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Related Experiment Video

Updated: May 8, 2026

Experimental Methods to Study Human Postural Control

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

Parameter non-identifiability of the Gyllenberg-Webb ODE model.

Niklas Hartung¹

¹Aix-Marseille Université, CMI 39 rue Frédéric Joliot-Curie, 13453 , Marseille cedex 13, France, niklas.hartung@univ-amu.fr.

Journal of Mathematical Biology

|August 31, 2013

Summary

This study analyzes the Gyllenberg-Webb tumor growth model, finding infinite solutions for cell state transition functions. This leads to a unique solution proof for the ordinary differential equation (ODE) model, even in complex cases.

Related Experiment Videos

Last Updated: May 8, 2026

Experimental Methods to Study Human Postural Control

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

Area of Science:

Mathematical Biology
Tumor Growth Modeling
Differential Equations

Background:

The Gyllenberg-Webb ordinary differential equation (ODE) model describes tumor growth via proliferating and quiescent cell dynamics.
Transition rates between cell states are modeled by functions dependent on tumor size, but these are not directly observable.

Purpose of the Study:

To investigate the identifiability of the transition functions (r0, ri) in the Gyllenberg-Webb ODE model.
To classify the infinite pairs of functions (r0, ri) that yield the same model solution.
To prove the uniqueness of the ODE model solution, particularly in non-Lipschitz conditions.

Main Methods:

Analysis of the Gyllenberg-Webb ODE model.
Classification of function pairs (r0, ri) based on model solution equivalence.
Development of a novel technique for uniqueness proofs in ODE models.

Main Results:

An infinite number of function pairs (r0, ri) can produce identical solutions for the ODE model.
The classification technique enables a uniqueness proof for the ODE model solution, even in non-Lipschitz scenarios.
The methodology extends to generalized models, including those with nonlinear birth rates.

Conclusions:

The study clarifies the non-identifiability of transition functions in the Gyllenberg-Webb model.
A new method provides a uniqueness proof for ODE tumor growth models.
Results have implications for preclinical applications and advanced tumor growth modeling.