Epidemic Superspreaders
SIR dynamics on heterogeneous networks — the k² effect
Superspreaders arise in heterogeneous networks where degree k varies widely.
The epidemic threshold on a network with degree distribution P(k) is:
R₀ = β/γ · ⟨k²⟩/⟨k⟩
For scale-free networks (P(k) ~ k⁻γ with γ≤3), ⟨k²⟩ → ∞, so the epidemic threshold vanishes — any β>0 causes an outbreak.
Hubs (high-degree superspreaders) both get infected early and spread disease to many contacts.
Targeted vaccination of hubs is far more efficient than random vaccination.