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Durrett, Rick; Schmidt, Deena; Schweinsberg, Jason

A waiting time problem arising from the study of multi-stage carcinogenesis. (English) Zbl 1219.92038

Ann. Appl. Probab. 19, No. 2, 676-718 (2009).
The authors propose a mathematical model for cancer development. They consider a (cell) population of fixed size \(N\) and assume that the population evolves according to the Moran model, that is, each individual of the population lives an exponentially distributed time span with mean \(1\) and upon its death is replaced by a new individual, the parent of which is chosen uniformly at random among the \(N\) individuals. Each individual has a type \(j \in \{0,\dots,m\}\) and all individuals initially have type \(0\). Newborn individuals inherit their type from their parent. Additionally, during their life times, individuals of type \(j-1\) may mutate to type \(j\), \(j=1,\dots,m\). \(\tau_m\) is the first time there is an individual of type \(m\). The authors study the asymptotic distribution of \(\tau_m\) when \(m \geq 2\) as \(N \to \infty\) using a broad variety of different methods.
Reviewer: Matthias Meiners (Uppsala)

Cited in 1 Review
Cited in 22 Documents

MSC:

92C50 Medical applications (general)
60J85 Applications of branching processes
60J25 Continuous-time Markov processes on general state spaces

Keywords:

Moran model; waiting times; Wright-Fisher diffusion
PDFBibTeX XMLCite
\textit{R. Durrett} et al., Ann. Appl. Probab. 19, No. 2, 676--718 (2009; Zbl 1219.92038)
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References:

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