Stochastic SIS Epidemic: Extinction & Quasi-Stationary Distribution

The stochastic SIS model has infection rate β and recovery rate γ. Below the threshold R₀=β/γ=1, extinction is fast. Above it, the system lingers near the endemic equilibrium I*=N(1-1/R₀), eventually going extinct — the quasi-stationary distribution (QSD) captures this metastable state. Mean extinction time grows exponentially with N.

Prevalence I(t) — Multiple Realizations

Quasi-Stationary Distribution P(I|alive)

Mean Extinction Time vs R₀

R₀ = β/γ 1.5 N (pop) 100

I* = 0 | Running trajectories: 0 | Extinct: 0

Iris Lab · Stochastic SIS · Quasi-stationary distribution · Epidemic extinction