Prediction plays an essential part in the building of models of geographical systems: it exposes weaknesses in our concepts, checks our credibility and encourages model reformulation. Despite this centrality, the notion of system predictability and the way it fits into model building is often weakly developed in the geographical literature. The nature of predictions is illustrated here by the attempts to build geographical models of the spread of epidemic waves. Three types of spatial models are explored and illustrated: (i) descriptive models of a spread process, (ii) predictive models of the future extent of spread and (iii) interdictive models which show how spread may be curtailed. From this review, the wider role of prediction and predictability in other areas of geographical model-building is explored.