Epidemic Pair Approximation
Beyond mean-field: tracking SI, SS, II pair correlations
Pair approximation (Keeling 1999) tracks [SI], [II], [SS] pair densities alongside [S],[I],[R]. The closure [SSI] ≈ (n−1)/n · [SS][SI]/[S] corrects for local clustering, giving a threshold R₀* = β(n−1)/(γn) that exceeds the mean-field R₀ = β/γ. Three curves shown: mean-field (dashed), pair-approx (solid), and stochastic agent simulation (dots).