Convergence results for contact branching processes

The link between the multi-type contact birth process and the spatial deterministic S → I epidemic is exploited to give convergence results for a multi-type Markovian contact branching process. Let U(t) be the position of furthest spread by time t in a specific direction. The asymptotic speed of translation of the distribution function of U(t) is derived and U(t)/t is shown to converge in probability to this speed.