Development of a Sigmoidal Power Model to Simplify the Description of Microbial Growth Curves

Predictive microbiology supports food safety and quality management systems by providing mathematical approaches to describe microbial responses under defined conditions. In this field, simplified models reduce mathematical complexity, improving usability and interpretability without compromising estimation robustness. This work aimed to develop a sigmoidal power model (SPM) for microbial growth estimation and compare its fitting performance with the modified Gompertz model. The SPM was developed by transposing and readapting Oswin equation parameters for water sorption isotherm modeling. Previously reported kinetic data for Pseudomonas spp. growth in chicken breast and thigh meat stored within a temperature range of 0–20 °C were used to estimate lag phase duration (LPD) and maximum growth rate. Model performance was evaluated using mean absolute percentage error (MAPE) and Akaike information criterion (AIC). Additionally, the temperature effect on the model parameters was described through a secondary model and integrated into the primary model to predict microbial load across the studied temperature range. Model fit was evaluated by comparing predicted and experimental log⁡ N_t  values. MAPE quantifies the percentage difference between predicted and observed values. For SPM, estimated values ranged from 0.8 to 3.6% while modified Gompertz model ranged from 0.7 to 4.2%, indicating high fitting accuracy for both models, with a narrower error range for SPM. Moreover, AIC accounts for goodness-of-fit and model complexity by penalizing models with a higher number of parameters to avoid overfitting, with smaller values indicating a better fit. Among the ten studied kinetics, only in six AIC was significantly different (>2) between models. Although SPM yielded a lower AIC value in three cases, the modified Gompertz model estimated negative LPD values in the remaining three, which lacks physical sense. Temperature dependence of SPM parameters (k =size, n =shape) was estimated using exponential and linear equations for k and n , respectively. Implementation of these parameters into log⁡ N_t predictions, produced a global increase below 3% relative to the original SPM primary model. Overall, these results position SPM as a robust and interpretable basis for microbial growth estimation, supporting its future use in shelf-life prediction and temperature-controlled food safety and quality decision-making.