Parameter Dependence in Identifiability Applied to FP-Fisher-KPP Reaction-Diffusion Equations Parameterized for Tauopathy Network Modeling

Parameterization and a priori identifiability analysis are two interconnected steps that should be carried out in advance of model calibration. In the first place, we propose a framework for parameterizing a recently introduced and analytically studied generalization of the celebrated Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) reaction-diffusion (Re-Di) equation with fractional polynomial (FP) terms to model heterogeneous nonlinear diffusion in the propagation of a given species through directed networks, exemplified by the tauopathy progression in Alzheimers disease (AD). Next, we present our results on identifiability in a generic sense for the parameterized FP-Fisher-KPP Re-Di equations with regular multi-experimental designs, seamlessly applicable to meromorphic systems, encompassing analytic systems. In particular, the concept of generic local minimal dependence of unknown parameters and regularly parameterized initial conditions will be formalized through the use of one-parameter Lie groups of transformations, and a decomposition method to explore this new concept will be devised. Finally, the Allen Mouse Brain Connectivity Atlas (AMBCA) dataset is utilized to develop a model for tauopathy progression in the mouse brain, which will subsequently be employed to implement the proposed methodology for analyzing a priori identifiability.