Bayesian methods for spatio-temporal epidemic models to accurately capture complex dynamics of disease spread

Statistical modeling of infectious diseases allows researchers to study epidemiological patterns, which are of practical importance to public health organizations and those attempting to stop the spread of such diseases. Infectious disease models yield important inference on disease transmission by appropriately accounting for the dynamics and uncertainty of the infection process. In addition to estimating transmission probabilities and characterizing disease progression, these statistical models allow researchers to assess disease risk and quantify the effectiveness of interventions. Many challenges arise in creating useful and informative models, both in terms of the data available and in terms of the statistical tools needed to run the models. This dissertation aims to advance the field of infectious disease modeling by addressing some of these challenges.

First, we detail two existing approaches to modeling disease dynamics which are applicable to a wide variety of epidemic data. Then, we address the computational and practical challenges which arise from modeling of the infectious period using limited data providing only symptom onset date. We propose a new method which is both computationally efficient and biologically plausible, and demonstrate its utility on data from an epidemic of Ebola Virus Disease from 1995. Finally, we consider the uncertainty arising from the use of imperfect diagnostic tests to detect when someone is truly infectious, particularly when tests are likely to produce false negative results. We propose a new modeling framework which accounts for this uncertainty, and use it to model the spread of mumps from an outbreak in Iowa from 2006, in which over 6,000 individuals were tested for mumps in a six-month period.