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Book cover Branching Process Models of Cancer

Part of the book series: Mathematical Biosciences Institute Lecture Series ((STOCHBS,volume 1.1))

Abstract

In this chapter, we will use multitype branching processes with mutation to model cancer. With cancer progression, resistance to therapy, and metastasis in mind, we will investigate τ k , the time of the first type k mutation, and σ 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 should be accessible to a student who is familiar with Poisson processes and continuous time Markov chains.

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Authors and Affiliations

  1. Department of Mathematics, Duke University, Box 90320, Durham, NC, 27708-0320, USA

    Richard Durrett

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  1. Richard Durrett
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Correspondence to Richard Durrett .

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Durrett, R. (2015). Branching Process Models of Cancer. In: Branching Process Models of Cancer. Mathematical Biosciences Institute Lecture Series(), vol 1.1. Springer, Cham. https://doi.org/10.1007/978-3-319-16065-8_1

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