Before revision:  The obtained results turn out to be relevant for infectious diseases with low R_0 but high mortality rates such as Ebola or H1N1 influenza. This study highlights the importance of control measures that minimize the possibility of global contacts, warning that a small reduction of them could produce a drastic reduction in the probability of huge outbreaks .
After revision:  These features are otherwise already known to hold for the standard stochastic SIR model at its threshold, \alpha=1: (i) the probability of having an outbreak of size n goes asymptotically as n^{-3/2 .