Hidden Markov modelling of spatio-temporal dynamics of measles in 1750–1850 Finland

Real world spatio-temporal datasets, and phenomena related to them, are often challenging to visualise or gain a general overview of. In order to summarise information encompassed in such data, we combine two well known statistical modelling methods. To account for the spatial dimension, we use the intrinsic modification of the conditional autoregression, and incorporate it with the hidden Markov model, allowing the spatial patterns to vary over time. We apply our method to parish register data considering deaths caused by measles in Finland in 1750–1850, and gain novel insight of previously undiscovered infection dynamics. Five distinctive, reoccurring states, describing spatially and temporally differing infection burden and potential routes of spread, are identified. We also find that there is a change in the occurrences of the most typical spatial patterns circa 1812, possibly due to changes in communication networks after major administrative transformations in Finland.