Fixed accuracy estimation for chain binomial models

In many epidemic models the initial infection rate, suitably defined, plays a major role in determining the probability of an outbreak of a disease becoming a major epidemic. Here we model the epidemic as a chain binomial model and consider an approximate maximum likelihood estimator of the infection rate. It is shown that under mild conditions sampling according to a simple stopping rule yields an asymptotically normally distributed estimator which may be computed during the course of an epidemic. A small simulation study suggests that the asymptotic results applied to small samples yield accurate confidence intervals.