Understanding the spatiotemporal spread of infectious diseases using mathematical and statistical models and methods of data analytics

Abstract

An ongoing challenge for the mathematical and statistical study of infectious disease spread is that many standard methods require an assumption of spatial homogeneity, even if the underlying mechanisms of disease transmission are intrinsically spatially-heterogeneous. One of the main goals of this thesis is to relax this assumption for the study of two different infectious diseases, Dengue Fever (DENV) and Ebola Virus Disease (EVD). The spatially-heterogeneous models for Dengue are primarily data-driven, relying on proxy data to provide information on the demographic and environmental factors of mosquito-borne virus transmission and spread. Modeling with large, diverse data requires effective variable selection and dimension reduction methods as even with ``clean'' high-dimensional data, the number of variables can quickly outpace the number of observations, leading to overfitting, redundant factors, and difficulties with model interpretation. Thus, prior to building models for Dengue risk, a novel dimension reduction method is proposed and applied. The spatial heterogeneity in the West Africa Ebola epidemic of 2014-2016 is then addressed by incorporating spatial mobility into a stochastic SEIR model by overlaying a directed graph structure over which the population can transition between spatial locations. Distinct spatial mobility structures are examined to explicate the most likely pathways of spatial infection spread. Epidemiological mechanisms are also investigated by estimating distributions for epidemiological parameters, such as the spatially and temporal varying infection/contact rate and the latent period. An empirically adjusted reproductive number is calculated for each spatial location using Bayesian inference methods in order to clarify the spatio-temporal transmission and population heterogeneity that drove the severity of the outbreak at the time.