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.