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Ancestral state reconstructions in Bayesian phylogeography of virus pandemics have been improved by utilizing a Bayesian stochastic search variable selection (BSSVS) framework. Recently, this framework has been extended to model the transition rate matrix between discrete states as a generalized linear model (GLM) of genetic, geographic, demographic, and environmental predictors of interest to the virus and incorporating BSSVS to estimate the posterior inclusion probabilities of each predictor. Although the latter appears to enhance the biological validity of ancestral state reconstruction, there has yet to be a comparison of phylogenies created by the two methods. In this paper, we compare these two methods, while also using a primitive method without BSSVS, and highlight the differences in phylogenies created by each. We test six coalescent priors and six random sequence samples of H3N2 influenza during the 2014–15 flu season in the U.S. We show that the GLMs yield significantly greater root state posterior probabilities than the two alternative methods under five of the six priors, and significantly greater Kullback-Leibler divergence values than the two alternative methods under all priors. Furthermore, the GLMs strongly implicate temperature and precipitation as driving forces of this flu season and nearly unanimously identified a single root state, which exhibits the most tropical climate during a typical flu season in the U.S. The GLM, however, appears to be highly susceptible to sampling bias compared with the other methods, which casts doubt on whether its reconstructions should be favored over those created by alternate methods. We report that a BSSVS approach with a Poisson prior demonstrates less bias toward sample size under certain conditions than the GLMs or primitive models, and believe that the connection between reconstruction method and sampling bias warrants further investigation., Author summary For the better part of the last decade, epidemiological researchers have employed a Bayesian framework to reconstruct phylogenetic trees and determine the spatiotemporal relationships between clades of viruses. Recently, an extension of this framework has enabled direct assessment of how various demographic, geographic, genetic, and environmental variables play a role in these relationships, but there has yet to be a comparison between the former and the latter. Here, we aim to assess the differences between the two reconstruction techniques, as well as an additional primitive method, using the 2014–15 influenza season in the U.S. as a case study under a variety of population growth scenarios. We highlight how the new method demonstrates significant increases in commonly-reported trends in phylogenies and that the method identifies climate predictors that appear to be consistent with known trends in seasonal trends in influenza. However, we found that this method appears to be the most heavily influenced by the locations at which the viruses were obtained. Our work offers valuable insight for researchers wishing to study the evolutionary history of viruses and also may prove useful in determining the correct method to choose for a given application of virus phylogeography.

Dengue is an important vector-borne virus that infects on the order of 400 million individuals per year. Infection with one of the virus's four serotypes (denoted DENV-1 to 4) may be silent, result in symptomatic dengue 'breakbone' fever, or develop into the more severe dengue hemorrhagic fever/dengue shock syndrome (DHF/DSS). Extensive research has therefore focused on identifying factors that influence dengue infection outcomes. It has been well-documented through epidemiological studies that DHF is most likely to result from a secondary heterologous infection, and that individuals experiencing a DENV-2 or DENV-3 infection typically are more likely to present with more severe dengue disease than those individuals experiencing a DENV-1 or DENV-4 infection. However, a mechanistic understanding of how these risk factors affect disease outcomes, and further, how the virus's ability to evolve these mechanisms will affect disease severity patterns over time, is lacking. In the second chapter of my dissertation, I formulate mechanistic mathematical models of primary and secondary dengue infections that describe how the dengue virus interacts with the immune response and the results of this interaction on the risk of developing severe dengue disease. I show that only the innate immune response is needed to reproduce characteristic features of a primary infection whereas the adaptive immune response is needed to reproduce characteristic features of a secondary dengue infection. I then add to these models a quantitative measure of disease severity that assumes immunopathology, and analyze the effectiveness of virological indicators of disease severity. In the third chapter of my dissertation, I then statistically fit these mathematical models to viral load data of dengue patients to understand the mechanisms that drive variation in viral load. I specifically consider the roles that immune status, clinical disease manifestation, and serotype may play in explaining viral load variation observed across the patients. With this analysis, I show that there is statistical support for the theory of antibody dependent enhancement in the development of severe disease in secondary dengue infections and that there is statistical support for serotype-specific differences in viral infectivity rates, with infectivity rates of DENV-2 and DENV-3 exceeding those of DENV-1. In the fourth chapter of my dissertation, I integrate these within-host models with a vector-borne epidemiological model to understand the potential for virulence evolution in dengue. Critically, I show that dengue is expected to evolve towards intermediate virulence, and that the optimal virulence of the virus depends strongly on the number of serotypes that co-circulate. Together, these dissertation chapters show that dengue viral load dynamics provide insight into the within-host mechanisms driving differences in dengue disease patterns and that these mechanisms have important implications for dengue virulence evolution.

In this dissertation, I present a general statistical framework for phylodynamic inference that can be used to estimate epidemiological parameters and reconstruct disease dynamics from pathogen genealogies. This framework can be used to fit a broad class of epidemiological models, including nonlinear stochastic models, to genealogies by relating the population dynamics of a pathogen to its genealogy using coalescent theory. By combining Markov chain Monte Carlo and particle filtering methods, efficient Bayesian inference of all parameters and unobserved latent variables is possible even when analytical likelihood expressions are not available under the epidemiological model. Through extensive simulations, I show that this method can be used to reliably estimate epidemiological parameters of interest as well as reconstruct past disease dynamics from genealogies, or jointly from genealogies and other common sources of epidemiological data like time series. I then extend this basic framework to include different types of host population structure, including models with spatial structure, multiple-hosts or vectors, and different stages of infection. The later is demonstrated by using a multistage model of HIV infection to estimate stage-specific transmission rates and incidence from HIV sequence data collected in Detroit, Michigan. Finally, to demonstrate how the approach can be used more generally, I consider the case of dengue virus in southern Vietnam. I show how earlier phylodynamic inference methods fail to reliably reconstruct the dynamics of dengue observed in hospitalization data, but by deriving coalescent models that take into consideration ecological complexities like seasonality, vector dynamics and spatial structure, accurate dynamics can be reconstructed from genealogies. In sum, by extending phylodynamics to include more ecologically realistic and mechanistic models, this framework can provide more accurate estimates and give deeper insight into the processes driving infectious disease dynamics.

Evolution by natural selection can occur at multiple biological scales. This is particularly the case for host-pathogen systems, where selection occurs both within each infected host as well as through transmission between hosts. Despite there being established mathematical models for understanding evolution at a single biological scale, fewer tractable models exist for multiscale evolutionary dynamics. Here I present mathematical approaches using tools from probability and stochastic processes as well as dynamical systems to handle multiscale evolutionary systems. The first problem I address concerns the antigenic evolution of influenza. Using a combination of ordinary differential equations and inhomogeneous Poisson processes, I study how immune selection pressures at the within-host level impact population-level evolutionary dynamics. The second problem involves the more general question of evolutionary dynamics when selection occurs antagonistically at two biological scales. In addition to host-pathogen systems, such situations arise naturally in the evolution of traits such as the production of a public good and the use of a common resource. I introduce a model for this general phenomenon that is intuitively visualized as a a stochastic ball-and-urn system and can be used to systematically obtain general properties of antagonistic multiscale evolution. Lastly, this ball-and-urn framework is in itself an interesting mathematical object which can studied as either a measure-valued process or an interacting particle system. In this mathematical context, I show that under different scalings, the measure-valued process can have either a propagation of chaos or Fleming-Viot limit.

Despite high vaccination rates and effective adaptive immune responses from the part of infected individuals, influenza A viruses cause significant morbidity and mortality annually. This is due to influenza's rapid antigenic evolution, whereby continual mutations occurring in epitope regions of the virus's hemagglutinin protein result in the diminishment of long-term antibody recognition, in a process that has been termed `antigenic drift'. Although it is clear that antigenic drift enables previously infected individuals to become reinfected, the mechanism that is responsible for influenza's antigenic drift is still under debate. As recently as 2009, a new hypothesis of antigenic drift was put forward that argues that binding avidity changes in the viral hemagglutinin result in antigenic drift as a side effect. This hypothesis stands in contrast to the traditionally accepted hypothesis that mutations in epitope regions are positively selected for their ability to evade immune recognition. This thesis focuses on the use of epidemiological models and empirical data analysis to explore different hypotheses of antigenic drift. In the first chapter, I am asking what effects on antigenic drift rate would be produced under the new hypothesis. I mathematically formulate the hypothesis that antigenic drift is simply a side effect of cellular receptor binding avidity changes that occur as the virus is transmitted between individuals of different immune status levels. I then use this formulation to explore how influenza's rate of antigenic drift depends on different epidemiological factors, including host contact rate, host lifespan, and the duration of infection. Finally, I use the model to assess alternative vaccination strategies by the impact they have on rates of antigenic drift and therewith rates of disease incidence/In the second chapter, I critically evaluate the binding avidity hypothesis by comparing predictions of the hypothesis against empirical data. I first use a `phylodynamic' extension of the model presented in the first chapter to determine whether the hypothesis is consistent with the ladderlike phylogeny of influenza's hemagglutinin protein. I then use viral sequence data and metadata to determine whether older aged individuals (with a higher number of previous infections) harbor viruses with higher binding avidity than younger aged individuals (with a lower number of previous infections), a prediction made by the binding avidity hypothesis. Finally, I perform a phylogenetic analysis to determine how rapidly binding avidity changes occur. From these analyses, I conclude that the binding avidity hypothesis is not well supported by empirical data.In the third chapter, I develop an integrated viral life cycle model, in which viral replication depends on three viral phenotypes: receptor binding avidity, neuraminidase activity, and antigenicity. This integrated model recognizes that receptor binding avidity changes will influence viral replication, but also allows for antigenic evolution to be brought about directly by epitope changes. I first use this model to show how the evolutionary dynamics of these phenotypes are dependent on one another and how antigenic drift can be interpreted within this framework. I then return to some of the questions addressed in the first chapter to ask how different epidemiological factors impact influenza's rate of antigenic drift.Together, these three chapters highlight the importance of viral phenotypes other than antigenicity in contributing to influenza's antigenic evolution, and, more generally, the importance of computational and mathematical research in understanding constraints on viral adaptation.