Structural identifiability analysis of linear reaction-advection-diffusion processes in mathematical biology

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Main Authors: Browning, Alexander P, Tască, Maria, Falcó, Carles, Baker, Ruth E
Format: Preprint
Published: 2023
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author Browning, Alexander P
Tască, Maria
Falcó, Carles
Baker, Ruth E
author_facet Browning, Alexander P
Tască, Maria
Falcó, Carles
Baker, Ruth E
contents Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Approaches to assess the so-called structural identifiability of models are well-established for ordinary differential equation models, yet there are no commonly adopted approaches that can be applied to assess the structural identifiability of the partial differential equation (PDE) models that are requisite to capture spatial features inherent to many phenomena. The differential algebra approach to structural identifiability has recently been demonstrated to be applicable to several specific PDE models. In this brief article, we present general methodology for performing structural identifiability analysis on partially observed reaction-advection-diffusion (RAD) PDE models that are linear in the unobserved quantities. We show that the differential algebra approach can always, in theory, be applied to such models. Moreover, despite the perceived complexity introduced by the addition of advection and diffusion terms, identifiability of spatial analogues of non-spatial models cannot decrease in structural identifiability. We conclude by discussing future possibilities and the computational cost of performing structural identifiability analysis on more general PDE models.
format Preprint
id arxiv_https___arxiv_org_abs_2309_15326
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Structural identifiability analysis of linear reaction-advection-diffusion processes in mathematical biology
Browning, Alexander P
Tască, Maria
Falcó, Carles
Baker, Ruth E
Quantitative Methods
Methodology
12H05, 35A24, 35Q92, 62F99
Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Approaches to assess the so-called structural identifiability of models are well-established for ordinary differential equation models, yet there are no commonly adopted approaches that can be applied to assess the structural identifiability of the partial differential equation (PDE) models that are requisite to capture spatial features inherent to many phenomena. The differential algebra approach to structural identifiability has recently been demonstrated to be applicable to several specific PDE models. In this brief article, we present general methodology for performing structural identifiability analysis on partially observed reaction-advection-diffusion (RAD) PDE models that are linear in the unobserved quantities. We show that the differential algebra approach can always, in theory, be applied to such models. Moreover, despite the perceived complexity introduced by the addition of advection and diffusion terms, identifiability of spatial analogues of non-spatial models cannot decrease in structural identifiability. We conclude by discussing future possibilities and the computational cost of performing structural identifiability analysis on more general PDE models.
title Structural identifiability analysis of linear reaction-advection-diffusion processes in mathematical biology
topic Quantitative Methods
Methodology
12H05, 35A24, 35Q92, 62F99
url https://arxiv.org/abs/2309.15326