Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model

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 combined into a uniform approximation across all three regions. Subsequently, the results are used to derive thresholds as functions of the population size N.

List 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.

Summary

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 combined into a uniform approximation across all three regions. Subsequently, the results are used to derive thresholds as functions of the population size N.

Product details

• Authors: Ingemar Nasell, Ingemar Nåsell
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 31.07.2011
• EAN: 9783642205293
• ISBN: 978-3-642-20529-3
• No. of pages: 199
• Dimensions: 157 mm x 235 mm x 13 mm
• Weight: 375 g
• Illustrations: XI, 199 p. 10 illus. in color.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics / Mathematical Biosciences Subseries; Mathematical Biosciences Subseries; Lecture Notes in Mathematics; Mathematical Biosciences Subseries
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; B, Biowissenschaften, allgemein, Life Sciences, Mathematics and Statistics, Life sciences: general issues, Probability Theory and Stochastic Processes, Probabilities, Stochastics, Probability Theory, Life Sciences, general