Stochastic Population and Epidemic Models

Persistence and Extinction

  • Linda J. S.¬†Allen

Part of the Mathematical Biosciences Institute Lecture Series book series (MBILS, volume 1.3)

Also part of the Stochastics in Biological Systems book sub series (STOCHBS, volume 1.3)

Table of contents

  1. Front Matter
    Pages i-x
  2. Linda J. S. Allen
    Pages 13-20
  3. Linda J. S. Allen
    Pages 21-27
  4. Back Matter
    Pages 37-47

About this book


This monograph provides a summary of the basic theory of branching processes for single-type and multi-type processes. Classic examples of population and epidemic models illustrate the probability of population or epidemic extinction obtained from the theory of branching processes. The first chapter develops the branching process theory, while in the second chapter two applications to population and epidemic processes of single-type branching process theory are explored. The last two chapters present multi-type branching process applications to epidemic models, and then continuous-time and continuous-state branching processes with applications. In addition, several MATLAB programs for simulating stochastic sample paths  are provided in an Appendix.

These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA.

Professor Linda Allen is a Paul Whitfield Horn Professor of Mathematics in the Department of Mathematics and Statistics at Texas Tech University, USA.


Branching process Extinction Persistence Population models Stochastic models

Authors and affiliations

  • Linda J. S.¬†Allen
    • 1
  1. 1.Mathematics and StatisticsTexas Tech UniversityLubbockUSA

Bibliographic information

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