Abstract Mathematical models are often used to predict microbial growth in food products. An important class of these models involves the adaptation of classical sigmoid functions, such as the Gompertz and logistic functions. This study aimed to validate the use of the modified Richards model in various situations, which have not previously been tested. The model was obtained through solving a system of two differential equations and could be applied to both isothermal and non-isothermal environments. To test and validate this model, we used published datasets containing data for the growth of Pseudomonas spp. in fish products. The results obtained after fitting the model showed that it could be effectively used to describe and predict the Pseudomonas growth curves under various temperature regimens. However, the influence of the shape parameter on the growth curve is an issue that needs further evaluation.

RESUMO. O principal objetivo deste estudo foi comparar a qualidade do ajuste de cinco modelos matemáticos recorrentemente utilizados na literatura para a descrição do ganho de peso animal. Ele também teve o objetivo de estudar a influência do parâmetro de forma sobre as curvas de crescimento. Os modelos de Brody, Gompertz, Logístico, von Bertalanffy e Richards, foram ajustados a dados experimentais de 14 grupos de animais diferentes. Como critério de qualidade de ajuste quatro índices estatísticos foram adotados: coeficiente de determinação (R2 ), raiz do quadrado médio do erro (RMSE) e os critérios de informação, Akaike (AIC) e Bayesian (BIC). Em geral, o modelo de Richards forneceu os melhores ajustes aos dados experimentais comparados aos demais modelos. No entanto, para alguns animais, diferentes modelos exibiram melhor desempenho. Foi possível obter uma possível interpretação para o significado do parâmetro de modo a fornecer ferramentas úteis para prever o comportamento do crescimento animal.

ABSTRACT. The main objective of this study was to compare the goodness of fit of five non-linear growth models, i.e. Brody, Gompertz, Logistic, Richards and von Bertalanffy in different animals. It also aimed to evaluate the influence of the shape parameter on the growth curve. To accomplish this task, published growth data of 14 different groups of animals were used and four goodness of fit statistics were adopted: coefficient of determination (R2 ), root mean square error (RMSE), Akaike information criterion (AIC) and Bayesian information criterion (BIC). In general, the Richards growth equation provided better fits to experimental data than the other models. However, for some animals, different models exhibited better performance. It was obtained a possible interpretation for the shape parameter, in such a way that can provide useful insights to predict animal growth behavior.

A mathematical model previously developed to study microbial growth in food products under an isothermal environment was adapted to a time-varying temperature regime. The resulting model was applied to study the growth of Clostridium perfringens in meat products. This micro-organism is of particular relevance to public health and economy due to the loss of productivity caused by it. Results showed a similar performance of the model used compared to the Baranyi model under an isothermal situation and a slightly better performance under a non-isothermal temperature profile.