SIR Dynamics · Degree Variance · Outbreak Probability
On heterogeneous networks, the epidemic threshold is β_c = γ⟨k⟩/⟨k²⟩. In scale-free networks ⟨k²⟩ diverges, making β_c → 0 — epidemics always spread. High degree variance ("superspreaders") dramatically lowers the outbreak threshold compared to homogeneous mixing.