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

TL;DR

This paper develops a general methodology using differential algebra to assess the structural identifiability of linear reaction-advection-diffusion PDE models in biology, extending existing approaches from ODE models to PDEs.

Contribution

It introduces a theoretical framework for applying differential algebra to PDE models, ensuring identifiability analysis can be performed on spatially extended biological systems.

Findings

Differential algebra approach is applicable to linear RAD PDE models.

Identifiability cannot decrease when extending models to include spatial features.

The methodology provides a foundation for future analysis of more complex PDE models.

Abstract

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.