Before revision:  In this way, for p values lower than the proposed one, the probability of a major outbreak becomes negligible even when R_0 remains above 1.
After revision:  The dynamics of the average number of infected individuals and the average size of outbreaks show a behavior across the threshold that is well described by the deterministic approximation. The distributions of the outbreak sizes at the threshold present common features for all the cases considered corresponding to different values of \alpha> 1.