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Defining and detecting structural sensitivity in biological models: developing a new framework.

M W Adamson1, A Yu Morozov

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Mathematical models of biological systems face uncertainty. This study introduces a new method to reveal structural sensitivity, improving biological model predictions by analyzing function shapes, not just parameters.

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Area of Science:

  • Mathematical Biology
  • Ecological Modeling
  • Systems Biology

Background:

  • Mathematical models are crucial for understanding biological systems.
  • Model uncertainty arises from parameter choices and function formulations.
  • Structural sensitivity, where minor function changes yield large prediction differences, hinders model accuracy.

Purpose of the Study:

  • To revisit and compare definitions of structural sensitivity.
  • To propose a novel, powerful method for detecting structural sensitivity.
  • To analyze sensitivity in ecological models and its implications.

Main Methods:

  • Exploration of infinite-dimensional neighborhoods of model functions.
  • Development of a rigorous method to assess sensitivity of local stability.
  • Specification of function neighborhoods using finite local properties with a completeness proof.

Main Results:

  • Demonstration of a powerful technique for revealing structural sensitivity beyond parameter variation.
  • Identification of structural sensitivity in several established multicomponent ecological models.
  • Proof of completeness for a method defining function neighborhoods.

Conclusions:

  • Structural sensitivity is an inherent property of biological models.
  • This sensitivity is a direct result of the complexity of real biological systems.
  • The proposed method offers a more robust approach to analyzing model behavior and improving predictive power.