In recent years, the availability of infectious disease counts in time and space has increased, and consequently there has been renewed interest in model formulation for such data. In this paper, we describe a model that was motivated by the need to analyze hand, foot and mouth disease (HFMD) surveillance data in China. The data are aggregated by geographical areas and by week, with the aims of the analysis being to gain insight into the space-time dynamics and to make short-term prediction to implement public health campaigns in those areas with a large predicted disease burden. The model we develop decomposes disease risk into marginal spatial and temporal components, and a space-time interaction piece. The latter is the crucial element, and we use a tensor product spline model with a Markov random field prior on the coefficients of the basis functions. The model can be formulated as a Gaussian Markov random field and so fast computation can be carried out using the integrated nested Laplace approximation (INLA) approach. A simulation study shows that the model can pick up complex space-time structure and our analysis of HFMD data in the central north region of China provides new insights into the dynamics of the disease.
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