and Canada, we apply these methods to the design of optimal control measures for respiratory diseases including influenza and SARS. We are also collaborating with field ecologists to better understand the contact network structures of wildlife populations and their epidemiological consequences.
Using mathematical modeling, we have addressed several fundamental questions about (a) the impact of environmental heterogeneity on evolutionary dynamics and (b) the structure of complex fitness landscapes. Our work in these areas have yielded important insights into the diversity of certain classes of biological molecules and the ability of some viruses to rapidly evolve as they spread through human populations.