Overview
- The first volume published in the new series Mathematical Biosciences Institute
- Concise and easy to understand for graduate students familiar with Poisson processes and continuous time Markov chains
- Includes examples and theorems throughout
Part of the book series: Mathematical Biosciences Institute Lecture Series (MBILS, volume 1.1)
Part of the book sub series: Stochastics in Biological Systems (STOCHBS)
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About this book
This volume develops results on continuous time branching processes and applies them to study rate of tumor growth, extending classic work on the Luria-Delbruck distribution. As a consequence, the author calculate the probability that mutations that confer resistance to treatment are present at detection and quantify the extent of tumor heterogeneity. As applications, the author evaluate ovarian cancer screening strategies and give rigorous proofs for results of Heano and Michor concerning tumor metastasis. These notes should be accessible to students who are familiar with Poisson processes and continuous time Markov chains.
Richard Durrett is a mathematics professor at Duke University, USA. He is the author of 8 books, over 200 journal articles, and has supervised more than 40 Ph.D students. Most of his current research concerns the applications of probability to biology: ecology, genetics and most recently cancer.
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Table of contents (1 chapter)
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Front Matter
Reviews
“It provides a survey of cancer modeling using multitype branching processes. … the text should be accessible for graduate students in mathematics and biology who are familiar with Poisson processes and continuous-time Markov chains.” (Matthias Meiners, zbMATH 1328.92004, 2016)
Authors and Affiliations
About the author
Richard Durrett is mathematics professor at Duke University, USA. He is the author of 8 books, over 200 journal articles and has supervised more than 40 Ph.D. students. Most of his current research concerns the applications of probability to biology: ecology, genetics, and most recently cancer.
Bibliographic Information
Book Title: Branching Process Models of Cancer
Authors: Richard Durrett
Series Title: Mathematical Biosciences Institute Lecture Series
DOI: https://doi.org/10.1007/978-3-319-16065-8
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: 978-3-319-16064-1Published: 06 July 2015
eBook ISBN: 978-3-319-16065-8Published: 20 June 2015
Edition Number: 1
Number of Pages: VII, 63
Number of Illustrations: 4 b/w illustrations, 2 illustrations in colour
Additional Information: Copublished with the Mathematical Biosciences Institute
Topics: Probability Theory and Stochastic Processes, Mathematical and Computational Biology, Cancer Research