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Quantifying uncertainty in partially specified biological models: how can optimal control theory help us?

M W Adamson¹, A Y Morozov², O A Kuzenkov³

¹Department of Mathematics , University of Leicester , Leicester LE1 7RH , UK.

Proceedings. Mathematical, Physical, and Engineering Sciences

|October 8, 2016

Summary

Mathematical models in biology face uncertainty due to simplified functions. This study introduces a new framework using optimal control theory to project function spaces, enabling robust uncertainty analysis in biological models.

Keywords:

bifurcation portrait predator–prey model predictability sensitivity analysis stability

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Area of Science:

Mathematical Biology
Computational Biology
Systems Biology

Background:

Biological models are simplified representations with inherent uncertainty in function specification.
Structural sensitivity in models, where different functions yield varied predictions, critically impacts reliability.
Existing frameworks struggle to address uncertainty propagation from model functions to predictions.

Purpose of the Study:

To develop a novel framework for uncertainty analysis in biological models.
To address the challenge of projecting infinite-dimensional function spaces into lower dimensions using biological constraints.
To enable more flexible and user-friendly uncertainty quantification for biological models.

Main Methods:

Utilizing partially specified models where functions are not rigidly defined.
Employing optimal control theory to construct functions that satisfy specified global properties.
Projecting function spaces while incorporating biological constraints to manage complexity.

Main Results:

Demonstration of a powerful technique for function space projection.
Successful application of optimal control theory for constructing biologically relevant functions.
Establishment of a method to handle uncertainty arising from model function specification.

Conclusions:

The proposed framework offers a flexible approach to uncertainty analysis in biological modeling.
Optimal control theory provides a viable solution for the projection challenge in partially specified models.
This method enhances the reliability and interpretability of predictions from complex biological models.