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

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journal contribution
posted on 2016-11-25, 09:58 authored by M. W. Adamson, A. Y. Morozov, O. A. Kuzenkov
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.

Funding

This research was supported by the Russian Foundation for Basic Research (RFBR grant no. 13-01-12452 ofi_m2).

History

Citation

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2016, 472 (2193)

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • AM (Accepted Manuscript)

Published in

Proceedings of the Royal Society A: Mathematical

Publisher

Royal Society, The

issn

1364-5021

eissn

1471-2946

Acceptance date

2016-08-18

Available date

2017-09-14

Publisher version

http://rspa.royalsocietypublishing.org/content/472/2193/20150627

Language

en

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