Superspreader Epidemic
Heterogeneous Network SIR — Degree Distribution & Herd Immunity
Network
Nodes N:
120
Mean degree ⟨k⟩:
4.0
Degree heterogeneity γ:
2.5
Rebuild Network
Epidemic Parameters
Transmission β:
0.15
Recovery γ:
0.10
Vaccination coverage v:
0%
Seed Epidemic
Statistics
R₀ (mean-field)
—
R₀ (network)
—
Herd immunity
—
Infected (peak)
—
Total attacked
—
Superspreaders
—
Theory
Heterogeneous mean-field:
R₀ = β/γ · ⟨k²⟩/⟨k⟩
Scale-free (power-law):
P(k) ~ k⁻ᵞ
⟨k²⟩ diverges for γ ≤ 3
→ R₀ → ∞, epidemic always spreads
Superspreaders: hubs (high-k nodes) disproportionately responsible for spread.