Modeling M. tuberculosis Response to Antibiotics: A Comparison of Logarithmic, Logistic, and Michaelis-Menten Models

Background: Antimicrobial resistance (AMR) poses a serious threat to global public health and requires truthful measurement to assess bacterial susceptibility to antibiotics. Mathematical modeling is a useful tool for quantifying and predicting antimicrobial susceptibility and its relationship to other features. Method:: This study aimed to identify the most appropriate mathematical model for the relationship between Minimum Inhibitory Concentration (MIC) and bacterial susceptibility. The models assessed were the Michaelis–Menten model, the logistic growth model and the logarithmic regression model. To ensure objective and comprehensive comparisons, various statistical indicators were used, including coefficient of determination (R²), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and the Akaike Information Criterion (AIC). Result: The logarithmic regression model provided the best fit to the data. It yielded the highest R² value and the lowest MSE, RMSE and AIC values compared to Michaelis–Menten and logistic growth models. On the other hand, the logistic growth model provided the poorest fit, with the lowest R² and the largest prediction errors. Although the Michaelis–Menten model outperformed the logistic growth model, the logarithmic regression model consistently achieved lower error metrics and provided a more accurate and informative representation of the relationship between MIC and bacterial susceptibility. Discussion: The logarithmic regression model performed best; thus, this model is appropriate for modeling antimicrobial susceptibility data. The findings indicate that mathematical modeling is important in AST and has the potential to become a powerful predictive tool in the fight against antibiotic resistance. Conclusion: The logarithmic regression is the strongest and most valid model for describing the relationship between MIC and bacterial susceptibility, and it can be useful for interpreting and predicting antimicrobial susceptibility data.