  There are various cases of animal movement where behaviour broadly switches
between two modes of operation, corresponding to a long distance movement state
and a resting or local movement state. Here a mathematical description of this
process is formulated, adapted from Friedrich et. al. (2006). The approach
allows the specification any running or waiting time distribution along with
any angular and speed distributions. The resulting system of partial
integro-differential equations are tumultuous and therefore it is necessary to
both simplify and derive summary statistics. An expression for the mean squared
displacement is derived which shows good agreement with experimental data from
the bacterium Escherichia coli and the gull Larus fuscus. Finally a large time
diffusive approximation is considered via a Cattaneo approximation (Hillen,
2004). This leads to the novel result that the effective diffusion constant is
dependent on the mean and variance of the running time distribution but only on
the mean of the waiting time distribution.
