Epidemic Threshold on Heterogeneous Networks

SIS model: λ_c = ⟨k⟩/⟨k²⟩ → 0 for scale-free networks (Pastor-Satorras 2001)

R₀ = 0 | Infected: 0
On scale-free networks with degree distribution P(k) ~ k^(-γ), the second moment ⟨k²⟩ diverges, making the epidemic threshold λ_c = ⟨k⟩/⟨k²⟩ → 0. Epidemics can spread at arbitrarily low infection rates (Pastor-Satorras & Vespignani, 2001). Hubs act as super-spreaders, maintaining endemic infection even with very low β/γ.