Complex Contagion — Synergistic Spreading

Threshold model vs. simple contagion · Hyperedge infection · Abrupt transitions

Pairwise β₁0.10

Synergy β₂ (2-body)0.30

Recovery δ0.10

Network 6

Threshold θ2

Complex contagion: infection requires multiple simultaneous contacts (threshold θ). Synergistic term: rate = β₁·I_neighbors + β₂·(I_pairs among neighbors). Creates discontinuous (explosive) transitions absent in simple SIS. Bistability region: both endemic and disease-free states are stable.