Extinction and quasi-stationarity in the stochastic logistic SIS model
By: Ingemar Nåsell
Series: Lecture notes in mathematics -- 2022; Mathematical biosciences subseries; Lecture notes in mathematics (Springer-Verlag); Lecture notes in mathematics (Springer-Verlag) -- 2022.
Publisher: Springer Verlag
Published: 2011
Place of publication: Heidelberg; New York
Language: eng
Number of pages: 199
ISBN-13: 9783642205293; 9783642205309
Subjects: Population biology; Mathematical models; Stochastic models; Relicts (Biology); Biomathematics
Description: "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.
Notes: Includes bibliographical references (p. 195-198) and index.

Also available online.
Table of contents: title: Introduction; title: Model formulation; title: Stochastic process background; title: The SIS model: first approximations of the quasi-stationary distribution; title: Some approximations involving the normal distribution; title: Preparations for the study of the stationary distribution p¹ of the SIS model; title: Approximation of the stationary distribution p¹ of the SIS model; title: Preparations of the stationary distribution p⁰ of the SIS model; title: Approximation of the stationary distribution of p⁰ of the SIS model; title: Approximation of some images under [psi] for the SIS model; title: Approximation of the quasi-stationary distribution q of the SIS model; title: Approximation of the time to extinction for the SIS model; title: Uniform approximations for the SIS model; title: Thresholds for the SIS model; title: Concluding comments; title: Notation; title: A maple module for numerical evaluations.