Dynamics of the vaccine response

Lab
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Project Description

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.

Evolutionary theory

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Project Description

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.

Mathematical Oncology

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Project Description

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.

Mathematical models on in vivo virus dynamics

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Project Description

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.