Predictive models have been used to predict kinetic behavior and to calculate the growth probability of foodborne pathogens under various conditions^{1,2)}. For kinetic modeling, a primary model and a secondary model need to be developed to estimate kinetic parameters of foodborne pathogens such as lag phase duration and growth rate. A primary model describes kinetic behavior over time, and a secondary model describes the effect of environmental factors on the kinetic parameters^{3,4)}. In addition, a probabilistic model has been used to estimate the probabilities of bacterial growth under a variety of factor-combinations^{3,5)}.

Although many predictive models are developed, they are difficult for nonspecialists to understand, especially for industry applications. Thus, the applications of previously developed models have been limited. The advent of computer technology and associated advances in computational power have made it possible to perform complex mathematical calculations that would otherwise be too timeconsuming for useful applications in predictive microbiology ^{6)}. Hence, computer software has been developed to simplify the prediction of growth or inactivation of foodborne pathogens under various conditions. However, this type of software is not considered user-friendly for those who are not specialized in predictive modeling. Thus, although predictive models are useful in processing meat products, this technology is not used in the industry. In addition, even for experts in predictive microbiological modelling, the development of a predictive model is timeconsuming.

Therefore, the objective of this study was to develop a user-friendly modeling software, which is equipped to handle both kinetic and probabilistic models, in order to predict bacterial growth and growth probability by simulating simple meat-product-related conditions.

## Materials and Methods

### Data collection

All the data were collected from our previous research^{7-13)}. A kinetic model was constructed with 5,400 samples of frankfurters for *Pseudomonas* spp., *Listeria monocytogenes* and *Salmonella*, and probabilistic models was constructed with 345,600 samples in broth for *L. monocytogenes*, Staphylococcus aureus, and *Salmonella*.

### Mathematical base

Kinetic models such as primary and secondary models can estimate kinetic parameters. Primary models describe the kinetic behavior of bacteria over time, and secondary models describe the effect of environmental factors on the kinetic parameters^{3,5)}. The primary model was based on a modified Gompertz model^{3,14)}, and the model equation was as follows:

where N_{t} is the cell number at any time t, A is the lower asymptotic line of the growth curve as t decreases to zero, C is the difference between the upper asymptotic line of the growth curve and the lower asymptotic line, B is the relative growth rate at time M, and M is the time at which the growth rate is at a maximum (h). μ_{max}, LPD, and N_{max} can be calculated by the equations:

### Development of predictive modeling software

The predictive modeling software, named FAME (Foodborne bacteria Animal product Modeling Equipment), was developed for predicting bacterial growth on meat products. FAME can calculate bacterial concentrations and bacterial growth probabilities of meat product processing in advance. The software was programmed using Javascript and HTML, and the software was developed for two distinct model types, kinetic models and probabilistic models.

In kinetic models, the cell counts of *L. monocytogenes*, *Pseudomonas* spp., and *Salmonella* spp., can be predicted by entering atmospheric conditions (aerobic or anaerobic), storage temperatures (0-40°C), NaNO_{2} concentrations (0 or 10 ppm), and NaCl concentrations (0-4.0%). In addition, a validation function was incorporated into FAME to compare experimental data and predicted bacterial concentrations.

In probabilistic models, bacterial growth probability (*L. monocytogenes*, *Salmonella* spp., S. aureus) can be predicted based on atmospheric conditions (aerobic or anaerobic), temperatures (0-15°C), NaCl concentrations (0, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50, or 1.75), NaNO_{2} concentrations (0- 150 ppm) and especially at 4°C, 7°C, 10°C, 12°C, and 15°C. The formulation for the validation of the predicted value with experimental data was incorporated into the software. In addition, in both the kinetic and the probabilistic models, all model equations can be edited by a user, and new model equations can be uploaded by a user.

### Application on meat products

In the application of FAME, eight scenarios for *Salmonella* spp. on meat products according to atmospheric conditions, storage temperatures, and NaCl concentrations were compared using the kinetic model (Table 1). In addition, growth probabilities of *Salmonella* spp. were calculated, using the probabilistic model, based on the scenarios.

## Results and Discussion

The user interface developed for FAME is shown Figs. 1- 3. In the kinetic model, the user can choose bacteria (Fig. 1(A)), and then select food atmospheric conditions (aerobic or anaerobic), NaNO_{2} concentrations, NaCl concentrations, assumed initial cell concentrations, maximum cell concentrations, and time intervals (Fig. 1(B)). Users can select ‘growth prediction’ to display the graph and value of predicted cell concentrations according to the database. In addition, if users want to validate their own laboratory data, users can input their experimental data by a simple copyand- paste from Microsoft® Excel into FAME. Then, B*f*, A*f*, and RMSE values are calculated by comparing experimental data and predicted data. Fig. 2

The probabilistic model also allows users to select the name of the bacteria (Fig. 2(A)), as well as variables such as packaging condition, growth probability (10%, 50%, and 90% interfaces), temperature, and NaCl concentration (Fig. 2(B)). When users click ‘growth probability prediction’, the graph of bacterial growth probability is displayed according to the strength of the probability, using blue (10% growth probability), red (50% growth probability), and/or yellow lines (90% growth probability). Users can estimate bacterial growth probability under selected environmental conditions, and the data can be used for determining the best conditions for the safety of meat products.

If users want to change the calculating equation, they can click the ‘setting’ button to edit, and users also can add new equations from their own data (Fig. 3). When editing an equation or adding a new equation, users can immediately confirm the growth prediction graph and cell concentration under certain conditions for both kinetic and probabilistic models.

Using FAME software, users can predict bacterial concentrations in advance and can thus, determine the best conditions for the safety of meat products with specific bacterial concentrations as set in FAME. Table 1 provides data on simple scenarios for the application of FAME for meat products. When users select environmental conditions based on these scenarios, the bacterial growth curve and concentrations according to time are presented. According to the scenarios, the times for 1 Log CFU/g growth on meat products, relative to initial concentrations, are predicted by the kinetic model as 288 h, 54 h, 160 h, 38 h, 510 h, 35 h, 165 h, and 20 h, respectively. Comparing scenarios 1 and 2, when the temperature is increased from 7°C to 15°C, time for 1 Log CFU/g *Salmonella* spp. growth is decreased from 288 h to 54 h in an anaerobic atmosphere. Also, when NaCl concentrations decreased 1.5% to 0.5%, time for 1 Log CFU/g *Salmonella* spp. growth is decreased from 288 h to 160 h at 7°C (scenarios 1 and 3), and from 54 h to 38 h at 15°C in an anaerobic atmosphere (scenarios 2 and 4). In addition, when meat products were packaged aerobically, time for 1 Log CFU/g *Salmonella* spp. growth is increased, compared to an aerobic packaging (scenarios 5-8). With these results, users can predict bacterial growth and determine appropriate plans for food safety for meat products.

## Conclusion

In conclusion, FAME can be useful in the meat processing industry for food safety, especially in terms of its rapid application. In addition, because of its user-friendly interface, even non specialists in predictive modeling can use the software to predict both bacterial concentrations from kinetic models and growth probabilities from probabilistic models.