A model of human population motion

We introduce a basic model for human mobility that accounts for the different dynamics arising from individuals embarking on short trips (and returning to their home locations) and individuals relocating to a new home. The differences between the two modes of motion comes to light on contrasting two recent studies, one tracking the geographical location of dollar bills \cite{brockmann}, the other that of mobile cell phones \cite{gonzalez}. Trips introduce two characteristic time scales; the time between trips, $\theta$, and the duration of each trip, $\tau$, and relocations introduces a third time scale, $T$, for the time between relocations. In practice, $T\sim{\rm years}$, $\theta\sim{\rm months}$, and $\tau\sim{\rm days}$, so the three time scales are widely separated. Traditionally, studies incorporating human motion assume only a single mode, using a generic rate to account for all types of motion.