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An efficient procedure to assist in the re-parametrization of structurally unidentifiable models.
Mathematical Biosciences ( IF 4.3 ) Pub Date : 2020-03-11 , DOI: 10.1016/j.mbs.2020.108328
D Joubert 1 , J D Stigter 1 , J Molenaar 1
Affiliation  

An efficient method that assists in the re-parametrization of structurally unidentifiable models is introduced. It significantly reduces computational demand by combining numerical and symbolic identifiability calculations. This hybrid approach facilitates the re-parametrization of large unidentifiable ordinary differential equation models, including models where state transformations are required. A model is first assessed numerically, to discover potential structurally unidentifiable parameters. We then use symbolic calculations to confirm the numerical results, after which we describe the algebraic relationships between the unidentifiable parameters. Finally, the unidentifiable parameters are substituted with new parameters and simplification ensures that all the unidentifiable parameters are eliminated from the original model structure. The novelty of this method is its utilisation of numerical results, which notably reduces the number of symbolic calculations required. We illustrate our procedure and the detailed re-parametrization process in 5 examples: (1) an immunological model, (2) a microbial growth model, (3) a lung cancer model, (4) a JAK/STAT model, and (5) a small linear model with a non-scalable re-parametrization.

中文翻译:

一种有效的过程,可帮助重新确定结构上无法识别的模型的参数。

介绍了一种有效的方法,该方法有助于对结构上无法识别的模型进行重新参数化。通过组合数字和符号可识别性计算,它显着减少了计算需求。这种混合方法有助于重新确定大型不可识别的常微分方程模型,包括需要状态转换的模型。首先对模型进行数字评估,以发现潜在的结构上无法识别的参数。然后,我们使用符号计算来确认数值结果,然后我们描述不可识别参数之间的代数关系。最后,将无法识别的参数替换为新参数,并且简化操作可确保从原始模型结构中消除所有无法识别的参数。这种方法的新颖之处在于它利用了数值结果,从而显着减少了所需的符号计算次数。我们在5个示例中说明了我们的程序和详细的重新参数化过程:(1)免疫模型,(2)微生物生长模型,(3)肺癌模型,(4)JAK / STAT模型,以及(5 )具有不可缩放的重新参数化的小型线性模型。
更新日期:2020-03-11
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