• Journal of Food Hygiene and Safety
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• v.26 no.2
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• pp.120-124
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• 2011

Predictive mathematical models were developed for predicting the kinetics of growth of Listeria monocytogenes in smoked salmon, which is the popular ready-to-eat foods in the world, as a function of temperature (4, 10, 20 and $30^{\circ}C$). At these storage temperature, the primary growth curve fit well ($r^2$=0.989~0.996) to a Gompertz equation to obtain specific growth rate (SGR) and lag time (LT). The Polynomial model for natural logarithm transformation of the SGR and LT as a function of temperature was obtained by nonlinear regression (Prism, version 4.0, GraphPad Software). Results indicate L. monocytogenes growth was affected by temperature mainly, and SGR model equation is $365.3-31.94^*Temperature+0.6661^*Temperature^{\wedge^2}$ and LT model equation is $0.1162-0.01674^*Temperature+0.0009303^*Temperature{\wedge^2}$. As storage temperature decreased $30^{\circ}C$ to $4^{\circ}C$, SGR decreased and LT increased respectively. Polynomial model was identified as appropriate secondary model for SGR and LT on the basis of most statistical indices such as bias factor (1.01 by SGR, 1.55 by LT) and accuracy factor (1.03 by SGR, 1.58 by LT).

• Journal of Food Hygiene and Safety
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• v.28 no.1
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• pp.7-12
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• 2013

This study presents the influence on growth properties determined using a novel predictive growth model of wild-type Salmonella spp. KSC 101 by variations in the temperature and time during cut packaging in cold, uncooked pork meat. The experiment performed for model development included an arrangement of different temperatures ($0^{\circ}C$, $5^{\circ}C$, $10^{\circ}C$, $15^{\circ}C$, and $20^{\circ}C$) and time durations (0, 1, 2, and 3 hours) that reflect actual pork-cut and packaging processes. No growth was observed at $0^{\circ}C$ and $5^{\circ}C$, whereas some growth was observed at $10^{\circ}C$, $15^{\circ}C$, and $20^{\circ}C$, with a mean increase of only 0.34 log CFU/g. The growth observed at $20^{\circ}C$ was more robust than that observed at $15^{\circ}C$, but the difference was not statistically significant (p > 0.05). However, compared with PMP (Pathogen Modeling Program), the wild-type Salmonella spp. KSC 101 showed a more rapid growth. We used the Gompertz 4 parameter equation as the primary model, and the exponential decay formula as the secondary model. The estimated $R^2$ values were 0.99 or higher. The developed model was evaluated by comparison of the experimental and predictive values, and the values were in agreement with the ${\pm}0.5$ log CFU/g, although the RMSE (Root mean square error) value was 0.103, which indicates a slight overestimation. Therefore, we suggest that the developed predictive growth model would be useful as a tool for evaluating sanitation criteria in pork cut-packaging processes.

• Food Science of Animal Resources
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• v.30 no.5
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• pp.730-738
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• 2010

We developed predictive growth models for Staphylococcus aureus and Bacillus cereus on various food matrices consisting primarily of ready-to-eat (RTE) foods. A cocktail of three S. aureus strains, producing enterotoxins A, C, and D, or a B. cereus strain, were inoculated on sliced bread, cooked rice, boiled Chinese noodles, boiled bean sprouts, tofu, baked fish, smoked chicken, and baked hamburger patties at an initial concentration of 3 log CFU/g and stored at 8, 10, 13, 17, 24, and $30^{\circ}C$. Growth kinetic parameters were determined by the Gompertz equation. The square-root and Davey models were used to determine specific growth rate and lag time values, respectively, as a function of temperature. Model performance was evaluated based on bias and accuracy factors. S. aureus and B. cereus growth were most delayed on sliced bread. Overall, S. aureus growth was significantly (p<0.05) more rapid on animal protein foods than carbohydrate-based foods and vegetable protein foods. The fastest growth of S. aureus was observed on smoked chicken. B. cereus growth was not observed at 8 and $10^{\circ}C$. B. cereus growth was significantly (p<0.05) more rapid on vegetable protein foods than on carbohydrate-based foods. The secondary models developed in this study showed suitable performance for predicting the growth of S. aureus and B. cereus on various food matrices consisting of RTE foods.

• Korean Journal of Food Science and Technology
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• v.37 no.2
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• pp.194-198
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• 2005

Growth curves of Listeria monocytogenes in modified surimi-based imitation crab (MIC) broth were obtained by measuring cell concentration in MIC broth at different culture conditions [initial cell numbers, $1.0{\times}10^{2},\;1.0{\times}10^{3}\;and\;1.0{\times}10^{4}$, colony forming unit (CFU)/mL; temperature, 15, 20, 25, 37, and $40^{\circ}C$] and applied to Gompertz model to determine microbial growth indicators, maximum specific growth rate constant (k), lag time (LT), and generation time (GT). Maximum specific growth rate of L. monocytogenes increased rapidly with increasing temperature and reached maximum at $37^{\circ}C$, whereas LT and GT decreased with increasing temperature and reached minimum at $37^{\circ}C$. Initial cell number had no effect on k, LT, and GT (p > 0.05). Polynomial and square root models were developed to express combined effects of temperature and initial cell number using Gauss-Newton Algorism. Relative coefficients of experimental k and predicted k of polynomial and square root models were 0.92 and 0.95, respectively, based on response surface model. Results indicate L. monocytogenes growth was mainly affected by temperature and square root model was more effective than polynomial model for growth prediction.

• Food Science and Biotechnology
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• v.14 no.1
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• pp.42-45
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• 2005

The present study was carried out to envisage the aerobic growth of Listeria monocytogenes and Yersinia enterocolitica on pork, which is one of the major meat sources in Korea. The results were compared with the previously developed predictive model systems for the verification of microbial growth in a real situation during pork processing. Pork loin samples (8.0 g, 5 mm thick) were aseptically prepared and inoculated with each pathogen by immersing into the respective inoculums for one min. Each of the samples were then wrapped with PE film and stored at 5, 10, and $15^{\circ}C$ up to 36 days to measure the growth profile of the respective pathogens. The growth parameters were calculated by using Gompertz equation and were compared with the previously reported data. The predicted generation time (GT) of L. monocytogenes at 5, 10 and $15^{\circ}C$ was 28.74, 7.85 and 4.02 hr, respectively, and for Y. enterocolitica was 10.29, 4.74 and 2.50 hr, at the same temperatures respectively. In this study, the GT values predicted on pork were slightly higher than the values predicted in other studies using liquid model systems. Unlike previous reports, both the pathogens were found to grow at $5^{\circ}C$ on pork. This finding recommends the necessity of controlling the growth of both the pathogens during the slaughtering process and distribution.

• Journal of Food Hygiene and Safety
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• v.34 no.4
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• pp.374-379
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• 2019

This study developed predictive growth models of Salmonella enterica Serovar Typhimurium on lettuce washed with chlorine (100~300 ppm) and ultrasound (US, 37 kHz, 380 W) treatment and stored at different temperatures ($10{\sim}25^{\circ}C$) using a polynomial equation. The primary model of specific growth rate (SGR) and lag time (LT) showed a good fit ($R^2{\geq}0.92$) with a Gompertz equation. A secondary model was obtained using a quadratic polynomial equation. The appropriateness of the secondary SGR and LT model was verified by coefficient of determination ($R^2=0.98{\sim}0.99$ for internal validation, 0.97~0.98 for external validation), mean square error (MSE=-0.0071~0.0057 for internal validation, -0.0118~0.0176 for external validation), bias factor ($B_f=0.9918{\sim}1.0066$ for internal validation, 0.9865~1.0205 for external validation), and accuracy factor ($A_f=0.9935{\sim}1.0082$ for internal validation, 0.9799~1.0137 for external validation). The newly developed models for S. Typhimurium could be incorporated into a tertiary modeling program to predict the growth of S. Typhimurium as a function of combined chlorine and US during the storage. These new models may also be useful to predict potential S. Typhimurium growth on lettuce, which is important for food safety purposes during the overall supply chain of lettuce from farm to table. Finally, the models may offer reliable and useful information of growth kinetics for the quantification microbial risk assessment of S. Typhimurium on washed lettuce.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.11
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• pp.1-10
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• 2021

This paper compares the performance of Fama-French three-factor and five-factor models using a dataset of 20 Pakistani commercial banks for the period 2011 to 2020. We focus on an emerging economy as the findings from earlier studies on developed countries cannot be generalized in emerging markets. For empirical analysis, twelve portfolios were developed based on size, market capitalization, investment strategy, and growth. Subsequently, we constructed five Fama-French factors namely, R_M, SMB, HML, RMW, and CMA. The OLS regression technique with robust standard errors was applied to compare the predictive power of both the Fama-French models. Further, we also compared the mean-variance efficiency of the Fama-French models through the GRS test. Our empirical analysis provides three unique and interesting findings. First, both asset pricing models have similar predictive power to explain the expected portfolio returns in most cases. Second, our results from the GRS test suggest that there is no noticeable difference in the mean-variance efficiency of one asset pricing model over the other. Third, we find that all factors of both Fama-French models are statistically significant and are important for explaining the volatility of expected commercial bank returns in the context of Pakistan.

• Journal of Preventive Veterinary Medicine
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• v.42 no.4
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• pp.143-147
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• 2018

The present study aimed to develop growth prediction models of Listeria monocytogenes in processed meat products, such as mixed pressed hams, to perform accurate microbial risk assessments. Considering cold storage temperatures and the amount of time in the stages of consumption after opening, the growth of L. monocytogenes was determined as a function of temperature at 0, 5, 10, and $15^{\circ}C$, and time at 0, 1, 3, 6, 8, 10, 15, 20, 25, and 30 days. Based on the results of these measurements, a Baranyi model using the primary model was developed. The input parameters of the Baranyi equation in the variable temperature for polynomial regression as a secondary model were developed: $SGR=0.1715+0.0199T+0.0012T^2$, $LT=5.5730-0.3215T+0.0051T^2$ with $R^2$ values 0.9972 and 0.9772, respectively. The RMSE (Root mean squared error), $B_f$ (bias factor), and $A_f$ (accuracy factor) on the growth prediction model were determined to be 0.30, 0.72, and 1.50 in SGR (specific growth rate), and 0.10, 0.84, and 1.35 in LT (lag time), respectively. Therefore, the model developed in this study can be used to determine microorganism growth in the stages of consumption of mixed pressed hams and has potential in microbial risk assessments (MRAs).

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.369-385
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• 1999

For the growth curve model with arbitrary covariance structure, known as unstructured covariance matrix, the problems of detecting outliers are discussed in this paper. In order to detect outliers in the growth curve model, the likelihood ratio testing statistics in mean shift model is established and its distribution is derived. After we detected outliers in growth curve model, we test homo and/or hetero-geneous covariance matrices using PSR Quasi-Bayes Criterion. For illustration, one numerical example is discussed, which compares between before and after outlier deleting.

• Journal of Food Hygiene and Safety
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• v.28 no.2
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• pp.168-173
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• 2013

This study was carried out to develop and validate predictive models of E. coli O157:H7 growth. Growth data of E. coli O157:H7 in Paprika were collected at 12, 24, 30 and $36^{\circ}C$. The population increased into 3.0 to 3.8 log10 CFU/g within 4 days, then continued to increase at a slower rate through 10 days of storage at $12^{\circ}C$. The lag time (LT) and maximum specific growth rate (SGR) obtained from each primary model was then modeled as a function of temperature using Davey and square root equations, respectively. For interpolation of performance evaluation, growth data for a mixture of E. coli O157:H7 were collected at time intervals in paprika incubated at the different temperatures, which was not used in model development. Results of model performance for interpolation data demonstrated that induced secondary models showed acceptable goodness of fit. Relative errors in the LT and SGR model for interpolation data (18 and $27^{\circ}C$) was 100%, which show acceptable goodness of fit and validated for interpolation. The primary and secondary models developed in this study can be used to establish tertiary models to quantify the effects of temperature on the growth of E. coli O157:H7 in paprika.