Spreading Dynamics Following Bursty Human Activity Patterns

TL;DR

This paper investigates how bursty human activity patterns with power-law waiting times influence spreading dynamics, revealing slow decay of infections and a relationship between activity and spreading exponents.

Contribution

It introduces a model linking individual bursty activity patterns to macroscopic spreading behavior, highlighting the impact of heterogeneity on epidemic decay rates.

Findings

Infection rate decays as a power law over time.

The spreading exponent relates to the waiting time distribution exponent.

Decay dynamics are insensitive to network topology.

Abstract

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.