Modeling Bacterial Population Growth from

9 Few bacterial cells may be sufficient to produce a food-borne illness outbreak, provided that 10 they are capable of adapting and proliferating on a food matrix. This is why any quantitative 11 health risk assessment policy must incorporate methods to accurately predict the growth of 12 bacterial populations from a small number of pathogens. In this aim, mathematical models 13 have become a powerful tool. Unfortunately, at low cell concentrations, standard determin14 istic models fail to predict the fate of the population, essentially because the heterogeneity 15 between individuals becomes relevant. 16 In this contribution a stochastic differential equation (SDE) model is proposed to describe 17 variability within single cell growth and division and to simulate population growth from a 18 given initial number of individuals. 19 We provide evidence of the model ability to explain the observed distributions of times to 20 division, including the lag-time produced by the adaptation to the environment, by com21 paring model predictions with experiments from the literature for Escherichia coli, Listeria 22 innocua and Salmonella enterica. The model is shown to accurately predict experimental 23 growth population dynamics both for small and large microbial populations. 24 ∗Author to whom correspondence should be addressed. E-mail: [email protected] 1 The use of stochastic models for the estimation of parameters to successfully fit experimental 1 data is a particularly challenging problem. For instance if Monte Carlo methods are employed 2 to model the required distributions of times to division, the parameter estimation problem 3 can become numerically intractable. We overcome this limitation by converting the stochastic 4 description to a partial differential equation (backward Kolmogorov) instead, which relates 5 to the distribution of division times. 6 Contrary to previous stochastic formulations based on random parameters, the present model 7 is capable of explaining the variability observed in populations that result from the growth of 8 a few number of initial cells as well as the lack of it when compared to populations initiated 9 by a larger number of individuals, where the random effects become negligible. 10