Transforming kinetic model into a stochastic inactivation model: Statistical evaluation of stochastic inactivation of individual cells in a bacterial population

Abstract

Kinetic models performing point estimation are effective in predicting the bacterial behavior. However, the large variation of bacterial behavior appearing in a small number of cells, i.e. equal or less than 10² cells, cannot be expressed by point estimation. We aimed to predict the variation of Escherichia coli O157:H7 behavior during inactivation in acidified tryptone soy broth (pH3.0) through Monte Carlo simulation and evaluated the accuracy of the developed model. Weibullian fitted parameters were estimated from the kinetic survival data of E. coli O157:H7 with an initial cell number of 10⁵. A Monte Carlo simulation (100 replication) based on the obtained Weibullian parameters and the Poisson distribution of initial cell numbers successfully predicted the results of 50 replications of bacterial inactivation with initial cell numbers of 10¹, 10², and 10³ cells. The accuracy of the simulation revealed that more than 83% of the observed survivors were within predicted range in all condition. 90% of the distribution in survivors with initial cells less than 100 is equivalent to a Poisson distribution. This calculation transforms the traditional microbial kinetic model into probabilistic model, which can handle bacteria number as discrete probability distribution. The probabilistic approach would utilize traditional kinetic model towards exposure assessment.

Keywords: Poisson distribution; Variability; Weibull distribution.