Bayesian parameter inference for dynamic infectious disease modelling: rotavirus in Germany

Abstract

Understanding infectious disease dynamics using epidemic models based on ordinary differential equations requires the calibration of model parameters from data. A commonly used approach in practice to simplify this task is to fix many parameters on the basis of expert or literature information. However, this not only leaves the corresponding uncertainty unexamined but often also leads to biased inference for the remaining parameters because of dependence structures inherent in any given model. In the present work, we develop a Bayesian inference framework that lessens the reliance on such external parameter quantifications by pursuing a more data-driven calibration approach. This includes a novel focus on residual autocorrelation combined with model averaging techniques in order to reduce these estimates' dependence on the underlying model structure. We applied our methods to the modelling of age-stratified weekly rotavirus incidence data in Germany from 2001 to 2008 using a complex susceptible-infectious-susceptible-type model complemented by the stochastic reporting of new cases. As a result, we found the detection rate in the eastern federal states to be more than four times higher compared with that of the western federal states (19.0% vs 4.3%), and also the infectiousness of symptomatically infected individuals was estimated to be more than 10 times higher than that of asymptomatically infected individuals (95% credibility interval: 8.1–19.6). Not only do these findings give valuable epidemiological insight into the transmission processes, we were also able to examine the considerable impact on the model-predicted transmission dynamics when fixing parameters beforehand.