SIS model · β_c = δ/λ_max(A) · random vs scale-free vs small-world networks
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β_c = δ / λ_max(A) Threshold from largest eigenvalue of adjacency matrix A.
Below threshold: epidemic dies Above threshold: endemic state R_eff = β·λ_max / δ
Scale-free networks (Barabási-Albert) have large λ_max → very low threshold. Small-world (Watts-Strogatz) has moderate λ_max. Random (Erdős-Rényi) threshold ≈ δ/k.