A stochastic approach for integrating strain variability in modeling Salmonella enterica growth as a function of pH and water activity Alexandra Lianou, Konstantinos P. Koutsoumanis ⁎ Laboratory of Food Microbiology and Hygiene, Department of Food Science and Technology, School of Agriculture, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece abstract article info Article history: Received 16 February 2011 Received in revised form 8 June 2011 Accepted 3 July 2011 Available online 13 July 2011 Keywords: Salmonella enterica Strain variability Stochastic growth model Strain variability of the growth behavior of foodborne pathogens has been acknowledged as an important issue in food safety management. A stochastic model providing predictions of the maximum specific growth rate (μ max ) of Salmonella enterica as a function of pH and water activity (a w ) and integrating intra-species variability data was developed. For this purpose, growth kinetic data of 60 S. enterica isolates, generated during monitoring of growth in tryptone soy broth of different pH (4.0–7.0) and a w (0.964–0.992) values, were used. The effects of the environmental parameters on μ max were modeled for each tested S. enterica strain using cardinal type and gamma concept models for pH and a w , respectively. A multiplicative without interaction-type model, combining the models for pH and a w , was used to describe the combined effect of these two environmental parameters on μ max . The strain variability of the growth behavior of S. enterica was incorporated in the modeling procedure by using the cumulative probability distributions of the values of pH min , pH opt and a wmin as inputs to the growth model. The cumulative probability distribution of the observed μ max values corresponding to growth at pH 7.0–a w 0.992 was introduced in the place of the model's parameter μ opt . The introduction of the above distributions into the growth model resulted, using Monte Carlo simulation, in a stochastic model with its predictions being distributions of μ max values characterizing the strain variability. The developed model was further validated using independent growth kinetic data (μ max values) generated for the 60 strains of the pathogen at pH 5.0–a w 0.977, and exhibited a satisfactory performance. The mean, standard deviation, and the 5th and 95th percentiles of the predicted μ max distribution were 0.83, 0.08, and 0.69 and 0.96 h -1 , respectively, while the corresponding values of the observed distribution were 0.73, 0.09, and 0.61 and 0.85 h -1 . The stochastic modeling approach developed in this study can be useful in describing and integrating the strain variability of S. enterica growth kinetic behavior in quantitative microbiology and microbial risk assessment. © 2011 Elsevier B.V. All rights reserved. 1. Introduction Quantitative microbiology, employing mathematical models that predict microbial behavior (growth or survival/inactivation), allows for the evaluation of microbial food-related risks, with the latter being critical for the development and implementation of effective mitigation strategies (Nauta, 2002). Due to the high level of variation characterizing microbial dynamics, the value of deterministic models (i.e., models that provide point estimates of microbial concentrations) in food safety management has been questioned (Nicolaï and Van Impe, 1996; Poschet et al., 2003). The information provided by deterministic models is often insufficient with regard to advanced quantitative microbiology applications, such as hazard analysis and critical control points (HACCP) and risk analysis projects (Poschet et al., 2003). Such a deficiency highlighted the need for the development of models capable of incorporating the variation of model parameters, and motivated the commencement of the so-called “stochastic predictive microbiology” (Nicolaï and Van Impe, 1996). Stochastic (or probabilistic) models take into account the variation of various factors affecting microbial behavior by using probability distributions of the input data, and provide predictions in the form of probability density functions instead of point estimates (Koutsoumanis et al., 2010; Poschet et al., 2003). Accounting for the variation characterizing microbial growth, stochastic predictive models are expected to be more efficient than other traditional modeling approaches, by allowing for a balanced relationship between food safety management and cost-effectiveness of employed processes (Couvert et al., 2010; Juneja et al., 2003). Several stochastic predictive modeling approaches, aiming at quan- tifying and integrating different variation sources, have been described the last decade (Augustin et al., 2011; Delignette-Muller et al., 2006; Membré et al., 2005). The approaches embraced in the above and other studies account for variation on empirical data and/or model parameters, and are pertinent to various issues of food safety International Journal of Food Microbiology 149 (2011) 254–261 ⁎ Corresponding author. Tel./fax: + 30 2310991647. E-mail address: kkoutsou@agro.auth.gr (K.P. Koutsoumanis). 0168-1605/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ijfoodmicro.2011.07.001 Contents lists available at ScienceDirect International Journal of Food Microbiology journal homepage: www.elsevier.com/locate/ijfoodmicro