Spreading Dynamics Following Human Activity Patterns

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.