Network analysis of measles data 1 A Network - based Analysis of the 1861 Hagelloch Measles Data

In this article, 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 class of Exponential-family Random Graph Models (ERGMs) while the transmission process that runs over the network is modeled as a stochastic Susceptible-Exposed-Infectious-Removed (SEIR) epidemic. We fit these models to very detailed data from a 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. This approach allows us to make meaningful statements about the structure of the population—separate from the transmission process— as well as to provide estimates of various biological quantities of interest, such as the basic reproductive number, R0. Using reversible jump Markov chain Monte Carlo, we produce samples from the joint posterior distribution of all the parameters of this model—the network, transmission tree, ERGM parameters and SEIR parameters—and perform Bayesian model selection to find the best-fitting network model. 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 provide a software package, written in R, that performs this type of analysis. Network analysis of measles data 2