Transient indicators of tipping points in infectious diseases

Abstract

The majority of known early warning indicators of critical transitions rely on asymptotic resilience and critical slowing down. In continuous systems, critical slowing down is mathematically described by a decrease in magnitude of the dominant eigenvalue of the Jacobian matrix on the approach to a critical transition. Here, we show that measures of transient dynamics, specifically, reactivity and the maximum of the amplification envelope, also change systematically as a bifurcation is approached in an important class of models for epidemics of infectious diseases. Furthermore, we introduce indicators designed to detect trends in these measures and find that they reliably classify time series of case notifications simulated from stochastic models according to levels of vaccine uptake. Greater attention should be focused on the potential for systems to exhibit transient amplification of perturbations as a critical threshold is approached, and should be considered when searching for generic leading indicators of tipping points. Awareness of this phenomenon will enrich understanding of the dynamics of complex systems on the verge of a critical transition.

Deep learning for early warning signals of regime shifts

“…processes 30 . However, the early warning signal is apparent in the variable x for the prevalence of pro-vaccine opinion, and the DL algorithm outperforms both lag-1 AC and variance in this respect.…”

“…For the SEIRx coupled behaviour-disease model, all of the classifiers are little better than random in the model variable for the number of infectious persons ( I , Figure 2e). This occurs due to non-normality of the system associated with differing timescales for demographic and epidemiological processes 30 . However, the early warning signal is apparent in the variable x for the prevalence of pro-vaccine opinion, and the DL algorithm outperforms both lag-1 AC and variance in this respect.…”

“…Other early warning approaches have been developed to predict the type of regime shift 18,20,30 . However, these approaches tend to be system-specific.…”

“…Simulations were perturbed weekly with σ i = 5 for i = 1 … 4, and σ 5 = 5 × 10 −4 . On account of the large timescale difference in vital dynamics and infection processes, the systems is non-normal 30 . We note that S + E + I + R = 1 and therefore since R can be obtained as R = 1 − S − E − I , the model is four dimensional.…”

Overlapping Time Scales Obscure Early Warning Signals of the Second COVID-19 Wave

“…The threshold R t = 1 corresponds to a (dynamic) transcritical bifurcation, which is a type of bifurcation that is preceded by critical slowing down (Kéfi et al, 2014;Kuehn, 2011). Early warning indicators based on critical slowing down have been studied extensively and led to a promising research line that aims to utilize them as a tool to forecast the (re)emergence as well as the elimination of infectious diseases (e.g., Brett et al, 2017;Brett et al, 2018;Dessavre et al, 2019;Dibble et al, 2016;Drake et al, 2019;Harris et al, 2020;Miller et al, 2017;O'Dea et al, 2018;O'Regan & Burton, 2018;O'Regan & Drake, 2013;O'Regan et al, 2020;Southall et al, 2020). Accordingly, some researchers have suggested that they could have been used to anticipate the second wave of COVID-19 (Liu et al, 2021;O'Brien & Clements, 2021;Proverbio et al, 2021).…”