Estimation of Epidemic Model Parameters: A Spatial Analysis using Bayesian Techniques

Emory UniversityDissertaion, Doctor of Philosophy, Biostatistics, Emory University, 2011

Jeffrey M. Switchenko

“Infectious disease models attempt to evaluate the effects on the spread and transmission of disease. One particular model, the susceptible-infected-recovered (SIR) model, places individuals into classes of disease progression, where a series of differential equations tracks the rates of transmission and recovery for a given disease through a susceptible population. Two parameters, the transmission parameter and the recovery parameter, drive the dynamics of the model, and their ratio, R0, is the average number of cases caused by one infectious individual within a completely susceptible population. R0 is seen as one of the most important quantities in the study of epidemics, and signals how quickly a particular disease can spread amongst a susceptible population. Previous analyses have focused primarily on tracking these epidemic disease parameters over time, and classifying individuals due to baseline differences which reflect heterogeneity within the population. For example, these differences can be based on age, gender, vaccination status, or behavior.

Estimates for R0 across Baltimore using the following set of xed R0 values: f1:0; 1:1; 1:2g, f1:3; 1:4; 1:5g, f1:6; 1:7; 1:8g, f1:9; 2:0; 2:1g

Estimates for R0 across Baltimore using the following set of xed R0 values: f1:0; 1:1; 1:2g, f1:3; 1:4; 1:5g, f1:6; 1:7; 1:8g, f1:9; 2:0; 2:1g

“However, we choose to quantify the spatial heterogeneity that exists in spatially-referenced data in an effort to define core areas of disease rates and transmission. We first consider geographically weighted regression (GWR) models in an effort to assess the spatial variability that exists between disease rates and baseline tract- level characteristics which can define core disease areas. Next, we build hierarchical Bayesian models which incorporate random effects structures, inducing correlation in local estimates of disease transmission with exchangeable random effects, which smooth local estimates based on global averages, and conditionally autoregressive (CAR) random effects, which smooth local estimates based on neighboring estimates. We extend a chain binomial model to predict the spread of disease, while considering two different parameterizations of the chain binomial model, and simulate outbreaks to assess model performance. In addition, we extend a general epidemic model, which incorporates aspects of frailty models in assessing heterogeneity within the population. Through our modeling approaches, we are able to identify cores areas for the transmission of sexually transmitted infections (STIs) in Baltimore, Maryland from 2002-05.”