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

TL;DR

This paper reviews methods for prediction under uncertainty in SIR-like epidemiological models, highlighting challenges in parameter identifiability that affect reliable forecasting of COVID-19 trends.

Contribution

It provides an overview of tools and fundamental challenges in data fitting and prediction for SIR-like models, emphasizing issues of parameter identifiability.

Findings

Parameter identifiability is often problematic in SIR models.

Difficulty in inferring parameters impacts the reliability of predictions.

Challenges discussed are applicable to broader inverse problems.

Abstract

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.