I have cell $A$ which will differentiate into either cells $A+B$ or cells $A+C$ with probability $p$ and $1-p$, respectively; and cell $C$, which will differentiate into cells $B+B$ or cells $C+C$ with probability $p$ and $1-p$; and the value of $p$ may change with time.
Can I more accurately explain these probabilistic cell lineages (with the aim of predicting an ultimate number of cells) using a deterministic (PDE/ODE) or stochastic model? What technique can be used to incorporate different probabilities at different steps of the lineage? Thank you for any advice.