Assessing the prediction ability of different mathematical models for the growth of Lactobacillus plantarum under non-isothermal conditions

Prediction of viscoelastic properties of peanut-based 3D printable food ink

Viscoelastic properties of 3D printable peanut-based food ink were investigated using frequency sweep and relaxation test. The incorporation of xanthan gum (XG) improved the shear thinning behavior (n value ranging from 0.139 to 0.261) and lowered the η*, G', and G'' values, thus making food ink 3D printable. The addition of XG also caused a downward shift in the relaxation curve. This study evaluates the possibility of an artificial neural network (ANN) approach as a substitute for the Maxwell three-element and Peleg model for predicting the viscoelastic behavior of food ink. The results revealed that all three models accurately predicted the decay forces. The inclusion of XG decreased the hardness and enhanced the cohesiveness, so enabling the 3D printing of food ink. The hardness was highly positively correlated with Maxwell model parameters Fe , F1 , F2 , F3, and Peleg constant k2 (0.57) and negatively correlated with k1 (-0.76).

Comparison of modelling approaches for the prediction of kinetic growth parameters of Pseudomonas spp. in oyster mushroom (Pleurotus ostreatus)

In predictive microbiology, primary and secondary models can be used to predict microbial growth, usually in a two-step modelling approach. The inverse dynamic modelling approach is an alternative method to direct modelling methods, in which the primary and secondary models are fitted simultaneously from non-isothermal data, minimising experimental effort and costs. Thus, the main aim of the present study was to compare the prediction capabilities of the mathematical modelling approaches used for calculating growth kinetics of microorganisms in predictive food microbiology field. For this purpose, the bacterial growth data of Pseudomonas spp. in oyster mushroom (Pleurotus ostreatus) subjected to isothermal and non-isothermal storage temperatures were collected from previously published growth curves. Temperature-dependent kinetic growth parameters (maximum specific growth rate 'µmax' and lag phase duration 'λ') were described as a function of storage temperature using the direct two-step, direct one-step and inverse dynamic modelling approach based on Baranyi and Huang models. The fitting capability of the modelling approaches was separately compared, and the one-step modelling approach for the direct methods provided better goodness of fit results regardless of used primary models, which leads the Huang model with being RMSE = 0.226 and R2adj = 0.949 became best for direct methods. Like seen in direct methods, the Huang model gave better goodness of fit results than Baranyi model for inverse method. Results revealed there was no significant difference (p > 0.05) between the growth kinetic parameters obtained from direct one-step modelling approach and inverse modelling approaches based on the Huang model. Satisfactorily statistical indexes show that the inverse dynamic modelling approach can be reliably used as an alternative way of describing the growth behaviour of Pseudomonas spp. in oyster mushroom in a fast and minimum labour effort.

Food safety and food security through predictive microbiology tools: a short review

This article discusses the issues of food safety and food security as a matter of global health. Foodborne illness and deaths caused by pathogens in food continue to be a worldwide problem, with a reported 600 million cases per year, leading to around 420,000 deaths in 2010. Predictive microbiology can play a crucial role in ensuring safe food through mathematical modelling to estimate microbial growth and behaviour. Food security is described as the social and economical means of accessing safe and nutritious food that meets people's dietary preferences and requirements for an active and healthy life. The article also examines various factors that influence food security, including economic, environmental, technological, and geopolitical challenges globally. The concept of food safety is described as a science-based process or action that prevents food from containing substances that could harm human health. Food safety receives limited attention from policymakers and consumers in low- and middle-income countries, where food safety issues are most prevalent. The article also highlights the importance of detecting contaminants and pathogens in food to prevent foodborne illnesses and reduce food waste. Food and Agriculture Organization (FAO), an institution belonging to World Health Organization (WHO) presented calls to action to solve some of the emerging problems in food safety, as it should be a concern of all people to be involved in the pursue of safer food. The guarantee of safe food pertaining to microbiological contamination, as there are different types of active microorganisms in foods, could be obtained using predictive microbiology tools, which study and analyse different microorganisms' behaviour through mathematical models. Studies published by several authors show the application of primary, secondary, or tertiary models of predictive microbiology used for different food products.

Modeling the effect of Croton blanchetianus Baill essential oil on pathogenic and spoilage bacteria

This study aimed to evaluate and model the antimicrobial action of different concentrations of Croton blanchetianus essential oil (CBEO) on the behavior of six bacterial species in vitro. CBEO extraction was performed by hydrodistillation and characterized by CG-MS. CBEO solutions in culture media were tested at 0.90, 1.80, 2.71, and 4.51 mg of CBEO/mL, against foodborne bacteria: pathogenic bacteria (Staphylococcus aureus, Listeria monocytogenes and Salmonella Enteritidis at 35 °C), a non-pathogenic Escherichia coli (at 35 °C), and spoilage bacteria (Weissella viridescens and Leuconostoc mesenteroides at 30 °C). The CBEO major compounds were eucalyptol, α-pinene, sativene, E-caryophyllene, bicyclogermacrene, and spatulenol. Baranyi and Roberts (growth) and Weibull (inactivation) primary models, along with power and hyperbolic secondary models, were able to describe the data. CBEO inactivated L. monocytogenes, S. aureus, L. mesenteroides and W. viridescens at all applied concentrations. CBEO did not inactivate S. Enteritidis and E. coli, but their growth rates were reduced.

Development of a New Modelling Approach and Performance Evaluation of Meta-heuristic Optimization Algorithms for the Prediction of Kinetic Growth Parameters for Pseudomonas spp. in Fish

The main aim of the current work was to build up a new mathematical modelling approach in predictive food microbiology field for the prediction of growth kinetics of microorganisms. For this purpose, the bacterial growth data of Pseudomonas spp. in whole fish (gilt-head seabream) subjected to isothermal and non-isothermal storage temperatures were collected from previously published growth curves. Maximum specific growth rate (1/h) and lag phase duration (h) were described as a function of storage temperature using the direct two-step, direct one-step and inverse dynamic modelling approaches based on various meta-heuristic optimization algorithms. The fitting capability of the modelling approaches and employed optimization algorithms was separately compared, and the one-step modelling approach for the direct methods and the Bayesian optimization method for the used algorithms provided the best goodness of fit results. These two were then further processed in validation step. The inverse dynamic modelling approach based on the Bayesian optimization algorithm yielded satisfactorily statistical indexes (1.02 > Bias factor > 1.09 and 1.07 > Accuracy factor > 1.13), which indicates it can be reliably used as an alternative way of describing the growth behaviour of Pseudomonas spp. in fish in a fast and efficient manner with minimum labour effort.

Development and validation of a mathematical model for pseudomonads growth as a basis for predicting spoilage of fresh poultry breast and thigh fillets

The growth of naturally contaminated pseudomonads on fresh breast and thigh poultry fillets during aerobic storage was studied and modeled as a function of temperature (0–30°C). A statistical comparison of the models for breast and thigh fillets showed that muscle type does not significantly affect the temperature dependence of pseudomonads growth kinetics. A unified model for breast and thigh was developed and validated against pseudomonads growth rate data under isothermal conditions extracted from literature and experimental data under dynamic temperature conditions. The validation results showed a satisfactory performance of the model with the bias and accuracy factors ranging from 0.85 to 1.09 and 1.02 to 1.21, respectively. The model was further used to predict the shelf life of fresh poultry as the time required by pseudomonads to reach the spoilage level for various scenarios of temperature, initial contamination level, and physiological state of pseudomonads demonstrating its application in a risk-based shelf-life assessment of fresh poultry products.

Development and validation of a predictive model for the effect of temperature, pH and water activity on the growth kinetics of Bacillus coagulans in non-refrigerated ready-to-eat food products

A cardinal model (CM) for the effects of temperature (range: 32-59 °C), pH (range: 5.0-8.5) and water activity (a_w) (range: 0.980-0.995) on Bacillus coagulans DSM 1 growth rate was developed in brain heart infusion broth (BHI), using the Bioscreen C method and further validated in selected food products. The estimated values for the cardinal parameters T_min, T_opt, T_max, pH_min, pH_opt, pH_max, [Formula: see text] and [Formula: see text] were 23.77 ± 0.19 °C, 52.89 ± 0.01 °C, 59.37 ± 0.07 °C, 4.70 ± 0.02, 6.43 ± 0.02, 8.56 ± 0.01, 0.969 ± 0.0007 and 0.998 ± 0.0011, respectively. The growth behaviour of B. coagulans was studied in five commercial non-refrigerated ready-to-eat food products under static conditions at 53 °C in order to estimate the optimum specific growth rate for each tested food product. The developed models were validated in the five selected food products under four different dynamic temperature profiles by comparing predicted and observed growth behaviour of B. coagulans. The validation results indicated a good performance of the model for all tested products with the overall Bias factor (B_f) and Accuracy factor (A_f) estimated at 1.00 and 1.12, respectively. The developed model can be considered an effective tool in predicting B. coagulans growth and spoilage risks of non-refrigerated ready-to-eat food products during distribution and storage.

Development and validation of an extended predictive model for the effect of pH and water activity on the growth kinetics of Geobacillus stearothermophilus in plant-based milk alternatives

The cardinal model for the effect of temperature on Geobacillus stearothermophilus ATCC 7953 growth developed by Kakagianni, Gougouli, & Koutsoumanis, 2016 was expanded for the effect of pH and water activity (a_w). The effect of pH (range: 5.7-8.5) and a_w (range: 0.985-0.999) on G. stearothermophilus growth rate was studied in tryptone soy broth (TSB) using the Bioscreen C method and further modelled using a Cardinal Model (CM). The estimated values for the cardinal parameters [Formula: see text] , and [Formula: see text] were 5.65 ± 0.14, 6.74 ± 0.03, 8.71 ± 0.03, 0.984 ± 0.007 and 0.998 ± 0.001, respectively. The growth behaviour of G. stearothermophilus was investigated in 7 commercial non-refrigerated plant-based milk alternatives under static conditions (62 °C) and the estimated maximum specific growth rates were used to determine the optimum growth rate for each product. The developed model was validated against observed growth of G. stearothermophilus in the 7 products during storage at non-isothermal conditions (testing 4 different temperature profiles). The validation results showed a good performance of the model with overall Bias factor (B_f) = 1.06 and Accuracy factor (A_f) = 1.12. The developed model can be used as an effective tool by the food industry in predicting spoilage of plant-based milk alternatives during distribution and storage at retail and domestic levels.

Prediction of population behavior of Listeria monocytogenes in food using machine learning and a microbial growth and survival database

In predictive microbiology, statistical models are employed to predict bacterial population behavior in food using environmental factors such as temperature, pH, and water activity. As the amount and complexity of data increase, handling all data with high-dimensional variables becomes a difficult task. We propose a data mining approach to predict bacterial behavior using a database of microbial responses to food environments. Listeria monocytogenes, which is one of pathogens, population growth and inactivation data under 1,007 environmental conditions, including five food categories (beef, culture medium, pork, seafood, and vegetables) and temperatures ranging from 0 to 25 °C, were obtained from the ComBase database (www.combase.cc). We used eXtreme gradient boosting tree, a machine learning algorithm, to predict bacterial population behavior from eight explanatory variables: ‘time’, ‘temperature’, ‘pH’, ‘water activity’, ‘initial cell counts’, ‘whether the viable count is initial cell number’, and two types of categories regarding food. The root mean square error of the observed and predicted values was approximately 1.0 log CFU regardless of food category, and this suggests the possibility of predicting viable bacterial counts in various foods. The data mining approach examined here will enable the prediction of bacterial population behavior in food by identifying hidden patterns within a large amount of data.

Application of deep neural techniques in predictive modelling for the estimation of Escherichia coli growth rate

AIMS

To develop a predictive model for Escherichia coli using deep neural networks.

METHODS AND RESULTS

Batch experiments are conducted at different temperatures closer to optimum value (36·5°C, 37°C, 37·5°C, 38°C and 38·5°C) to obtain the growth curves of E .coli K-12. Two primary models namely modified Gompertz and new logistic are chosen. Three secondary models namely Gaussian, nonlinear autoregressive eXogenous (NARX) model and long short-term memory (LSTM) are developed. The novelty in this paper is the development of secondary models using artificial neural network (ANN) and deep network. The performance measures chosen to compare the developed primary and secondary models are correlation coefficient (R² ), root-mean-square error (RMSE) and accuracy factor (A_f ). Results show that modified Gompertz model has better R² (0·99) and RMSE (0·019) when compared to new logistic model. Also, the deep network model outperforms other secondary models. Based on the primary and novel secondary model, a predictive model (tertiary model) is developed with improved accuracy and is validated.

CONCLUSIONS

The proposed predictive model exhibit good validation results in terms of RMSE and R² values and can be applied for determining the growth rate of E. coli at a particular temperature value.

SIGNIFICANCE AND IMPACT OF THE STUDY

The proposed model can be used in food processing industries during enzyme production such as Chymosin, to predict the growth rate of E. coli as a function of temperature. Also, the developed LSTM and NARX models can be used to predict maximum specific growth rate of other microbial strains with proper training.

In vitro screening of probiotic properties of Lactobacillus plantarum isolated from fermented milk product

Objectives

The screening of traditional fermented products is essential for the assessment of safety, security, and further development of functional foods for the well-being of human health. The aim of the present study was to isolate and identify bacteria from fermented raw milk samples that exhibit health benefits upon consumption.

Methods

In order to confirm the isolates as probiotics, several in vitro assays were conducted to assess the probiotic properties of isolated bacteria. The initial screening includes tolerance to acid, bile, pancreatin, and NaCl. The cell surface properties demonstrate their interaction with mucosal epithelium, which includes hydrophobicity and auto-aggregation assay. Safety assessment was done by performing haemolytic test and antibiotic susceptibility test. The antagonistic activity of probiotic strain was further evaluated against some pathogenic bacteria.

Results

Lactobacillus plantarum (L. plantarum) isolated from fermented raw milk was preliminarily identified by biochemical tests and further confirmed using 16S rRNA identification. The isolate designated as L. plantarum strain GCC_19M1 demonstrated significant tolerance to low pH, 0.3% bile, 0.5% pancreatin, and 5% NaCl. In the presence of simulated gastric juice (at pH 3), the isolate exhibited a survival rate of 93.48–96.97%. Furthermore, the development of ecological niches in the human gut and their successful accumulation have been revealed by auto-aggregation and hydrophobicity properties. Absence of haemolytic activity ensures the non-virulent nature of the strain. Lactobacillus plantarum strain GCC_19M1 showed susceptibility towards gentamicin, tetracycline, kanamycin, meropenem, and ceftriaxone and exhibited an antagonistic effect on pathogenic bacteria.

Conclusion

The obtained results conveyed that L. plantarum strain GCC_19M1 has strong probiotic potential, and its presence in the fermented raw milk products may serve as a potent functional probiotic food.

Quantifying the bioprotective effect of Lactobacillus sakei CTC494 against Listeria monocytogenes on vacuum packaged hot-smoked sea bream

In this study, the bioprotective potential of Lactobacillus sakei CTC494 against Listeria monocytogenes CTC1034 was evaluated on vacuum packaged hot-smoked sea bream at 5 °C and dynamic temperatures ranging from 3 to 12 °C. The capacity of three microbial competition interaction models to describe the inhibitory effect of L. sakei CTC494 on L. monocytogenes was assessed based on the Jameson effect and Lotka-Volterra approaches. A sensory analysis was performed to evaluate the spoiling capacity of L. sakei CTC494 on the smoked fish product at 5 °C. Based on the sensory results, the bioprotection strategy against the pathogen was established by inoculating the product at a 1:2 ratio (pathogen:bioprotector, log CFU/g). The kinetic growth parameters of both microorganisms were estimated in mono-culture at constant storage (5 °C). In addition, the inhibition function parameters of the tested interaction models were estimated in co-culture at constant and dynamic temperature storage using as input the mono-culture kinetic parameters. The growth potential (δ log) of L. monocytogenes, in mono-culture, was 3.5 log on smoked sea bream during the experimental period (20 days). In co-culture, L. sakei CTC494 significantly reduced the capability of L. monocytogenes to grow, although its effectiveness was temperature dependent. The LAB strain limited the growth of the pathogen under storage at 5 °C (<1 log increase) and at dynamic profile 2 (<2 log increase). Besides, under storage at dynamic profile 1, the growth of L. monocytogenes was inhibited (<0.5 log increase). These results confirmed the efficacy of L. sakei CTC494 for controlling the pathogen growth on the studied fish product. The Lotka-Volterra competition model showed slightly better fit to the observed L. monocytogenes growth response than the Jameson-based models according to the statistical performance. The proposed modelling approach could support the assessment and establishment of bioprotective culture-based strategies aimed at reducing the risk of listeriosis linked to the consumption of RTE hot-smoked sea bream.

Modeling the Growth and Interaction Between Brochothrix thermosphacta, Pseudomonas spp., and Leuconostoc gelidum in Minced Pork Samples

The aim of this study was to obtain the growth parameters of specific spoilage micro-organisms previously isolated in minced pork (MP) samples and to develop a three-spoilage species interaction model under different storage conditions. Naturally contaminated samples were used to validate this approach by considering the effect of the food microbiota. Three groups of bacteria were inoculated on irradiated samples, in mono- and in co-culture experiments (n = 1152): Brochothrix thermosphacta, Leuconostoc gelidum, and Pseudomonas spp. (Pseudomonas fluorescens and Pseudomonas fragi). Samples were stored in two food packaging [food wrap and modified atmosphere packaging (CO2 30%/O2 70%)] at three isothermal conditions (4, 8, and 12°C). Analysis was carried out by using both 16S rRNA gene amplicon sequencing and classical microbiology in order to estimate bacterial counts during the storage period. Growth parameters were obtained by fitting primary (Baranyi) and secondary (square root) models. The food packaging shows the highest impact on bacterial growth rates, which in turn have the strongest influence on the shelf life of food products. Based on these results, a three-spoilage species interaction model was developed by using the modified Jameson-effect model and the Lotka Volterra (prey-predator) model. The modified Jameson-effect model showed slightly better performances, with 40-86% out of the observed counts falling into the Acceptable Simulation Zone (ASZ). It only concerns 14-48% for the prey-predator approach. These results can be explained by the fact that the dynamics of experimental and validation datasets seems to follow a Jameson behavior. On the other hand, the Lotka Volterra model is based on complex interaction factors, which are included in highly variable intervals. More datasets are probably needed to obtained reliable factors, and so better model fittings, especially for three- or more-spoilage species interaction models. Further studies are also needed to better understand the interaction of spoilage bacteria between them and in the presence of natural microbiota.

A mathematical modeling approach to the quantification of lactic acid bacteria in vacuum-packaged samples of cooked meat: Combining the TaqMan-based quantitative PCR method with the plate-count method

The TaqMan-based quantitative Polymerase Chain Reaction (qPCR) method and the Plate Count (PC) method are both used in combination with primary and secondary mathematical modeling, to describe the growth curves of Leuconostoc mesenteroides and Weissella viridescens in vacuum-packaged meat products during storage under different isothermal conditions. Vacuum-Packaged Morcilla (VPM), a typical cooked blood sausage, is used as a representative meat product, with the aim of improving shelf-life prediction methods for those sorts of meat products. The standard curves constructed by qPCR showed good linearity between the cycle threshold (C_T) and log₁₀ CFU/g, demonstrating the high precision and the reproducible results of the qPCR method. The curves were used for the quantification of L. mesenteroides and W. viridescens in artificially inoculated VPM samples under isothermal storage (5, 8, 13 and 18 °C). Primally, both the qPCR and the PC methods were compared, and a linear regression analysis demonstrated a statistically significant linear correlation between the methods. Secondly, the Baranyi and Roberts model was fitted to the growth curve data to estimate the kinetic parameters of L. mesenteroides and W. viridescens under isothermal conditions, and secondary models were used to establish the dependence of the maximum specific growth rate on the temperature. The results proved that primary and secondary models were adequate for describing the growth curves of both methods in relation to both bacteria. In conclusion, the results of all the experiments proved that the qPCR method in combination with the PC method can be used to construct microbial growth kinetics and that primary and secondary mathematical modeling can be successfully applied to describe the growth of L. mesenteroides and W. viridescens in vacuum-packaged morcilla and, by extension, other cooked meat products with similar characteristics.

Predictive Model of Listeria monocytogenes Growth in Queso Fresco

Listeria monocytogenes is a hardy psychrotrophic pathogen that has been linked to several cheese-related outbreaks in the United States, including a recent outbreak in which a fresh cheese (queso fresco) was implicated. The purpose of this study was to develop primary, secondary, and tertiary predictive models for the growth of L. monocytogenes in queso fresco and to validate these models using nonisothermal time and temperature profiles. A mixture of five strains of L. monocytogenes was used to inoculate pasteurized whole milk to prepare queso fresco. Ten grams of each fresh cheese sample was vacuum packaged and stored at 4, 10, 15, 20, 25, and 30°C. From samples at each storage temperature, subsamples were removed at various times and diluted in 0.1% peptone water, and bacteria were enumerated on Listeria selective agar. Growth data from each temperature were fitted using the Baranyi model as the primary model and the Ratkowsky model as the secondary model. Models were then validated using nonisothermal conditions. The Baranyi model was fitted to the isothermal growth data with acceptable goodness of fit statistics (R² = 0.928; root mean square error = 0.317). The Ratkowsky square root model was fitted to the specific growth rates at different temperatures (R² = 0.975). The tertiary model developed from these models was validated using the growth data with two nonisothermal time and temperature profiles (4 to 20°C for 19 days and 15 to 30°C for 11 days). Data for these two profiles were compared with the model prediction using an acceptable prediction zone analysis; >70% of the growth observations were within the acceptable prediction zone (between -1.0 and 0.5 log CFU/g). The model developed in this study will be useful for estimating the growth of L. monocytogenes in queso fresco. These predictions will help in estimation of the risk of listeriosis from queso fresco under extended storage and temperature abuse conditions.

Effect of soluble solids concentration on Neosartorya fischeri inactivation using UV-C light

Ascospores of Neosartorya fischeri are heat-resistant and can survive thermal commercial treatments normally applied to the juices, as apple juice. Non-thermal processing of food such as exposure to ultraviolet light (UV-C) is reported to induce minimal quality changes while reduces microbial load. The main objective of this study was to determine the effect at different soluble solids concentration (12, 25, 30, 40, 50, 60 and 70 °Brix) on N. fischeri ascospores inactivation in apple juice, using UV-C light intensity (38 W/m²). Weibull model was fitted to experimental data. Then, a secondary model was used to describe how the inactivation kinetic parameters varied with the changes in soluble solids concentration. Results showed that the UV-C light had influence on N. fischeri ascospores inactivation in apple juice even at the highest soluble solids concentrations used, reaching approximately 4 log reductions at all concentrations used. The inactivation parameters, obtained by Weibull model, were δ (dose for the first decimal reduction) and p (the shape factor). Exponential model was chosen to describe the influence of soluble solids concentration on δ and p parameters. It can be concluded that UV-C light is a promising treatment with a drastic impact on the loads of N. fischeri, especially when low soluble solids concentration is used and a model was obtained to describe Brix effect.

Encapsulation of Lactobacillus fermentum K73 by Refractance Window drying

The purpose of this work was to model the survival of the microorganism and the kinetics of drying during the encapsulation of Lactobacillus fermentum K73 by Refractance Window drying. A whey culture medium with and without addition of maltodextrin were used as encapsulation matrices. The microorganism with the encapsulation matrices was dried at three water temperatures (333, 343 and 353 K) until reaching balanced moisture. Microorganism survival and thin layer drying kinetics were studied by using mathematical models. Results showed that modified Gompertz model and Midilli model described the survival of the microorganism and the drying kinetics, respectively. The most favorable process conditions found with the mathematical modelling were a drying time of 2460 s, at a temperature of 353 K. At these conditions, a product with 9.1 Log CFU/g and a final humidity of 10% [wet basis] using the culture medium as encapsulation matrix was obtained. The result shows that Refractance Window can be applied to encapsulate the microorganism probiotic with a proper survival of the microorganism.

Modelling the interaction of the sakacin-producing Lactobacillus sakei CTC494 and Listeria monocytogenes in filleted gilthead sea bream (Sparus aurata) under modified atmosphere packaging at isothermal and non-isothermal conditions

The objective of this work was to quantitatively evaluate the effect of Lactobacillus sakei CTC494 (sakacin-producing bioprotective strain) against Listeria monocytogenes in fish juice and to apply and validate three microbial interaction models (Jameson, modified Jameson and Lotka Volterra models) through challenge tests with gilthead sea bream (Sparus aurata) fillets under modified atmosphere packaging stored at isothermal and non-isothermal conditions. L. sakei CTC494 inhibited L. monocytogenes growth when simultaneously present in the matrix (fish juice and fish fillets) at different inoculation ratios pathogen:bioprotector (i.e. 1:1, 1:2 and 1:3). The higher the inoculation ratio, the stronger the inhibition of L. monocytogenes growth, with the ratio 1:3 yielding no growth of the pathogen. The maximum population density (N_max) was the most affected parameter for L. monocytogenes at all inoculation ratios. According to the microbiological and sensory analysis outcomes, an initial inoculation level of 4 log cfu/g for L. sakei CTC494 would be a suitable bioprotective strategy without compromising the sensory quality of the fish product. The performance of the tested interaction models was evaluated using the Acceptable Simulation Zone approach. The Lotka Volterra model showed slightly better fit than the Jameson-based models with 75-92% out of the observed counts falling into the Acceptable Simulation Zone, indicating a satisfactory model performance. The evaluated interaction models could be used as predictive modelling tool to simulate the simultaneous behaviour of bacteriocin-producing Lactobacillus strains and L. monocytogenes; thus, supporting the design and optimization of bioprotective culture-based strategies against L. monocytogenes in minimally processed fish products.

Use of modified Richards model to predict isothermal and non-isothermal microbial growth

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.

Application of a Predictive Growth Model of Pseudomonas spp. for Estimating Shelf Life of Fresh Agaricus bisporus

For prediction of the shelf life of the mushroom Agaricus bisporus, the growth curve of the main spoilage microorganisms was studied under isothermal conditions at 2 to 22°C with a modified Gompertz model. The effect of temperature on the growth parameters for the main spoilage microorganisms was quantified and modeled using the square root model. Pseudomonas spp. were the main microorganisms causing A. bisporus decay, and the modified Gompertz model was useful for modelling the growth curve of Pseudomonas spp. All the bias factors values of the model were close to 1. By combining the modified Gompertz model with the square root model, a prediction model to estimate the shelf life of A. bisporus as a function of storage temperature was developed. The model was validated for A. bisporus stored at 6, 12, and 18°C, and adequate agreement was found between the experimental and predicted data.

Growth and Modeling of Staphylococcus aureus in Flour Products under Isothermal and Nonisothermal Conditions

This study was conducted to investigate the growth of Staphylococcus aureus in traditional Chinese flour products under isothermal (10, 15, 20, 25, 30, and 37°C) and nonisothermal (10 to 20, 20 to 30, and 25 to 37°C) conditions. Then, models for the growth of S. aureus in flour products as a function of storage temperature, pH, and water activity (a_w) were developed, and the goodness of fit of models was evaluated using the determination coefficient (R²), root mean square error (RMSE), bias factor (B_f), and accuracy factor (A_f). Based on the above information, S. aureus growth in steamed bread under nonisothermal conditions was predicted from experiments performed under isothermal conditions. It was shown that different combinations of temperature and a_w in flour products have a strong influence on the growth of S. aureus . The modified Gompertz model was found to be more suitable for describing the growth data of S. aureus in flour products, with an R² of >0.99 and an RMSE of <0.37. The newly developed secondary models were validated, and for the specific growth rate and the lag time, the R² values were 0.96 and 0.97, A_f was 1.12 and 1.06, and B_f was 1.13 and 1.05, respectively. The predicted nonisothermal growth curves of S. aureus were in agreement with the reported experimental ones, with RMSE <0.29, A_f value 1.02 to 1.09, and B_f value 0.92 to 0.99. These results indicated that the predictive models provided useful information for the establishment of safety standards and a risk assessment for S. aureus in flour products.

Methodology for modeling the microbial contamination of air filters

In this paper, we propose a theoretical model to simulate microbial growth on contaminated air filters and entrainment of bioaerosols from the filters to an indoor environment. Air filter filtration and antimicrobial efficiencies, and effects of dust particles on these efficiencies, were evaluated. The number of bioaerosols downstream of the filter could be characterized according to three phases: initial, transitional, and stationary. In the initial phase, the number was determined by filtration efficiency, the concentration of dust particles entering the filter, and the flow rate. During the transitional phase, the number of bioaerosols gradually increased up to the stationary phase, at which point no further increase was observed. The antimicrobial efficiency and flow rate were the dominant parameters affecting the number of bioaerosols downstream of the filter in the transitional and stationary phase, respectively. It was found that the nutrient fraction of dust particles entering the filter caused a significant change in the number of bioaerosols in both the transitional and stationary phases. The proposed model would be a solution for predicting the air filter life cycle in terms of microbiological activity by simulating the microbial contamination of the filter.