Decoding how higher-order network interactions shape contagion dynamics
István Z Kiss1,2, Christian Bick3,4,5,6, Péter L Simon7,8,9
1Network Science Institute, Northeastern University London, London, UK. istvan.kiss@nulondon.ac.uk.
Journal of Mathematical Biology
|August 19, 2025
Summary
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.
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.
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