Analysis of a generalized Fujikawa's growth model

Area of Science:

• Mathematical Biology
• Population Dynamics
• Growth Modeling

Background:

• The standard Fujikawa growth model requires enhancement to accurately capture the initial lag phase observed in many biological populations.
• Existing models often struggle to represent the transition from initial stasis to exponential growth.

Purpose of the Study:

• To generalize the Fujikawa growth model by introducing an adaptation function to improve the representation of the lag phase.
• To analyze the mathematical properties and parameter effects of the proposed generalized model.

Main Methods:

• Development of an autonomous growth model combining power law, saturation, and a novel adaptation function.
• Analysis of model convergence, boundedness, and inflection point characteristics.
• Investigation of parameter influence on lag phase and inflection point existence.
• Analytical determination of lag time using a simplified model approach.

Main Results:

• The adaptation function significantly improves the representation of the lag phase, while the power law term influences exponential growth.
• Model parameters critically affect the existence and characteristics of the lag phase and inflection point.
• Lag phase duration is primarily dependent on the adaptation function's exponent parameter.
• Analytical lag time determination confirmed model assumptions when applied to experimental data.

Conclusions:

• The generalized Fujikawa model with an adaptation function provides a more accurate representation of population growth, particularly during the lag phase.
• The study offers insights into parameter-dependent growth dynamics and a method for analytical lag time calculation.
• The model's applicability was validated through its successful application to experimental data.