Information Content of Household-stratied Epidemics

Household epidemic models have been identified as important tools in the design of targeted vaccination programmes as well as infection prediction. For these models to be of maximum benefit, they require parameterisation from time-series infection data from households. Such data has increasingly become available and in this paper we concern ourselves with the optimal design in the collection of such household epidemiological data. We describe the tradeoff between the number of observation time points and the number of households to observe in order to optimize the expected information content of the model parameters against the background of constrained resources. Using a Metropolis-Hastings random walk MCMC algorithm that draws random parameters for any given design, and a Markovian household model, we estimate the utility of the design by evaluating how closely the random parameters approach the true parameter values. As would be expected, we observe that increasing both the number of time points and the households sampled increases the information content. Interestingly, the utility of increasing the number of households sampled often generates more information than increasing the number of time points at which a fixed number of households are observed.