In this paper, we have presented a new methodology that adapts the existing GMRF class of models to deal with spatio-temporal surveillance data. When the data are mainly spatial and coarsely discretized in time, simple models such as the CAR model will continue to be valuable for descriptive analysis. However, when data have a fine resolution in both the spatial and temporal dimensions, our model, which explicitly incorporates the directional nature of time by conditioning future events on past outcomes, is likely to be more insightful.