Suppression of epidemic outbreaks with heavy-tailed contact dynamics

We study the epidemic spreading process following contact dynamics with heavy-tailed waiting time distributions. We show both analytically and numerically that the temporal heterogeneity of contact dynamics can significantly suppress the disease's transmissibility, hence the size of epidemic outbreak, obstructing the spreading process. Furthermore, when the temporal heterogeneity is strong enough, one obtains the vanishing transmissibility for any finite recovery time and regardless of the underlying structure of contacts, the condition of which was derived.