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 MN infections have occurred, as long as
MN = o(N2/3), where N denotes the total number of hosts.