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Spreading dynamics following bursty human activity patterns.

Byungjoon Min1, K-I Goh, Alexei Vazquez

  • 1Department of Physics, Korea University, Seoul 136-713, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 27, 2011
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Summary
This summary is machine-generated.

This study models disease spread using power-law waiting times, revealing slow prevalence decay due to heterogeneous human activity. Spreading dynamics are linked to activity patterns, not network structure, unifying individual behavior and collective dynamics.

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Area of Science:

  • Epidemiology
  • Network Science
  • Statistical Physics

Background:

  • Understanding disease spread dynamics is crucial.
  • Heterogeneous human activity patterns significantly influence spreading phenomena.
  • Power-law waiting time distributions model complex waiting behaviors.

Purpose of the Study:

  • To investigate the susceptible-infected model with power-law waiting time distributions.
  • To analyze the impact of heterogeneous human activity on disease prevalence decay.
  • To establish the relationship between spreading dynamics and waiting time distributions.

Main Methods:

  • Utilized the susceptible-infected (SI) model.
  • Incorporated power-law waiting time distributions (P(τ)~τ^{-α}).
  • Analyzed long-time limit behavior of new infections n(t)~t^{-β}.

Main Results:

  • Identified extremely slow prevalence decay governed by a power law (n(t)~t^{-β}).
  • Established a relationship between the spreading exponent (β) and the waiting time exponent (α).
  • Demonstrated that this relationship is dependent on agent interactions but independent of network topology.

Conclusions:

  • Individual activity patterns directly influence macroscopic collective dynamics in spreading phenomena.
  • The findings unify individual behavior with network-level emergent properties.
  • The model provides a theoretical basis for observed long prevalence decay times in real-world social spreading.