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  • © 2011

Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model

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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
  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. Uniform Approximations for the SIS Model

    • Ingemar Nåsell
    Pages 155-170
  6. Thresholds for the SIS Model

    • Ingemar Nåsell
    Pages 171-175
  7. Concluding Comments

    • Ingemar Nåsell
    Pages 177-182
  8. Back Matter

    Pages 183-199

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.

Keywords

  • 60-J28; 92-D30
  • Birth-death processes
  • Extinction time
  • Logistic SIS model
  • Quasi-stationarity
  • Threshold results

Authors and Affiliations

  • Mathematics, Royal Institute of Technology, Stockholm, Sweden

    Ingemar Nåsell

Bibliographic Information

  • Book Title: Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model

  • Authors: Ingemar Nåsell

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-20530-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2011

  • Softcover ISBN: 978-3-642-20529-3Published: 06 July 2011

  • eBook ISBN: 978-3-642-20530-9Published: 06 July 2011

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XI, 199

  • Number of Illustrations: 10 illustrations in colour

  • Topics: Probability Theory, Life Sciences

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions