  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 underlying
structure of contacts, the condition of which was derived.
