SIR Epidemic — Heterogeneous Network

Scale-Free vs Random Network: Epidemic Threshold & Spreading Dynamics
β (infection)0.10
γ (recovery)0.05
Network
R₀ = — ⟨k⟩ = — ⟨k²⟩/⟨k⟩ = — Threshold β_c = — Final size = 0%
On heterogeneous (scale-free) networks, the epidemic threshold β_c = γ⟨k⟩/⟨k²⟩ → 0 as N→∞ (Pastor-Satorras & Vespignani 2001). Hubs (high-degree nodes) act as super-spreaders, enabling epidemic persistence at vanishingly small transmission rates. Random networks have a finite threshold β_c ≈ γ/⟨k⟩, making them more resilient.