Exact solution of a two-type branching process: Models of tumor progression

Details Exact solution of a two-type branching process: Models of tumor progression Exact solution of a two-type branching process: Models of tumor progression

2011-05-05

arxiv.org/abs/1105.1157v1

J. Stat. Mech. (2011) P08018

Biology

Quantitative Biology

Populations and Evolution

11 pages, 3 figures

Scientific paper

10.1088/1742-5468/2011/08/P08018

An explicit solution for a general two-type birth-death branching process with one way mutation is presented. This continuous time process mimics the evolution of resistance to treatment, or the onset of an extra driver mutation during tumor progression. We obtain the exact generating function of the process at arbitrary times, and derive various large time scaling limits. In the simultaneous small mutation rate and large time scaling limit, the distribution of the mutant cells develops some atypical properties, including a power law tail and diverging average.

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