Most influenza surveillance utilizes antibody responses from ferrets (outnumbering the amount of human data by 10-fold). While it is known that ferret responses can differ from human responses, it is not clear when or how their responses will differ. Using ferret data, we will predict the value±error for human experiments, which will help refine influenza vaccine selection (that is currently determined through ferret studies).

The influenza vaccine changes every 1-2 years. While we can separately model each vaccine, we would like to train a model on the combined data from all prior studies. Our current approach describes each virus according to its interactions with antibodies. By adding sequence information, we will develop a single unified model that can predict all past vaccines and explore the space of potential future vaccines.

Most vaccine studies measure the antibody response pre-vaccination and 1-month post-vaccination, but an ideal response must last for the duration of the influenza season (4 months) and ideally until you get your next vaccine (12 months). We will use pre-vaccination data to predict the response out as far as possible and quantify how additional measurements (e.g. at 1 month) further improve prediction accuracy.

This project develops basic evolutionary theory, with relevance to biomedical applications. For example, we study the evolution and emergence of mutants in spatially structured populations under various assumptions. Much remains to be discovered about the principles of mutant evolution in structured populations, and this has important applications for cancer biology and cancer therapy, since most tumor grow as a mass of cells with strong spatial structure.

This project is concerned with mathematical models of cancer initiation, cancer progression, and cancer therapy. This involves mathematical models of tissue stem cell dynamics, clonal cellular evolution in tissues during aging in relation to the development of cancer, and evolutionary models of drug resistance in cancers. Hematological malignancies are a major focus of this work. With respect to therapies and drug resistance, this work involves the use of mathematical models with patient-specific parameters to make personalized predictions about treatment outcome.

The project will be concerned with mathematical models of virus replication within hosts, and the interactions of viruses with immune responses. Much of this modeling work is concerned with human immunodeficiency virus (HIV), due to the availability of experimental and clinical data. Topics include the evolution of HIV within hosts, the effect of spatial lymphoid tissue structure on HIV dynamics and evolution, and the dynamics of HIV during antiretroviral therapy in relation to the latent viral reservoir.