A stochastic model for the bacterial growth exhibiting staged growth, desynchronization, saturation and persistence

We consider a model of population growth based on the stochastic variation of the population size-controlled duplication of bacterial cells. It is shown that the proper choice of the control function allows for reproducing a variety of regimes: a logistic growth with saturation, a hindered growth typical for persistent bacterial systems, and a linear population growth detected for some mycobacterial populations. When supplied with the rectangular function having the width equal to the generation time, this approach represents the solution generalizing Rubinow's age-maturity model reproducing systems with desynchronization and saturation. The model's plausibility is confirmed by the direct comparison with real data for the growth of M. tuberculosis populations obtained with the BACTEC MGIT system under different conditions of growth synchronization.