Rapid parameter estimation of modified Gompertz and Logistic model for analyzing the growth of Escherichia Coli K2

Bacteria are living microorganisms that play an essential role in the biodegradation process. They can break down and detoxify harmful substances, thereby mitigating environmental contamination through natural means. The Gompertz and Logistic models are two growth models commonly utilized to examine population growth in biological systems. In this study, we have modified these models to investigate the growth of Escherichia Coli K2 bacteria. The mathematical parameters have been substituted with biologically meaningful parameters, and five new estimation methods have been introduced to evaluate the model parameters using standard growth data for E. Coli K2. The best method is selected based on a standardized criterion used in this study. The proposed methods demonstrate strong performance, and the estimated parameters are both logically coherent and biologically relevant.