Contact Process SIS

The contact process (SIS model) on a square lattice. Each infected cell recovers at rate δ. Each susceptible cell adjacent to an infected neighbor gets infected at rate λ per infected neighbor. The critical point λ_c/δ ≈ 1.65 (on the square lattice) separates extinction from an active endemic phase. Near the critical point, clusters are fractal and fluctuations are large — directed percolation universality class.