A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth. The model was applied to five different sets of data of microbial growth in dairy products selected from Combase, which is the most important database in the area with thousands of datasets from around the world, and the results showed a good fit. In addition, the model provides equations for the evaluation of the maximum specific growth rate and the duration of the lag phase which may provide useful information about microbial growth. Neste trabalho, um modelo matemático que descreve o crescimento de populações de microrganismos no leite foi desenvolvido, aplicado e validado. Para este fim, foi proposto um sistema de duas equações diferenciais de primeira ordem, as quais descreveram hipóteses físicas do crescimento de populações. O modelo foi aplicado para dados de crescimento de cinco diferentes microrganismos em produtos lácteos retirados da Combase, a qual contém uma grande quantidade de dados referentes ao crescimento de microrganismos nos mais diversos alimentos, e os resultados indicaram um bom ajuste com coeficiente de determinação superior a 0,99 para todos os dados. A partir dos parâmetros do modelo, foi possível estimarem-se os valores da taxa de crescimento máxima e a duração da fase lag, os quais podem fornecer informações importantes sobre o comportamento do microrganismo estudado

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.