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Title: Quantifying uncertainty in partially specified biological models: How can optimal control theory help us?
Authors: Adamson, M. W.
Morozov, A. Y.
Kuzenkov, O. A.
First Published: 14-Sep-2016
Publisher: Royal Society, The
Citation: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2016, 472 (2193)
Abstract: Mathematical models in biology are highly simplified representations of a complex underlying reality and there is always a high degree of uncertainty with regards to model function specification. This uncertainty becomes critical for models in which the use of different functions fitting the same dataset can yield substantially different predictions-a property known as structural sensitivity. Thus, even if the model is purely deterministic, then the uncertainty in the model functions carries through into uncertainty in model predictions, and new frameworks are required to tackle this fundamental problem. Here, we consider a framework that uses partially specified models in which some functions are not represented by a specific form. The main idea is to project infinite dimensional function space into a low-dimensional space taking into account biological constraints. The key question of how to carry out this projection has so far remained a serious mathematical challenge and hindered the use of partially specified models. Here, we propose and demonstrate a potentially powerful technique to perform such a projection by using optimal control theory to construct functions with the specified global properties. This approach opens up the prospect of a flexible and easy to use method to fulfil uncertainty analysis of biological models.
DOI Link: 10.1098/rspa.2015.0627
ISSN: 1364-5021
eISSN: 1471-2946
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Creative Commons “Attribution Non-Commercial No Derivatives” licence CC BY-NC-ND, further details of which can be found via the following link: Archived with reference to SHERPA/RoMEO and publisher website.
Appears in Collections:Published Articles, Dept. of Mathematics

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