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Structural identifiability analysis of age-structured PDE epidemic models.
Marissa Renardy1, Denise Kirschner2, Marisa Eisenberg3,4
1Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, USA. renardy@umich.edu.
Journal of Mathematical Biology
|January 4, 2022
Summary
We developed a new method for analyzing the identifiability of age-structured partial differential equation (PDE) models. This framework helps determine how well model parameters can be estimated from data, crucial for reliable predictions.
Area of Science:
- Mathematical Biology
- Computational Biology
- Epidemiology
Background:
- Model parameter estimation is vital for computational and mathematical models.
- Identifiability analysis assesses parameter estimability from data, ensuring reliable predictions.
- Structural identifiability of ordinary differential equation (ODE) models is well-established, but less so for age-structured partial differential equation (PDE) models.
Purpose of the Study:
- To establish a pipeline for structural identifiability analysis of age-structured PDE models.
- To derive identifiability results for specific age-structured models.
- To demonstrate the framework using epidemic models and compare PDE with ODE systems.
Main Methods:
- Utilized a differential algebra framework for structural identifiability analysis.
- Applied the pipeline to age-structured PDE models, specifically a Susceptible-Exposed-Infected (SEI) epidemic model.
- Compared identifiability results between PDE and corresponding ODE models and explored age-dependent parameter effects.
Main Results:
- Successfully established a pipeline for structural identifiability analysis of age-structured PDE models.
- Derived identifiability results for specific age-structured models, demonstrating the framework's utility.
- Showcased the application of practical identifiability analysis within the developed framework.
Conclusions:
- The differential algebra framework provides a robust method for analyzing the structural identifiability of age-structured PDE models.
- The framework facilitates a deeper understanding of parameter estimability in complex biological systems.
- This work bridges a gap in identifiability analysis for PDE models, with implications for various fields including epidemiology.
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