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

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES
Alexander P. Browning, Maria Taşcă, Carles Falcó, Ruth E. Baker
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引用次数: 0

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 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, consideration of spatial analogues of non-spatial models cannot exacerbate structural identifiability. We conclude by discussing future possibilities and the computational cost of performing structural identifiability analysis on more general PDE models.

数学生物学中线性反应-平流-扩散过程的结构可识别性分析
要有效地应用数学模型来解释生物数据并做出准确的预测,通常需要模型参数是可识别的。评估模型的所谓结构可识别性的方法已在常微分方程模型中得到广泛应用,但对于偏微分方程(PDE)模型的结构可识别性却没有普遍采用的方法,而偏微分方程模型是捕捉许多现象固有的空间特征所必需的。结构可识别性的微分代数方法最近被证明适用于几个特定的偏微分方程模型。在这篇短文中,我们介绍了对部分观测到的反应-平流-扩散 PDE 模型进行结构可识别性分析的一般方法,这些模型在未观测量中是线性的。我们表明,微分代数方法在理论上总是可以应用于这类模型。此外,尽管增加平流和扩散项会带来复杂性,但考虑非空间模型的空间类比并不会加剧结构可识别性。最后,我们讨论了对更一般的 PDE 模型进行结构可识别性分析的未来可能性和计算成本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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