In homogeneous populations, an epidemic spreads if R₀ = β/γ > 1. On heterogeneous networks, the threshold shifts: R₀_eff = β/γ · ⟨k²⟩/⟨k⟩. For scale-free networks with degree exponent γ_d < 3, ⟨k²⟩ diverges, making the threshold vanish — any pathogen can spread! Herd immunity requires vaccinating the highest-degree "super-spreaders" preferentially.