Population growth: Stochastic treatment in compartments

The growth of microbial cultures is studied by means of stochastic processes. A compartment structure is used to take into account cell maturation stages, having an inflow of cells from one compartment to the next. Dilution and cell division are also considered. A differential equation, first proposed by Kiefer, is studied and the expected number of cells in each compartment is found for several interesting cases.