Stochastic SIS model showing extinction threshold. Below R₀=1 epidemics always go extinct. Above R₀=1, quasi-stationary state persists for exponentially long times. Watch the transition and mean extinction times.
Stochastic SIS: infection rate β, recovery γ. R₀=β/γ is the basic reproduction number. Deterministic threshold: I*=N(1-1/R₀) for R₀>1. Stochastic: mean extinction time T_ext ∝ exp(N·f(R₀)) — exponential in N (Weiss-Dishon 1971). Near criticality R₀≈1, epidemic size distribution is power-law (1/f² tail). The extinction event is a rare fluctuation in the quasi-stationary state.