Document Type


Date of Degree

Spring 2015

Degree Name

PhD (Doctor of Philosophy)

Degree In


First Advisor

Jacob J. Oleson


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 spatio-temporal 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. Finally, we demonstrate the application of these techniques both under simulation, and in the context of a diverse set of real diseases, including Ebola Virus Disease, Smallpox, Methicillin-resistant Staphylococcus aureus, and Influenza.

Public Abstract

The study of epidemics is complex. Not only are disease processes driven by constantly evolving pathogens spreading through real populations, but even at an aggregate level epidemic behavior is affected by a wide array of influences. Environmental factors like humidity and temperature may modify the infectivity of disease agents, while contact patterns in human populations respond to everything from sporting events to news reports. In the face of such variability, statisticians and epidemiologists are called upon to describe, explain, and forecast infectious disease outbreaks with increased rapidity.

This dissertation aims to provide methodological and computational tools to enable rapid and thorough analysis of past as well as emerging epidemics. We develop a general class of spatiotemporal epidemic models capable of addressing many types of spatially distributed data over changing temporal landscapes. We introduce an implementation of these techniques as an open source package for the popular statistical computing environment, R. In addition to the tools required to fit epidemic models, we examine measures of model adequacy in order to guide epidemic predictions under substantial uncertainty. These developments are explored in the context of simulations, and are applied to real outbreaks of Ebola Virus Disease, Influenza, MRSA, and Smallpox. We conclude with an examination of the ways in which this work expands the capabilities of public health practitioners and epidemic modeling professionals, and a description of promising avenues for future research.


publicabstract, Compartmental Modeling, Ebola, Infectious Disease, Spatial Statistics


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Copyright 2015 Grant Donald Brown

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Biostatistics Commons