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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.