  The aim of this paper is to understand the extreme variability on the
estimated reproduction ratio $R_0$ observed in practice. For expository purpose
we consider a discrete time stochastic version of the
Susceptible-Infected-Recovered (SIR) model, and introduce different approximate
maximum likelihood (AML) estimators of $R_0$. We carefully discuss the
properties of these estimators and illustrate by a Monte-Carlo study the width
of confidence intervals on $R_0$.
