Generalized logistic model of bacterial growth

This work proposes a new mathematical model describing the dynamics of growing bacterial cultures. The model, described by a first order non-linear differential equation, as a generalization of the logistic equation, was compared with the most studied mathematical models. All models were numerically implemented and fitted to the experimental data, collected from the incubation of a bacterial strain of Pseudomonas fluorescens, to obtain the growth parameters. The experimental data showed the lowest fit error for both the Baranyi-Roberts and new models, which turned out to be equivalent. Simulations of the fitting algorithm were also implemented and repeated for a large number of initial guesses of the parameters, chosen in order to test the fitting and convergence performances. The innovative feature that makes the new model easier to use than Baranyi-Roberts model is definitely its simple and manageable analytical form and its good performance in terms of convergence time.

Automated summary

This study proposes a new mathematical model for describing the dynamics of growing bacterial cultures, which is a first order non-linear differential equation and a generalization of the logistic equation. The model is compared with other widely studied mathematical models and numerically fitted to experimental data collected from the incubation of Pseudomonas fluorescens. The experimental data shows that the new model, as well as the Baranyi-Roberts model, has the lowest fit error and equivalent performance. Simulations of the fitting algorithm also demonstrate the new model's simplicity, manageability, and good convergence time compared to the Baranyi-Roberts model.