A probabilistic model for the dynamics of a structured population of unicellular organisms

The importance of stochastic modeling of a structured population of unicellular organisms has been well recognized. In the present study, a stochastic model is proposed to characterize the dynamics of growth and reproduction of such unicellular organisms, e.g., yeast and bacteria, in a batch or continuous flow bioreactor. The model gives rise to the differential equations for the probability distribution of the numbers of cells in various states, the mean and variance in each state, and the covariance between any pair of states. The mean, variance, and covariance of the number of cells were determined by Monte Carlo simulation as well as by solving the differential equations of the model. The two sets of results are in good agreement.