Pair Approximation — SIS Epidemics on Networks

Mean-field SIS assumes homogeneous mixing; pair approximation tracks [SI] correlations via the closure [ABC]≈[AB][BC]/[B], capturing network heterogeneity. Compare MF (dashed), PA (solid), and stochastic simulations on a random k-regular graph.

Stochastic

Pair Approx

Mean Field

Transmission rate β: 0.3 Recovery rate γ: 0.1 Degree k: 6 N nodes: 500

R₀ (MF): —

R₀ (PA): —

Endemic I* (MF): —

Endemic I* (PA): —

PA closure: [SSI]≈(k-1)/k · [SS][SI]/[S]

Phase diagram: endemic I* vs β/γ