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Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model

  • Book
  • © 2011

Overview

Authors:
  1. Ingemar Nåsell

    1. Mathematics, Royal Institute of Technology, Stockholm, Sweden

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 2022)

Part of the book sub series: Mathematical Biosciences Subseries (LNMBIOS)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    • Ingemar Nåsell
    Pages 1-7

  3. Model Formulation

    • Ingemar Nåsell
    Pages 9-16

  4. Stochastic Process Background

    • Ingemar Nåsell
    Pages 17-40

  5. The SIS Model: First Approximations of the Quasi-stationary Distribution

    • Ingemar Nåsell
    Pages 41-46

  6. Some Approximations Involving the Normal Distribution

    • Ingemar Nåsell
    Pages 47-72

  7. Preparations for the Study of the Stationary Distribution p(1) of the SIS Model

    • Ingemar Nåsell
    Pages 73-91

  8. Approximation of the Stationary Distribution p(1) of the SIS Model

    • Ingemar Nåsell
    Pages 93-99

  9. Preparations for the Study of the Stationary Distribution p(0) of the SIS Model

    • Ingemar Nåsell
    Pages 101-113

  10. Approximation of the Stationary Distribution p(0) of the SIS Model

    • Ingemar Nåsell
    Pages 115-118

  11. Approximation of Some Images Under Ψ for the SIS Model

    • Ingemar Nåsell
    Pages 119-139

  12. Approximation of the Quasi-stationary Distribution q of the SIS Model

    • Ingemar Nåsell
    Pages 141-147

  13. Approximation of the Time to Extinction for the SIS Model

    • Ingemar Nåsell
    Pages 149-154

  14. Uniform Approximations for the SIS Model

    • Ingemar Nåsell
    Pages 155-170

  15. Thresholds for the SIS Model

    • Ingemar Nåsell
    Pages 171-175

  16. Concluding Comments

    • Ingemar Nåsell
    Pages 177-182

  17. Back Matter

    Pages 183-199
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Keywords

About this book

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.

Authors and Affiliations

  • Mathematics, Royal Institute of Technology, Stockholm, Sweden

    Ingemar Nåsell

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