A Network‐based Analysis of the 1861 Hagelloch Measles Data

Abstract

Summary 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 dyadic independence 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 the 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 effective reproductive number, R. 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, network 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.

epinet: An R Package to Analyze Epidemics Spread across Contact Networks

“…The dyadic-independence property of these models also makes them computationally manageable. As described in Groendyke, Welch, and Hunter (2012), all of the manipulations of the network in the MCMC algorithm can be done iteratively by cycling through the dyads. The normalizing function κ(η) in Equation 1, which is in general intractable, becomes computationally tractable for this subclass.…”

“…The network and transmission tree are included so that the likelihood can be more easily calculated, but these parameters may not always be of interest. Full details of the implementation of the algorithm are given in Groendyke et al (2011) and Groendyke et al (2012).…”

“…This algorithm is based on that described in Britton and O'Neill (2002), Groendyke et al (2011), and Groendyke et al (2012):…”

“…This data was originally collected by Pfeilsticker (1863) and later augmented by Oesterle (1992). This data set has been analyzed in various manners by many researchers, including Lawson and Leimich (2000), Neal and Roberts (2004), Britton, Kypraios, and O'Neill (2011), Groendyke et al (2012) and Meyer et al (2017), among others.…”

Reality Mining with Mobile Data: Understanding the Impact of Network Structure on Propagation Dynamics

“…For studying the quantized disease dynamics, a wide range of methods have been proposed to estimate or predict R [21][27] [28][1] [11] based on the assumptions of network structure, e.g., the contact networks for the spread of disease are best described as having exponential degree distributions [2].…”