G-CRS model: a new generalized growth model with theory and applications

Abstract This study introduces a novel generalized growth model, referred to as the G-CRS model, which includes two adjustable parameters: $t_{0}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>t</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> , denoting the time delay, and k , which influences the growth curvature. The introduction of these parameters markedly increases the model’s flexibility in capturing real-world growth patterns with lag phases and changing acceleration dynamics. For the new model, essential theoretical aspects such as the inflection point, lag time, and maximum growth rate are analytically derived. A simulation-based sensitivity analysis reveals the unique and complementary effects of $t_{0}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>t</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> and k on the model’s dynamics. The performance of the G-CRS model is assessed using both simulated data and various real-world datasets from biological, demographic, and epidemiological fields. Goodness-of-fit is evaluated employing standard accuracy metrics, including R 2 , MAE, RMSE, and MAPE. The findings suggest that the G-CRS model offers a flexible and robust framework for effectively capturing complex growth patterns across a diverse array of applications.