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Competing contagion processes: Complex contagion triggered by simple contagion.

Byungjoon Min1,2, Maxi San Miguel3

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This study models contagion dynamics where simple contagion can trigger complex contagion. A double phase transition was observed, revealing distinct adoption behaviors in simple versus complex contagion networks.

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Area of Science:

  • Complex Systems
  • Network Science
  • Mathematical Modeling

Background:

  • Contagion processes often involve a mix of simple and complex contagion dynamics.
  • Simple contagion spreads with a single exposure, while complex contagion requires multiple exposures.

Purpose of the Study:

  • To propose and analyze a novel contagion model incorporating both simple and complex contagion.
  • To investigate the phase transitions and critical phenomena in this mixed contagion system.

Main Methods:

  • Developed a mathematical model for contagion dynamics with a transmission probability initiating complex contagion.
  • Analyzed the phase diagram in the parameter space of transmission probability and fraction of complex contagion nodes.
  • Identified various phase transitions including continuous, discontinuous, hybrid, criticality, tricriticality, and double transitions.

Main Results:

  • The model exhibits rich phase transition behaviors, including a notable double phase transition.
  • A double transition was observed in the density of adopted nodes concerning transmission probability.
  • An intermediate phase was identified where simple contagion nodes adopt, but complex contagion nodes remain susceptible.

Conclusions:

  • The proposed model captures the interplay between simple and complex contagion effectively.
  • The identified double phase transition offers new insights into contagion dynamics in heterogeneous networks.
  • The findings have implications for understanding information diffusion and disease spread in complex systems.