some time ago i met with researcher that wants to see if stem cells are generating new cells in their favorite system.

the data is collected by labeling certain cells and then counting them at number of time points.

literature search reveals that it is mostly modeled by a differential equation that is then fitted to data.

as someone raised in a stochastic simulation world i wonder why it is not modeled by a stochastic birth and death process. Has anyone compared the fit of these 2 approaches?