Degree-based mean field · epidemic threshold 1/⟨k²/k⟩
Epidemic Parameters
Network (BA scale-free)
R₀ = β⟨k²⟩/μ⟨k⟩: —
Threshold β_c: —
Infected: —
State: —
On scale-free networks (Barabási-Albert), the SIS epidemic threshold becomes β_c = μ⟨k⟩/⟨k²⟩. Since BA networks have ⟨k²⟩ → ∞ as N → ∞ (Pastor-Satorras & Vespignani 2001), β_c → 0: any non-zero infection rate sustains the epidemic. High-degree hubs act as super-spreaders and reservoirs. Green nodes = susceptible; Red = infected.