  We study the susceptible-infected model with power-law waiting time
distributions $P(\tau)\sim \tau^{-\alpha}$, as a model of spreading dynamics
under heterogeneous human activity patterns. We found that the average number
of new infections $n(t)$ at time $t$ decays as a power law in the long time
limit, $n(t) \sim t^{-\beta}$, leading to extremely slow revalence decay.We
also found that the exponent in the spreading dynamics, $\beta$, is related to
that in the waiting time distribution, $\alpha$, in a way depending on the
interactions between agents but is insensitive to the network topology. These
observations are well supported by both the theoretical predictions and the
long prevalence decay time in real social spreading phenomena. Our results
unify individual activity patterns with macroscopic collective dynamics at the
network level.
