The ability to predict how infectious disease will spread is of great importance in the face of the numerous emergent and re-emergent pathogens that currently threatening human well-being. We identified a variety of alternative models that predict human mobility as as a function of population distribution across a landscape. These consider some models that account for pair-wise interactions between population centers, as well as some that allow for higher-order interactions. We trained the models using a uniquely rich spatiotemporal data set on pre-vaccination measles in England and Wales (1944–65), which comprises more than a million records from 954 cities and towns. Likelihood rankings of the different models reveal strong evidence for higher-order interactions in the form of competition among cities as destinations for travelers and, thus, dilution of spatial transmission. The currently most commonly used so-called `gravity’ models were far from the best in capturing spatial disease dynamics.