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Epidemics on hypergraphs: spectral thresholds for extinction
Desmond J Higham1, Henry-Louis de Kergorlay1
1School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, UK.
Proceedings. Mathematical, Physical, and Engineering Sciences
|February 14, 2022
Summary
This study introduces hypergraph models for epidemic spreading, moving beyond simple contact graphs to include group interactions. These models offer better insights into disease transmission and intervention effectiveness.
Area of Science:
- Epidemiology
- Network Science
- Mathematical Biology
Background:
- Traditional epidemic models use contact graphs, simplifying human interactions to pairwise relationships.
- Real-world human interactions occur in groups, necessitating more complex modeling approaches.
- Higher-order interactions are crucial for understanding disease propagation dynamics.
Purpose of the Study:
- To develop and analyze contagion models on hypergraphs to better represent group interactions.
- To derive spectral conditions for disease vanishing in hypergraph epidemic models.
- To differentiate pathogen-inherent infectiousness from behavior-driven transmission.
Main Methods:
- Utilizing hyperedges to model higher-order interactions and group dynamics.
- Developing stochastic susceptible-infected-susceptible (SIS) models on hypergraphs.
- Employing deterministic mean-field ordinary differential equation (ODE) approximations.
- Deriving spectral conditions for disease eradication.
Main Results:
- Spectral conditions are derived to characterize disease extinction in hypergraph models.
- The hypergraph approach allows for nonlinear dependence of infection rates on group size and infectious neighbors.
- Numerical simulations validate the theoretical analysis.
Conclusions:
- Hypergraph models provide a more realistic framework for epidemic dynamics than traditional graph models.
- This framework can distinguish between pathogen characteristics and behavioral factors influencing spread.
- The model enhances the potential for accurately quantifying the impact of public health interventions.
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