Heterogeneous mean-field (Pastor-Satorras & Vespignani 2001): degree class k has its own infected fraction i_k(t). On scale-free networks (P(k) ∝ k⁻ᵞ), the epidemic threshold β_c = μ⟨k⟩/⟨k²⟩ → 0 as network size → ∞ (for γ ≤ 3): epidemics spread at arbitrarily small β!