Application Of Heterogeneous Computing Techniques To Compartmental Spatiotemporal Epidemic Models

Abstract

The application of spatial methods to epidemic estimation and prediction problems is a vibrant and active area of research. In many cases, however, well thought out and laboratory supported models for epidemic patterns may be easy to specify but extremely difficult to fit efficiently. While this problem exists in many scientific disciplines, epidemic modeling is particularly prone to this challenge due to the rate at which the problem scope grows as a function of the size of the spatial and temporal domains involved. An additional barrier to widespread use of spatiotemporal epidemic models is the lack of user friendly software packages capable of fitting them. In particular, compartmental epidemic models are easy to understand, but in most cases difficult to fit. This class of epidemic models describes a set of states, or compartments, which captures the disease progression in a population. This dissertation attempts to expand the problem scope to which spatiotemporal compartmental epidemic models are applicable both computationally and practically. In particular, a general family of spatially heterogeneous SEIRS models is developed alongside a software library with the dual goals of high computational performance and ease of use in fitting models in this class. We emphasize the task of model specification, and develop a framework describing the components of epidemic behavior. In addition, we establish methods to estimate and interpret reproductive numbers, which are of fundamental importance to the study of infectious disease.