A Network-Based Analysis of the 1861 Hagelloch Measles Data

• Activity Number: 49
• Type: Invited
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Chris Groendyke and David Welch and David Hunter*+
• Companies: Robert Morris University and University of Auckland and Pennsylvania State University
• Keywords: Exponential-family Random Graph Model ; Reversible jump

Abstract

We demonstrate a statistical method for fitting the parameters of a sophisticated network and epidemic model to disease data. The pattern of contacts between hosts is described by a dyadic independence Exponential-family Random Graph Model (ERGM) while the transmission process on the network is modeled as a Susceptible-Exposed-Infectious-Removed (SEIR) epidemic. We fit these models to detailed data from an 1861 measles outbreak in Hagelloch, Germany. The network models include parameters for all recorded host covariates including age, sex, household and classroom membership and household location while the SEIR epidemic model has exponentially distributed transmission times with gamma distributed latent and infective periods. Our approach allows us to make inferences about the structure of the population along with various biological quantities of interest, such as the effective reproductive number, R. We compare our results with those of previous analyses and show that the ERGM network model better fits the data than a Bernoulli network model previously used. We also discuss a software package, written in R, that performs this type of analysis.