Pair Approximation (Keeling 1999, Eames & Keeling 2002):
Standard mean-field SIS assumes random mixing: dI/dt = βkSI − γI. This ignores network correlations.
Pair approximation tracks pairs [SS], [SI], [II] with closure [ABC] ≈ (n−1)/n · [AB][BC]/[B],
corrected for clustering (φ). This captures the key effect: infected nodes tend to be surrounded by
infected neighbours (correlation buildup), reducing effective transmission below mean-field. The epidemic
threshold R₀ = βk/γ is shifted: pair approximation gives a higher threshold, especially for clustered networks.
Clustering inhibits spread because SI pairs become surrounded by II pairs (wasted transmission attempts).