Heterogeneous Mean Field (Pastor-Satorras 2001)
ρ̇_k = -γρ_k + β·k·(1-ρ_k)·Θ
Θ = Σ_k k·P(k)·ρ_k / ⟨k⟩
Threshold: β/γ > ⟨k⟩/⟨k²⟩
Scale-free (γ≤3): ⟨k²⟩→∞ → no threshold!
R₀ = β·⟨k²⟩/(γ·⟨k⟩)
On scale-free networks (P(k)~k^-γ with γ≤3), the second moment ⟨k²⟩ diverges, making R₀ = β⟨k²⟩/(γ⟨k⟩) → ∞. This means any nonzero transmission rate causes an epidemic — hubs act as superspreaders. Targeted vaccination of high-degree nodes is far more effective than random vaccination.