Quantum-Like Approaches Unveil the Intrinsic Limits of Predictability in Compartmental Models

Area of Science:

• Epidemiology
• Theoretical Biology
• Mathematical Modeling

Background:

• Deterministic compartmental models for epidemic forecasting face trajectory degeneracy, where different parameters yield similar early predictions but divergent future scenarios.
• The inherent uncertainty in epidemic forecasts is a significant challenge for public health preparedness.

Purpose of the Study:

• To investigate whether the stochastic nature of epidemic processes contributes to forecast uncertainty.
• To extend classical deterministic compartmental models using a quantum-like formalism.

Main Methods:

• Utilized the Doi-Peliti approach to develop a quantum-like formalism for compartmental models.
• Generated a probabilistic ensemble of epidemic trajectories to analyze uncertainty over time.

Main Results:

• Epidemic forecast uncertainty is not uniform across the outbreak timeline.
• Uncertainty is maximal around the epidemic peak and diminishes at the early and late stages.
• The stochasticity of contagion and recovery processes inherently constrains forecast accuracy.

Conclusions:

• Stochastic processes in epidemics impose a fundamental limit on the predictability of outbreak evolution, irrespective of model complexity.
• A quantum-like formalism provides insights into the temporal dynamics of epidemic forecast uncertainty.