SIR dynamics on contact networks with degree heterogeneity and super-spreaders
On heterogeneous contact networks, epidemic threshold R₀* = ⟨k⟩/⟨k²−k⟩ · β/γ. For scale-free networks (Barabási-Albert), ⟨k²⟩→∞ makes the threshold vanish — any R₀>0 causes epidemics (Pastor-Satorras & Vespignani 2001). Super-spreader nodes (high degree) transmit disproportionately; targeted vaccination of these nodes is far more efficient than random vaccination. Heterogeneity parameter controls degree variance from Poisson (homogeneous) to power-law (scale-free).