Optimization of a new mathematical model for bacterial growth

The objective of this work was to optimize a mathematical equation for use as a primary kinetic model that employed a new approach to describe the three-phase growth of bacteria under constant temperature conditions. This research adopted an optimization algorithm in combination with the Runge–Kutta method to solve the differential form of the new growth model in search of an optimized lag phase transition coefficient (LPTC), which is used to define the adaption and duration of lag phases of bacteria prior to exponential growth. Growth curves of Listeria monocytogenes, Escherichia coli O157:H7, and Clostridium perfringens, selected from previously published data, were analyzed to obtain an optimized LPTC for each growth curve and a global LPTC for all growth curves. With the new optimized LPTC, the new growth model could be used to accurately describe the bacterial growth curves with three distinctive phases (lag, exponential, and stationary). The new optimized LPTC significantly improved the performance and applicability of the new model. The results of statistical analysis (ANOVA) suggested that the new growth model performed equally well with the Baranyi model. It can be used as an alternative primary model for bacterial growth if the bacterial adaption is more significant in controlling the lag phase development.