An example of the stages in the development of a predictive mathematical model for microbial growth: the effects of NaCl, pH and temperature on the growth of Aeromonas hydrophila.

The stages involved in developing a predictive model are illustrated using data describing the effects of temperature (3-20 degrees C), NaCl concentration (0.5-4.5% w/v) and pH (4.6-7.0) on the aerobic growth of Aeromonas hydrophila (cocktail of 6 strains). Optical density measurements using micro-titre plates were used as an initial screen, to determine the appropriate sampling times for viable counts to be made and to determine the approximate boundaries for growth. Growth curves were generated from viable counts and fitted using a modified Gompertz equation. Quadratic response surface equations were fitted to the log of lag and generation times, in response to the variables of temperature, NaCl and pH (in terms of hydrogen ion concentration). The effects of various combinations of these controlling factors are described. Comparisons between predicted growth rates and lag times from our response surface equations and other models for growth of A. hydrophila, developed with viable count data and optical density measurements, are made, together with comparisons with data from the literature on the growth of this bacterium in foods.