<p>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.</p> / Dissertation

The ability to accelerate the accumulation of favorable combinations of mutations renders recombination a potent force underlying the emergence of forms of HIV that escape multi-drug therapy and specific host-immune responses. In this study, a mathematical model is developed that describes the dynamics of the emergence of recombinant forms of HIV following infection with diverse viral genomes. Mimicking recent in vitro experiments, target cells simultaneously exposed to two distinct, homozygous viral populations are considered and dynamical equations are constructed that predict the time-evolution of populations of uninfected, singly infected, and doubly infected cells, and homozygous, heterozygous, and recombinant viruses. Model predictions capture several recent experimental observations quantitatively and provide insights into the role of recombination in HIV dynamics. Comparisons of data from single round infection experiments with model predictions of the probability with which recombination accumulates distinct mutations present on the two genomic strands in a vision, indicates that »8 recombinational strand transfer events occur on average (95% confidence interval: 6-10) during reverse transcription of HIV in T cells. Model predictions of virus and cell dynamics describe the time-evolution and the relative prevalence of various infected cell subpopulations following the onset of infection observed experimentally. Remarkably, model predictions are in quantitative agreement with the experimental scaling relationship that the percentage of cells infected with recombinant genomes is proportional to the percentage of cells co-infected with the two genomes employed at the onset of infection. The model developed thus presents an accurate description of the influence of recombination on HIV dynamics in vitro. When distinctions between different viral genomes are ignored, the model reduces to the standard model of viral dynamics, which successfully predicts viral load changes in HIV patients undergoing therapy. The model developed may thus serve as a useful framework to predict the emergence of multi-drug resistant forms of HIV in infected individuals.

<div>The family Flaviviridae includes important genera such as flavivirus and hepacivirus which comprise significant human pathogens that affect hundreds of millions annually. The understanding of these viruses, the viral life cycle, and pathogenicity is vital when it comes to developing therapeutics. Flavivirus virions undergo major conformational rearrangements during the life cycle, including the assembly and maturation steps. In order to create a reagent to investigate these processes, luminescent reporter viruses have been constructed. Luminescent reporter tags have yet to be incorporated into the structural proteins of dengue virus (DENV) without significantly affecting replication or infectivity and successful tagging would allow for targeted studies examining access to specific structural epitopes. Engineering tags in DENV structural proteins is particularly difficult because most reporter tags involve large insertions which may create steric hindrance and inhibit proper protein folding. However, the reporter system described here, developed by Promega, is much smaller than a full-size luciferase protein. It involves an eleven amino acid subunit (HiBiT) tagged to a viral protein that creates measurable luminescence when incubated with the larger subunit (LgBiT). Using the structure of the virion as a guide, the HiBiT reporter tag was incorporated into the structural region of the DENV genome including sites in capsid (C) as well as the glycoproteins membrane (M) and envelope (E). Resulting recombinant viruses were characterized and tag sites within the C protein membrane anchor as well as the transmembrane domain of M protein were found to tolerate HiBiT insertion and produce infectious particles. The recombinant virus possessing HiBiT in C protein was found to be stable over three rounds of serial passaging while virus containing the M protein tag site was found to be unstable. HiBiT activity of the capsid tagged virus was also found to directly correlate with purified infectious particles, suggesting the capsid membrane anchor may remain associated with the virus even after polyprotein processing. Additionally, insert composition was found to be a key determinant for the production of infectious virus. The lessons learned from engineering HiBiT in the DENV system were then applied to hepatitis C virus (HCV). </div><div>The highly lipophilic and pleiomorphic nature of HCV has made structural studies particularly difficult. However, by constructing multi-tagged reporter viruses containing both HiBiT and various purification tags, researchers will save time and resources in preparation for structural studies which are vital for vaccine development. In this study, HiBiT was incorporated into sites within HCV previously shown to tolerate tags of various sizes. Different insert compositions were engineered within the genome and the construct containing both FLAG and HiBiT tags within the N-terminus of E2 yielded highly infectious and quantifiable, luminescent virus. The recombinant HCV containing FLAG and HiBiT displayed similar peak titer as compared to WT while also demonstrating HiBiT activity. Furthermore, the FLAG peptide was found to be partially surface exposed and capable of being used for virus purification purposes. The multi-tagged reporter virus characterized in this study provides a robust platform for quantification and purification of HCV, two facets of research that are critical for the determination of viral structure via cryo-EM and other imaging techniques. The findings from both the DENV and HCV studies provide a robust foundation for future tagging of viruses within the family Flaviviridae and offer insight on the structural proteins that compose the virion.</div>

In this thesis we develop a mathematical model to describe HIV-1 evolution during the first stages of infection (approximately within 40-60 days since onset), when one can assume exponential growth and random accumulation of mutations under a neutral drift. We analyze the Hamming distance (HD) distribution under different models (synchronous and asynchronous) in the absence of selection and recombination. In the second part of the thesis, we introduce recombination and develop a combinatorial approach to estimate the new HD distribution. We conclude describing a T statistic to test significance differences between the HD of two genetic samples, which we derive using U-statistics.