β=0.15 γ=0.10
R₀≈-
Herd immunity: -
About: On heterogeneous networks with power-law degree distributions P(k)∝k^(-γ), hubs (high-degree nodes) dramatically lower the epidemic threshold. The effective R₀ = β/γ · ⟨k²⟩/⟨k⟩ can be much larger than the homogeneous estimate. Scale-free networks (γ≤3) have ⟨k²⟩→∞ and thus vanishing epidemic threshold — any infection spreads. Herd immunity threshold p_c = 1 - 1/R₀ requires vaccinating high-degree hubs preferentially.