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A note on tools for prediction under uncertainty and identifiability of SIR-like dynamical systems for epidemiology

Chiara Piazzola and Lorenzo Tamellini and Raúl Tempone,  "A note on tools for prediction under uncertainty and identifiability of SIR-like dynamical systems for epidemiology", arXiv preprint arXiv:2008.01400
Chiara Piazzola, Lorenzo Tamellini, and Raúl Tempone
Dynamical Systems, Mathematical Epidemiology, Uncertainty Quantification, Model Identifiability, Bayesian Inversion, Fisher Approximation
2020
We provide an overview of the methods that can be used for prediction under uncertainty and data fitting of dynamical systems, and of the fundamental challenges that arise in this context. The focus is on SIR-like models, that are being commonly used when attempting to predict the trend of the COVID-19 pandemic. In particular, we raise a warning flag about identifiability of the parameters of SIR-like models; often, it might be hard to infer the correct values of the parameters from data, even for very simple models, making it non-trivial to use these models for meaningful predictions. Most of the points that we touch upon are actually generally valid for inverse problems in more general setups.​