Reconsidering stochasticity in modeling of bacterial population growth and inactivation with technical and biological variability.

Abstract

Considering variability in microbial behavior has been recognized as a crucial element for predictive microbiology and quantitative microbial risk assessment. Although some sources of variability have been listed so far, a mathematical description of the variability in bacterial population behavior has not yet been realized. The present paper illustrates stochastic bacterial population growth and/or inactivation behavior from a mathematical point of view. Among various stochastic factors, sampling for the quantification of bacterial numbers and single-cell division/inactivation responses to food environments are highlighted as sources of technical and biological variability. Furthermore, the variability in sampling and single-cell division/inactivation responses emerges as variability in both number and time from the viewpoint of population dynamics. The aforementioned mathematical description of variability enables combining Poisson, binomial, and negative binomial distributions into traditional kinetic equations as its residual distribution. The primary focus is on the stochastic nature of variability, while it also includes discussions on incorporating parameter uncertainty into mathematical models. The traditional kinetic equation integrated with technical and biological variability and uncertainty enables a precise estimate of variation in population behavior, which would facilitate exposure assessment in quantitative microbial risk assessment.