A stochastic approach for integrating strain variability in modeling Salmonella enterica growth as a function of pH and water activity

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 (μmax) of Salmonella enterica as a function of pH and water activity (aw) 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 aw (0.964–0.992) values, were used. The effects of the environmental parameters on μmax were modeled for each tested S. enterica strain using cardinal type and gamma concept models for pH and aw, respectively. A multiplicative without interaction-type model, combining the models for pH and aw, was used to describe the combined effect of these two environmental parameters on μmax. 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 pHmin, pHopt and awmin as inputs to the growth model. The cumulative probability distribution of the observed μmax values corresponding to growth at pH 7.0–aw 0.992 was introduced in the place of the model's parameter μopt. 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 μmax values characterizing the strain variability. The developed model was further validated using independent growth kinetic data (μmax values) generated for the 60 strains of the pathogen at pH 5.0–aw 0.977, and exhibited a satisfactory performance. The mean, standard deviation, and the 5th and 95th percentiles of the predicted μmax 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.

► A growth model integrating strain variability of Salmonella enterica was developed.
► The effects of pH and aw were modeled using cardinal type and gamma concept models.
► Strain variability was incorporated by using distributions of the values of pHmin, pHopt and awmin.
► The model was validated and exhibited a satisfactory performance.
► The developed stochastic model can be useful in microbial risk assessment.