Person:

Hill, Alison

Modern-day management of infectious diseases is critically linked to the use of mathematical models to understand and predict dynamics at many levels, from the mechanisms of pathogenesis to the patterns of population-wide transmission and evolution. This thesis describes the development and application of mathematical techniques for HIV infection and dynamics on social networks. Treatment of HIV infection has improved dramatically in the past few decades but is still limited by the development of drug resistance and the inability of current therapies to completely eradicate the virus from an individual. We begin with a synthesis of the important evolutionary principles governing the HIV epidemic, emphasizing the role of modeling. We then describe a modeling framework to study the emergence of drug-resistant HIV within a patient. Our model integrates laboratory data and patient behavior, with the goal of predicting outcomes of clinical trials. Current results demonstrate how pharmacologic properties of antiretroviral drugs affect selection for drug resistance, and can explain drug-class-specific resistance risks. Thirdly, we describe models for a new class of drugs that aim to eliminate cells with latent viral infection. We provide estimates for the required efficacy of these drugs and describe the potential challenges of future clinical trials. Finally, models and mechanisms for understanding viral dynamics are increasingly finding applications outside traditional virology. They can be used to study the dynamics of behaviors, to help predict and intervene in their spread. We describe techniques for applying infectious disease models to social contagion, drawing on techniques for network epidemiology. We use this framework to interpret data on the interpersonal spread of health-related behaviors.

Limiting dilution assays are widely used in infectious disease research. These assays are crucial for current human immunodeficiency virus (HIV)-1 cure research in particular. In this study, we offer new tools to help investigators design and analyze dilution assays based on their specific research needs. Limiting dilution assays are commonly used to measure the extent of infection, and in the context of HIV they represent an essential tool for studying latency and potential curative strategies. Yet standard assay designs may not discern whether an intervention reduces an already miniscule latent infection. This review addresses challenges arising in this setting and in the general use of dilution assays. We illustrate the major statistical method for estimating frequency of infectious units from assay results, and we offer an online tool for computing this estimate. We recommend a procedure for customizing assay design to achieve desired sensitivity and precision goals, subject to experimental constraints. We consider experiments in which no viral outgrowth is observed and explain how using alternatives to viral outgrowth may make measurement of HIV latency more efficient. Finally, we discuss how biological complications, such as probabilistic growth of small infections, alter interpretations of experimental results.

Monitoring the efficacy of novel reservoir-reducing treatments for HIV is challenging. The limited ability to sample and quantify latent infection means that supervised antiretroviral therapy (ART) interruption studies are generally required. Here we introduce a set of mathematical and statistical modeling tools to aid in the design and interpretation of ART-interruption trials. We show how the likely size of the remaining reservoir can be updated in real-time as patients continue off treatment, by combining the output of laboratory assays with insights from models of reservoir dynamics and rebound. We design an optimal schedule for viral load sampling during interruption, whereby the frequency of follow-up can be decreased as patients continue off ART without rebound. While this scheme can minimize costs when the chance of rebound between visits is low, we find that the reservoir will be almost completely reseeded before rebound is detected unless sampling occurs at least every two weeks and the most sensitive viral load assays are used. We use simulated data to predict the clinical trial size needed to estimate treatment effects in the face of highly variable patient outcomes and imperfect reservoir assays. Our findings suggest that large numbers of patients—between 40 and 150—will be necessary to reliably estimate the reservoir-reducing potential of a new therapy and to compare this across interventions. As an example, we apply these methods to the two “Boston patients”, recipients of allogeneic hematopoietic stem cell transplants who experienced large reductions in latent infection and underwent ART-interruption. We argue that the timing of viral rebound was not particularly surprising given the information available before treatment cessation. Additionally, we show how other clinical data can be used to estimate the relative contribution that remaining HIV+ cells in the recipient versus newly infected cells from the donor made to the residual reservoir that eventually caused rebound. Together, these tools will aid HIV researchers in the evaluating new potentially-curative strategies that target the latent reservoir.