Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model

• Main Author: Nåsell, Ingemar (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011.
• Series: Lecture Notes in Mathematics, 2022
• Subjects: Mathematics.; Life sciences.; Probabilities.; Probability Theory and Stochastic Processes.; Life Sciences, general.

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. The approximations are derived separately in three different parameter regions, and then comb...

Table of Contents:

• 1 Introduction
• 2 Model Formulation
• 3 A Birth-Death Process with Finite State Space and with an Absorbing State at the Origin
• 4 The SIS Model: First Approximations of the Quasi-Stationary Distribution
• 5 Some Approximations Involving the Normal Distribution
• 6 Preparations for the Study of the Stationary Distribution p(1) of the SIS Model
• 7 Approximation of the Stationary Distribution p(1) of the SIS Model
• 8 Preparations for the Study of the Stationary Distribution p(0) of the SIS Model
• 9 Approximation of the Stationary Distribution p(0) of the SIS Model
• 10 Approximation of Some Images UnderY for the SIS Model
• 11 Approximation of the Quasi-Stationary Distribution q of the SIS Model
• 12 Approximation of the Time to Extinction for the SIS Model
• 13 Uniform Approximations for the SIS Model
• 14 Thresholds for the SIS Model
• 15 Concluding Comments.