Numerical solution of a microbial growth model applied to dynamic environments

• A simplified numerical solution of the Baranyi and Roberts model was derived.
• It can be used to calculate microbial growth curves and estimate model parameters in Excel.
• It is easy to incorporate into practical applications due to its simplicity.

The Baranyi and Roberts model is one of the most frequently used microbial growth models. It has been successfully applied to numerous studies of various microorganisms in different food products. Under dynamic conditions, the model is implicitly formulated as a set of two coupled differential equations which could be numerically solved using the Runge–Kutta method. In this study, a simplified numerical solution of the coupled differential equations was derived and used to simulate microbial growth under dynamic conditions in Microsoft Excel. As expected, the results obtained were the same as those from solving the coupled differential equations using a MATLAB Solver. In addition, model parameters were accurately identified by fitting the numerical solution to simulated growth curves under dynamic (time-varying) temperature conditions using the Microsoft Excel Solver.