Risk mapping in epidemiology enables the epidemiologist to identify regions with high or low risk of contamination and understand the underlying mechanisms of the spread of the disease. In this work we are presenting a method of risk mapping based on finite mixture models, in which the allocation to the mixture components is modelled through a correlated process, the Potts model. The inference is performed using an approximation of the Expectation Maximisation (EM) algorithm based on the mean-field theory. One advantage of this model is that the classification of the risk is done automatically and not performed in a second step as in current risk mapping.
Methods We are presenting also a way of initialisation able to overcome the sensitivity of this algorithm to its initial parameters. Combining the proposed model to this way of initialisation is leading to good results even in the case of animal non contagious diseases, in which the risk level is very small. This is illustrated in both simulated data and real data: The bovine spongiform Encephalopathy disease in France. We will also introduce an extension of this model to the spatial-temporal context since taking in account the temporal dependencies besides the spatial ones usually provides more useful cues. This methodology will be illustrated on simulated data.