Matrix models for childhood infections: a Bayesian approach with applications to rubella and mumps

Mathematical modelling is an established tool for planning and monitoring vaccination programmes. However, the matrices describing contact rates are based on subjective choices, which have a large impact on results. This paper reviews published models and obtains prior model probabilities based on publication frequency and expert opinion. Using serological survey data on rubella and mumps, Bayesian methods of model choice are applied to select the most plausible models. Estimates of the basic reproduction number R, are derived, taking into account model uncertainty and individual heterogeneity in contact rates. Twenty-two models are documented, for which publication frequency and expert opinion are negatively correlated. Using the expert prior with individual heterogeneity, R-0 = 6.1 [95% credible region (CR) 4.3-9.2] for rubella and R-0= 19-3 (95% CR 4.0-31.5) for mumps. The posterior modes are insensitive to the prior for rubella but not for mumps. Overall, assortative models with individual heterogeneity are recommended.