On modeling and simulating transitions between microbial growth and inactivation or vice versa

Area of Science:

• Microbiology
• Mathematical Modeling
• Biostatistics

Background:

• Microbial populations can exhibit resumed growth after stress or mortality under increasing stress.
• Transitions between growth and inactivation are common in microbial dynamics.
• Conventional models struggle with determining coefficients from isothermal data.

Purpose of the Study:

• To simulate continuous transitions between microbial growth and inactivation.
• To address mathematical challenges in fitting empirical models for microbial dynamics.
• To demonstrate a modified numerical procedure for solving rate equations.

Main Methods:

• Simulation of growth-to-inactivation and inactivation-to-growth transitions.
• Utilized log-linear, Weibullian-power law, and logistic models (shifted logistic, Baranyi-Roberts, shifted arctan).
• Employed a modified numerical procedure to solve rate equations, addressing issues with negative numbers in log/power operations.

Main Results:

• Successfully simulated continuous transitions between microbial growth and inactivation.
• Demonstrated the efficacy of modified numerical solutions for empirical microbial models.
• Overcame mathematical limitations in fitting models like Weibull and logistic functions.

Conclusions:

• Modified numerical procedures enable accurate simulation of microbial growth and inactivation dynamics.
• This approach facilitates the application of empirical models when analytical solutions are not feasible.
• The study provides a robust method for analyzing microbial responses to environmental changes.