Contact Process / SIS Epidemic

Infected sites infect neighbors at rate λ, recover at rate 1. Phase transition at λ_c ≈ 1.65 (directed percolation universality class). Below λ_c: extinction; above: survival.

Parameters

1.65
λ_c ≈ 1.648 (directed percolation)

State

Active fraction ρ—
Time steps0
Phase—

Speed

5

Active fraction ρ(t)

Green = infected, Dark = susceptible
Near λ_c: power-law relaxation ρ~t^{-δ}
Below λ_c: exponential extinction
Critical exponents: β≈0.276, δ≈0.159