Limits of epidemic prediction using SIR models

TL;DR

This paper investigates the fundamental limits of predicting epidemic trajectories using SIR models, especially when early, noisy data makes parameter estimation challenging, highlighting theoretical constraints on epidemic forecasting.

Contribution

It offers new theoretical insights into the practical identifiability issues of SIR models and enhances understanding of their inferential limitations in real-world epidemic prediction.

Findings

Theoretical bounds on parameter identifiability in SIR models.

Illustration of implications using real epidemic data.

Enhanced understanding of limits in epidemic forecasting.

Abstract

The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the model parameters based on noisy observations early in the outbreak, well before the epidemic reaches its peak. This allows prediction of the subsequent course of the epidemic and design of appropriate interventions. However, accurately inferring SIR model parameters in such scenarios is problematic. This article provides novel, theoretical insight on this issue of practical identifiability of the SIR model. Our theory provides new understanding of the inferential limits of routinely used epidemic models and provides a valuable addition to current simulate-and-check methods. We illustrate some practical implications through application to a real-world epidemic data set.