The emergence and re‐emergence of disease epidemics is a complex question that may be influenced by diverse factors, including the space–time dynamics of human populations, environmental conditions, and associated uncertainties. This study proposes a stochastic framework to integrate space–time dynamics in the form of a Susceptible‐Infected‐Recovered (SIR) model, together with uncertain disease observations, into a Bayesian maximum entropy (BME) framework. The resulting model (BME‐SIR) can be used to predict space–time disease spread. Specifically, it was applied to obtain a space–time prediction of the dengue fever (DF) epidemic that took place in Kaohsiung City (Taiwan) during 2002. In implementing the model, the SIR parameters were continually updated and information on new cases of infection was incorporated. The results obtained show that the proposed model is rigorous to user‐specified initial values of unknown model parameters, that is, transmission and recovery rates. In general, this model provides a good characterization of the spatial diffusion of the DF epidemic, especially in the city districts proximal to the location of the outbreak. Prediction performance may be affected by various factors, such as virus serotypes and human intervention, which can change the space–time dynamics of disease diffusion. The proposed BME‐SIR disease prediction model can provide government agencies with a valuable reference for the timely identification, control, and prevention of DF spread in space and time.