Stochastics in Biological Systems

Stochastic Population and Epidemic Models

Persistence and Extinction

Authors: Allen, Linda S.

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  • Summarizes basic theory of branching processes for single-type and multi-type processes
  • Includes classic examples of population and epidemic models
  • MATLAB codes to simulate stochastic sample paths provided 
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  • ISBN 978-3-319-21554-9
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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.

About the authors

Linda J. S. Allen is a Professor in the Department of Mathematics and Statistics at Texas Tech University. Allen's primary research interest is mathematical modeling in biology. She formulates and analyzes deterministic and stochastic models in describing population, epidemic, viral and immune-system dynamics.

Reviews

“The readers will certainly appreciate the quality of a text written in a very clear way, well-organized and with high pedagogical standard. … Stochastic Population and Epidemic Models (Persistence and Extinction) is indeed a short, but complete, manual for the study of stochastic population and epidemic models indispensable for graduate students, for whom it was thought, but also accessible to many more audiences: professionals or simply curious on these subjects.” (Manuel Alberto M. Ferreira, Acta Scientiae et Intellectus, Vol. 3 (2), 2017)


Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $39.99
price for USA in USD
  • ISBN 978-3-319-21554-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts from 10 eBooks
Softcover $49.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Population and Epidemic Models
Book Subtitle
Persistence and Extinction
Authors
Series Title
Stochastics in Biological Systems
Series Volume
1.3
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-21554-9
DOI
10.1007/978-3-319-21554-9
Softcover ISBN
978-3-319-21553-2
Series ISSN
2364-2297
Edition Number
1
Number of Pages
X, 47
Number of Illustrations
12 illustrations in colour
Topics