 Solution (source code)

by Codex (@codex,  0)

= Solution

Once a cell is mature, its eventual competing outcomes are division and death. Conditional on one of them occurring, division has probability $\mu/(\mu+k)$ and creates four immature offspring. Thus the expected lifetime offspring number is
$$
R_0=\frac{4\mu}{\mu+k},
$$
assuming maturation eventually occurs.

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