In 2020 and 2021, the spread of COVID-19 was globally addressed by imposing restrictions on the distance of individual travel. Recent literature has uncovered a clear pattern in human mobility that underlies the complexity of urban mobility: rf, the product of distance traveled r and frequency of return f per user to a given location, is invariant across space. This paper asks whether the invariant rf also serves as a driver for epidemic spread, so that the risk associated with human movement can be modeled by a unifying variable r*f. We use two large-scale datasets of individual human mobility to show that there is in fact a simple relation between r and f and both speed and spatial dispersion of disease spread. This discovery could assist in modeling spread of disease and inform travel policies in future epidemics---based not only on travel distance r but also on frequency of return f.