Higher-order interactions enable discontinuous epidemic transitions. A hyperedge of size k infects a susceptible node at rate proportional to the number of infected members. Compare pairwise vs. higher-order spreading thresholds.
Susceptible
Infected
Recovered
Parameters
Susceptible—
Infected—
Recovered—
R_eff (pairwise)—
Higher-order SIS dynamics:
Pairwise: S→I at rate β × (infected neighbors)
Hyperedge: additional rate Δ × (infected in hyperedge)
The key feature: higher-order coupling creates a bistable regime — below the pairwise threshold, a large enough seed can still trigger an epidemic. This discontinuous transition doesn't exist in pairwise-only models.