Quantum-like approaches unveil the intrinsic limits of predictability in compartmental models

TL;DR

This paper introduces a quantum-like formalism to analyze epidemic models, revealing that stochasticity inherently limits forecast accuracy, especially around the epidemic peak, regardless of model complexity.

Contribution

It extends classical epidemic models using a quantum-like approach to quantify how stochasticity constrains predictability over time.

Findings

Forecast uncertainty peaks around the epidemic peak.

Stochasticity imposes a natural limit on forecast accuracy.

Uncertainty diminishes at early and late outbreak stages.

Abstract

Obtaining accurate forecasts for the evolution of epidemic outbreaks from deterministic compartmental models represents a major theoretical challenge. Recently, it has been shown that these models typically exhibit trajectories' degeneracy, as different sets of epidemiological parameters yield comparable predictions at early stages of the outbreak but disparate future epidemic scenarios. Here we use the Doi-Peliti approach and extend the classical deterministic SIS and SIR models to a quantum-like formalism to explore whether the uncertainty of epidemic forecasts is also shaped by the stochastic nature of epidemic processes. This approach allows getting a probabilistic ensemble of trajectories, revealing that epidemic uncertainty is not uniform across time, being maximal around the epidemic peak and vanishing at both early and very late stages of the outbreak. Our results therefore show that, independently of the models' complexity, the stochasticity of contagion and recover processes poses a natural constraint for the uncertainty of epidemic forecasts.