Partial identification of underdetermined compartmental models: a method based on positive linear Lyapunov functions

Area of Science:

• Mathematical modeling
• Systems analysis
• Parameter estimation

Background:

• Models with more parameters than equations present challenges in accurate estimation.
• Simplification strategies are crucial for analyzing complex systems.

Purpose of the Study:

• To investigate the properties of simplified models derived by reducing unknown parameters.
• To explore the implications of setting exit parameters to zero in overparameterized models.

Main Methods:

• Analysis of a class of models where parameters exceed independent equations.
• Application of a method based on positive linear Lyapunov functions.
• Investigating the impact of reducing unknown parameters by setting exit parameters to zero.

Main Results:

• Functions of time for compartment amounts are constant multiples of the fallacious model.
• A subset of fractional transfer coefficients in the simplified model match the true model.
• Other fractional transfer coefficients yield interval bounds.

Conclusions:

• Simplifying overparameterized models by zeroing exit parameters can yield insightful results.
• Lyapunov function-based methods offer a robust approach to analyzing such simplified models.
• The study provides a framework for understanding parameter reduction effects in model analysis.