ABSTRACT

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.

摘要

这项工作提出了一种新的数学模型来描述细菌培养物生长的动态。该模型由一阶非线性微分方程描述，作为逻辑方程的推广，与大多数研究的数学模型进行了比较。所有模型均以数值方式实现并适合实验数据，这些数据是从荧光假单胞菌菌株的培养中收集的，获得生长参数。实验数据显示 Baranyi-Roberts 模型和新模型的拟合误差最低，结果是等效的。还对拟合算法进行了模拟，并针对大量参数的初始猜测进行了重复，选择这些参数是为了测试拟合和收敛性能。使新模型比 Baranyi-Roberts 模型更易于使用的创新特征无疑是其简单且易于管理的分析形式以及在收敛时间方面的良好性能。