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Decoding how higher-order network interactions shape contagion dynamics.

István Z Kiss1,2, Christian Bick3,4,5,6, Péter L Simon7,8,9

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Complex contagion models on higher-order structures can be unified using a generalized mean-field approach. This framework reveals how network complexity and interaction types influence disease spread dynamics and model behaviors.

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Area of Science:

  • Mathematical modeling
  • Epidemiology
  • Network science

Background:

  • Complex contagion models analyze disease spread on intricate network structures beyond simple pairs.
  • Mean-field models simplify complex systems by averaging interactions, but their application to higher-order structures is evolving.
  • Existing models often yield similar differential equation forms and bifurcation patterns, suggesting a unifying principle.

Purpose of the Study:

  • To develop a generalized mean-field model unifying diverse complex contagion models.
  • To derive analytical conditions for different bifurcation regimes in models with increasing complexity.
  • To elucidate the relationship between model structure and emergent behaviors in contagion dynamics.

Main Methods:

  • Formulation of a generalized mean-field model for higher-order contagion.
  • Derivation of analytical conditions for bifurcation analysis.
  • Investigation of models with three-body, four-body, and two-population interactions.

Main Results:

  • Complete characterization of outcomes for three- and four-body interaction models.
  • Demonstration of multistability in a two-population model with only three-body interactions.
  • Identification of specific conditions for transcritical transitions, bistability, and multistability based on interaction types and network parameters.

Conclusions:

  • The generalized mean-field model provides a unified framework for analyzing complex contagion dynamics.
  • Model behavior, including multistability, is strongly dependent on interaction order and population structure.
  • Network and dynamic properties critically influence contagion outcomes, with implications for understanding disease spread mechanisms.