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The effect of heterogeneity on hypergraph contagion models.
Nicholas W Landry1, Juan G Restrepo1
1Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309, USA.
Chaos (Woodbury, N.Y.)
|November 3, 2020
Summary
Higher-order interactions in hypergraphs can lead to explosive transitions in contagion processes. Heterogeneity in link distribution can suppress these explosive transitions, impacting epidemic spreading and opinion dynamics.
Area of Science:
- Complex Systems
- Network Science
- Epidemiology
Background:
- Social contagion processes, like epidemic spreading and opinion formation, are influenced by node interactions.
- Higher-order interactions in networks can significantly alter contagion dynamics, causing phenomena like bistability and explosive transitions.
Purpose of the Study:
- To analyze the susceptible-infected-susceptible (SIS) model on hypergraphs using a hyperdegree-based mean-field approach.
- To investigate how higher-order interactions, specifically links and triangles, affect contagion dynamics.
- To explore mechanisms for suppressing explosive transitions in these complex network structures.
Main Methods:
- Developed a hyperdegree-based mean-field model for contagion dynamics on hypergraphs.
- Applied the model to a hypergraph with both pairwise (links) and three-way (triangles) interactions.
- Investigated various hypergraph structures and contagion/healing mechanisms.
- Verified model predictions using microscopic simulations and analytical derivations.
Main Results:
- Explosive transitions in contagion processes can be suppressed by heterogeneity in the link degree distribution.
- Suppression of explosive transitions is observed when links and triangles are independently chosen or positively correlated.
- Results were consistent between the mean-field model and microscopic simulations.
Conclusions:
- The structural organization of higher-order interactions in hypergraphs critically influences contagion processes.
- Heterogeneity in network structure offers a mechanism to control or mitigate explosive transitions in epidemic spreading and opinion dynamics.
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