Statistical evaluation of mathematical models for microbial growth

López, S.; Prieto, Miguel; Dijkstra, J.; Dhanoa, M. S.

doi:10.1016/j.ijfoodmicro.2004.03.026

Cited by 217 publications

(200 citation statements)

References 26 publications

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“…The sigmoidal functions with a variable point of inflection (Richards and Morgan) provided the best fits and accurate estimates of lactation peak, yield at peak, and total milk production over the lactation. Interestingly, such findings on model accuracy are largely in line with the use of these functions to describe somatic or microbial growth (López et al, 2000(López et al, , 2004Darmani-Kuhi et al, 2010). The sigmoidal functions with a fixed point of inflection also provided an acceptable fit to the data and an accurate estimate of total milk production, but showed large variability in the estimates of DIM and yield at peak because the position of the point of inflection, which defines these traits, is imposed by the functional form of the equations.…”

Section: Discussionmentioning

confidence: 55%

On the analysis of Canadian Holstein dairy cow lactation curves using standard growth functions

López

Odongo

McBride

et al. 2015

Journal of Dairy Science

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Section: Discussionmentioning

confidence: 55%

On the analysis of Canadian Holstein dairy cow lactation curves using standard growth functions

López

Odongo

McBride

et al. 2015

Journal of Dairy Science

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“…Similar studies have also been performed for comparing bacterial growth rates (López, S. et al, 2004). Lòpez 2004 used two data sets and nine different growth functions as opposed to four or five, and found that the most effective models for bacterial population growth were Baranyi, threephase-linear, Richards and Weibull growth models.…”

Section: Previous Researchmentioning

confidence: 90%

A Comparison and Catalog of Intrinsic Tumor Growth Models

2014

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Determining the dynamics and parameter values that drive tumor growth is of great interest to mathematical modelers, experimentalists and practitioners alike. We provide a basis on which to estimate the growth dynamics of ten different tumors by fitting growth parameters to at least five sets of published experimental data per type of tumor. These timescale tumor growth data are also used to determine which of the most common tumor growth models (exponential, power law, logistic, Gompertz, or von Bertalanffy) provides the best fit for each type of tumor. In order to compute the best-fit parameters, we implemented a hybrid local-global least squares minimization algorithm based on a combination of Nelder-Mead simplex direct search and Monte Carlo Markov Chain methods.

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“…The modified Gompertz and logistic equations' parameters (A, B, C, M) were subsequently used to calculate: lag phase duration (h) = M − (1/B), generation time (h) = (log 2e)/BC (log denotes the decimal basis of the logarithm), exponential growth rate [(log cfu/g)/h] = BC/e, and maximum population density (log cfu/g) = A + C (15,21,24).…”

Section: Methodsmentioning

confidence: 99%

Modelling the growth rate ofListeria monocytogenesin cooked ham stored at different temperatures

Szczawinski

Szczawinska

Łobacz

et al. 2017

Journal of Veterinary Research

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Introduction: The purpose of the study was to determine and model the growth rates of L. monocytogenes in cooked cured ham stored at various temperatures. Material and Methods: Samples of cured ham were artificially contaminated with a mixture of three L. monocytogenes strains and stored at 3, 6, 9, 12, or 15ºC for 16 days. The number of listeriae was determined after 0, 1, 2, 3, 5, 7, 9, 12, 14, and 16 days. A series of decimal dilutions were prepared from each sample and plated onto ALOA agar, after which the plates were incubated at 37ºC for 48 h under aerobic conditions. The bacterial counts were logarithmised and analysed statistically. Five repetitions of the experiment were performed. Results: Both storage temperature and time were found to significantly influence the growth rate of listeriae (P < 0.01). The test bacteria growth curves were fitted to three primary models: the Gompertz, Baranyi, and logistic. The mean square error (MSE) and Akaike's information criterion (AIC) were calculated to evaluate the goodness of fit. It transpired that the logistic model fit the experimental data best. The natural logarithms of L. monocytogenes' mean growth rates from this model were fitted to two secondary models: the square root and polynomial. Conclusion: Modelling in both secondary types can predict the growth rates of L. monocytogenes in cooked cured ham stored at each studied temperature, but mathematical validation showed the polynomial model to be more accurate.

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Statistical evaluation of mathematical models for microbial growth

Cited by 217 publications

References 26 publications

On the analysis of Canadian Holstein dairy cow lactation curves using standard growth functions

On the analysis of Canadian Holstein dairy cow lactation curves using standard growth functions

A Comparison and Catalog of Intrinsic Tumor Growth Models

Modelling the growth rate ofListeria monocytogenesin cooked ham stored at different temperatures

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