Contact Process & Epidemic Threshold

Sites on a 2D lattice become infected at rate λ per infected neighbor and recover at rate 1. Critical threshold λ_c ≈ 1.6488 (1D), ≈ 1.65 (2D square). Directed percolation universality class.

Controls

Sub-critical
Directed Percolation

λ < λ_c → absorbing state (extinction)
λ > λ_c → active phase (endemic)

Critical exponents (DP class):
β ≈ 0.583, ν⊥ ≈ 0.734, z ≈ 1.76

Mean-field: λ_c = 1 (z-regular lattice where z=4 neighbors → λ_c ≈ 1.65)