The quasi-stationary distribution of the closed endemic sis model

The quasi-stationary distribution of the closed stochastic SIS model changes drastically as the basic reproduction ratio R 0 passes the deterministic threshold value 1. Approximations are derived that describe these changes. The quasi-stationary distribution is approximated by a geometric distribution (discrete!) for R 0 distinctly below 1 and by a normal distribution (continuous!) for R 0 distinctly above 1. Uniformity of the approximation with respect to R 0 allows one to study the transition between these two extreme distributions. We also study the time to extinction and the invasion and persistence thresholds of the model.