SIS Epidemic on Annealed Heterogeneous Networks
Vanishing threshold in scale-free networks via mean-field theory
ρ = 0.000 | β_c = — | β/μ = —
Annealed network approximation: links rewired each step; dynamics depend only on degree distribution P(k).
Mean-field theory gives ρ_k ≈ ρβk⟨k⟩/(μ + βk⟨k²⟩/⟨k⟩).
For scale-free networks with γ≤3, ⟨k²⟩→∞ → threshold β_c = μ⟨k⟩/⟨k²⟩ → 0.
For Poisson (ER) networks: β_c = μ/⟨k⟩ > 0.