We propose a class of Cox processes as models for the times of occurrence of cases of a disease, and develop associated methods of Bayesian inference for parameter estimation and for prediction of the temporal variation in disease risk. The data may consist of either incidence times of individual cases or counts of the numbers of incident cases in disjoint time-intervals. We explore the consequences of working with different levels of temporal aggregation of the data. We use a simulated example to demonstrate the feasibility of our methodology, which we then apply to data giving daily counts of incident cases of gastrointestinal infections in the county of Hampshire, UK. Copyright (C) 2009 John Wiley & Sons, Ltd.