Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematical Biosciences Institute Lecture Series (MBILS, volume 1.3)
Part of the book sub series: Stochastics in Biological Systems (STOCHBS)
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Table of contents (4 chapters)
Keywords
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 theDepartment of Mathematics and Statistics at Texas Tech University, USA.
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Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Stochastic Population and Epidemic Models
Book Subtitle: Persistence and Extinction
Authors: Linda J. S. Allen
Series Title: Mathematical Biosciences Institute Lecture Series
DOI: https://doi.org/10.1007/978-3-319-21554-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2015
Softcover ISBN: 978-3-319-21553-2Published: 02 September 2015
eBook ISBN: 978-3-319-21554-9Published: 20 August 2015
Edition Number: 1
Number of Pages: X, 47
Number of Illustrations: 12 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Genetics and Population Dynamics, Theoretical Ecology/Statistics