1 results
A spatial mutation model with increasing mutation rates
- Part of
-
- Journal:
- Journal of Applied Probability / Volume 60 / Issue 4 / December 2023
- Published online by Cambridge University Press:
- 03 April 2023, pp. 1157-1180
- Print publication:
- December 2023
-
- Article
-
- You have access
- HTML
- Export citation
-
We consider a spatial model of cancer in which cells are points on the d-dimensional torus
$\mathcal{T}=[0,L]^d$, and each cell with 
$k-1$ mutations acquires a kth mutation at rate 
$\mu_k$. We assume that the mutation rates 
$\mu_k$ are increasing, and we find the asymptotic waiting time for the first cell to acquire k mutations as the torus volume tends to infinity. This paper generalizes results on waiting for 
$k\geq 3$ mutations in Foo et al. (2020), which considered the case in which all of the mutation rates 
$\mu_k$ are the same. In addition, we find the limiting distribution of the spatial distances between mutations for certain values of the mutation rates.
