Mathematical Modeling of Viral Evolution and Epidemiology

Phylogenetic trees can be used to study the evolution of any sequence that evolves, including viruses. In a viral epidemic, the history of transmission events defines constraints on the evolutionary history of the viral population. The spread of many viruses is driven by social and sexual networks, and because of the relationship between their evolutionary and transmission histories, phylogenetic inference from viral sequences can be used to improve the inference of patterns of the epidemic, which in turn may be able to enhance epidemiological intervention. The simultaneous simulation of viral transmission networks, phylogenetic trees, and sequences can provide a method to observe the effects of virus model parameters on the epidemic as well as to study the accuracies and errors of transmission inference tools, but the success of such simulations relies on the existence of appropriate models. Further, the development of massively-scalable tools to analyze ultra-large datasets of viral sequences can aid epidemiologists in the real-time surveillance of the spread of disease. To enable viral epidemic simulation analyses, I developed FAVITES: a novel framework to simulate viral transmission networks, phylogenetic trees, and sequences, and I used FAVITES to study the effects of model parameters on epidemic outcomes. In an effort to better capture the unbalanced topologies commonly observed in retroviral phylogenies, I developed a novel evolutionary model (dual-birth), derived probabilistic distributions and theoretical expectations of trees sampled under the model, developed an approach to estimate model parameters given real data, and used the model to analyze Alu retrotransposons in the human genome. In order to potentially aid public health officials, I developed a scalable and non-parametric phylogenetic method of viral transmission risk prioritization, which I evaluated against current best-practice methods via simulation and real data. Lastly, I contributed to Bioinformatics education by developing multiple publicly-accessible adaptive online interactive texts