Branching Process Models of Cancer by Richard DurrettBranching Process Models of Cancer by Richard Durrett

Branching Process Models of Cancer

byRichard Durrett

Paperback | July 6, 2015

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These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA. In this contribution the author uses multitype branching processes with mutation to model cancer. With cancer progression, resistance to therapy, the time of the first type $k$ mutation, and $\sigma_k$, the time of the first type $k$ mutation that founds a family line that does not die out, as well as the growth of the number of type $k$ cells. The last three sections apply these results to metastasis, ovarian cancer, and tumor heterogeneity. Even though martingales and stable laws are mentioned, these notes with examples and applications should be accessible to students and researchers who are familiar with Poisson processes and continuous time Markov chains.

Richard Durrett is Professor of Mathematics 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.

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.
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Title:Branching Process Models of CancerFormat:PaperbackDimensions:63 pages, 23.5 × 15.5 × 0.01 inPublished:July 6, 2015Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319160648

ISBN - 13:9783319160641

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Table of Contents

Multistage Theory of Cancer.- Mathematical Overview.- Branching Process Results.- Time forZ_0 to Reach SizeM.- Time Until the First Type 1.- Mutation Before Detection?.- Accumulation of Neutral Mutations.- Properties of the Gamma Function.- Growth ofZ_1(t).- Movements ofZ_1(t).- Luria-Delbruck Distributions.- Number of Type 1's at TimeT_M.- Gwoth ofZ_k(t).- Transitions Between Waves.- Time to the First Type \tau_k, k \ge 2.- Application: Metastasis.- Application: Ovarian Cancer.- Application: Intratumor Heterogeneity.