Early warning signals of non-critical transitions from linearised time-varying dynamics with applications to epidemic systems

TL;DR

This paper investigates early warning signals for non-critical transitions in epidemic models, demonstrating how fluctuations can predict infection waves without traditional bifurcation indicators, with applications to COVID-19 modeling.

Contribution

It introduces a framework for detecting early warning signals from non-normal dynamics in stochastic epidemic models, expanding beyond classical critical slowing down theory.

Findings

Fluctuation variance and return time can signal impending infection waves.

Non-normal dynamics can produce critical-like behavior without bifurcations.

The approach is demonstrated on the susceptible-infectious-recovered model.

Abstract

In the wake of the SARS-CoV-2 pandemic, there has been heightened interest from applied mathematicians in infectious disease modelling. Modelling efforts often focus on predicting whether diseases are likely to be eliminated or, instead, (re-)emerge, especially as a result of control measures.This tipping point between elimination and infection waves has been successfully anticipated in the literature through the use of early warning signals and such signals often rely on the theory of critical slowing down. Recent developments have shown that these signals (increases in fluctuation variance and return time) can emerge from the system geometry in the case of non-normal dynamics rather than a change in asymptotic stability. We show how such dynamical behaviour occurs in the fluctuations from the mean-field in general stochastic systems. Using the susceptible-infectious-recovered model as an example application, we analyse how critical-like behaviour can be exploited to anticipate infection waves in the absence of an equilibrium bifurcation.