Short-time human travel behaviour can be well described by a power law with respect to distance. We incorporate this information in space-time models for infectious disease surveillance data to better capture the dynamics of disease spread. Two previously established model classes are extended, which both decompose disease risk additively into endemic and epidemic components: a space-time point process model for individual point-referenced data, and a multivariate time series model for aggregated count data. In both frameworks, the power-law spread is embedded into the epidemic component and its decay parameter is estimated simultaneously with all other unknown parameters using (penalised) likelihood inference. The performance of the new approach is investigated by a re-analysis of individual cases of invasive meningococcal disease in Germany (2002-2008), and count data on influenza in 140 administrative districts of Southern Germany (2001-2008). In both applications, the power-law formulations substantially improve model fit and predictions. Implementation in the R package surveillance allows to apply the approach in other settings.