A Stochastic Model for Measles Epidemics in a Multi-Region Setting

In this paper, a regionally based stochastic model for the diffusion of measles epidemics is developed. The model is tested with an application to ten contiguous sub-areas centred on Bristol. IN this paper we explore some ways in which a stochastic version of the classic Hamer-Soper deterministic model for measles epidemics (Soper, 1929) may be extended to analyse patterns of measles outbreaks in a regional setting. The models developed are applied to a set of ten con- tiguous sub-areas centred on the city of Bristol. Following a description of the nature of the data and the regional setting, the Hamer-Soper model and a stochastic equivalent are outlined for a single areal unit and some of the properties of the stochastic model are illustrated using an arti- ficial data set. The multi-region model is then described and fitted to notifications of measles cases in the ten sub-area system and the results of the analysis are outlined. A modification of the model to give a better fit to the incidence of measles in Bristol itself is also discussed.