Numerical solution of a microbial growth model applied to dynamic environments.

Area of Science:

• Food science
• Microbiology
• Mathematical modeling

Background:

• The Baranyi and Roberts model is a widely used tool for predicting microbial growth.
• Dynamic conditions, such as fluctuating temperatures, present challenges for traditional model applications.
• Existing numerical solutions often require specialized software.

Purpose of the Study:

• To develop a simplified numerical solution for the Baranyi and Roberts model.
• To enable microbial growth simulations under dynamic conditions using accessible software like Microsoft Excel.
• To validate the accuracy of the simplified model against established methods.

Main Methods:

• Derivation of a simplified numerical solution for the coupled differential equations of the Baranyi and Roberts model.
• Simulation of microbial growth under dynamic temperature conditions using Microsoft Excel.
• Parameter identification by fitting the numerical solution to simulated growth curves using the Excel Solver.
• Comparison of results with simulations performed using MATLAB Solver.

Main Results:

• The simplified numerical solution accurately simulated microbial growth under dynamic conditions.
• Results obtained using Microsoft Excel were consistent with those from MATLAB Solver.
• The Microsoft Excel Solver effectively identified model parameters for dynamic temperature scenarios.

Conclusions:

• A simplified, accessible method for applying the Baranyi and Roberts model under dynamic conditions has been established.
• Microsoft Excel can be effectively utilized for microbial growth modeling and parameter estimation.
• This approach facilitates broader application of microbial growth models in food safety and research.