  Branching process approximation to the initial stages of an epidemic process
has been used since the 1950's as a technique for providing stochastic
counterparts to deterministic epidemic threshold theorems. One way of
describing the approximation is to construct both branching and epidemic
processes on the same probability space, in such a way that their paths
coincide for as long as possible. In this paper, it is shown, in the context of
a Markovian model of parasitic infection, that coincidence can be achieved with
asymptotically high probability until o(N^{2/3}) infections have occurred,
where N denotes the total number of hosts.
