SIR on Heterogeneous Networks

Degree heterogeneity lowers the epidemic threshold

S: - I: - R: - R₀: - λc: -
Heterogeneous mean-field (Pastor-Satorras & Vespignani 2001): for scale-free networks with P(k)~k^−γ and γ≤3, the epidemic threshold λ_c = <k>/<k²> → 0 as N→∞. Hubs act as super-spreaders. R₀ = (λ/μ)·(<k²>/<k>). Try both network types and compare outbreak sizes.