Table of Contents

Introduction.
Model formulation.
Stochastic process background.
The SIS model: first approximations of the quasi-stationary distribution.
Some approximations involving the normal distribution.
Preparations for the study of the stationary distribution p¹ of the SIS model.
Approximation of the stationary distribution p¹ of the SIS model.
Preparations of the stationary distribution p⁰ of the SIS model.
Approximation of the stationary distribution of p⁰ of the SIS model.
Approximation of some images under [psi] for the SIS model.
Approximation of the quasi-stationary distribution q of the SIS model.
Approximation of the time to extinction for the SIS model.
Uniform approximations for the SIS model.
Thresholds for the SIS model.
Concluding comments.
Notation.
A maple module for numerical evaluations. "This volume presents explicit approximations of the quasi-stationary distribution and of the expected time to extinction from the state one and from quasi-stationarity for the stochastic logistic SIS model. Qualitatively different approximations are derived separately in three different parameter region, and then combined into a uniform approximation across all three regions. Subsequently, the results are used to derive thresholds as functions of the population size N."--P. [4] of cover.