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Next-generation sequencing technology is now enabling the genomes of many organisms, including many infectious agents, to be sequenced quickly and inexpensively. Vast amounts of sequence data are being generated for important infectious diseases, including viruses such as HIV and influenza and now also for a number of bacteria, including C. difficile, S. aureus and M. tuberculosis. These data will be used to understand how pathogens are spreading and evolving, including how they are adapting to the introduction of vaccines and how, where, and how quickly drug resistance is emerging.While there is a mathematical theory of epidemiology which is the primary modelling tool for the study of infections, it has largely been focussed on understanding the spreading dynamics of a single, static pathogen, for example in terms of its basic reproduction number (defined as the number of secondary infections caused by a single infectious case in a fully susceptible population). But this theory offers very little about pathogen evolution, and still less about how to predict, model and interpret the vast quantities of genetic data that are becoming available. While there are mathematical models focussing on trait evolution, these do not focus on complex epidemic dynamics, and also do not explicitly predict features of sequence data. In contrast, there is a long tradition of mathematical population genetics aiming to answer questions such as how allele frequency is maintained, but these do not account for the kinds of structure that arise when the pathogen population is constrained by epidemic dynamics in human hosts. In this proposal, I aim to bridge this gap, and develop a theory of how pathogen sequences are related to the underlying epidemic dynamics. Characterising the relationship between epidemic dynamics and pathogen sequence data will require new mathematics, first in the form of the construction and analysis of models describing both, and then in the form of theorems relating the structure of epidemic dynamics to quantitative features of the phylogenetic trees used to summarise sequence data. These theoretical tools will be crucial as genomic data become increasingly available. This proposal provides an approach to making substantial progress in this direction through four core Objectives, moving from relating competition between several distinct, fixed pathogen strains to the resulting phylogenies, to explicitly modelling the relationship between host transmission and pathogen evolution. I will also develop better quantitative measures to identify similarities between phylogenetic trees on different datasets. This work will provide a theoretical underpinning linking epidemic population dynamics to sequence data, and will have a wide range of applications in addition to its new theoretical developments. Sequence data for many pathogens are currently being generated rapidly, and the analysis of these data is expected to benefit not only our understanding of pathogen evolution, but our ability to intervene for the benefit of public health. For example, the UK CRC Modernising Medical Microbiology Consortium is using whole-genome sequencing technology combined with population-based sampling, focusing on M. tb, norovirus, C. difficile and S. aureus. I have also been asked to provide modelling expertise for a community-based study in which HIV sequence data will be collected alongside individuals' sexual network data, providing a unique dataset for linking spreading patterns to viral sequences. My work under this grant would provide new insights into what these data mean for how these pathogens are spreading, which in turn will provide researchers and health policy makers with information to design improved prevention measures.
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