Detecting critical slowing down in high-dimensional epidemiological systems.

Tobias Brett,Quan-Hui Liu,Mary G Krauland,Willem G Van Panhuis,Alessandro Vespignani,John M Drake,Pejman Rohani,John J Grefenstette,Marco Ajelli

doi:10.1371/journal.pcbi.1007679

Abstract

Despite medical advances, the emergence and re-emergence of infectious diseases continue to pose a public health threat. Low-dimensional epidemiological models predict that epidemic transitions are preceded by the phenomenon of critical slowing down (CSD). This has raised the possibility of anticipating disease (re-)emergence using CSD-based early-warning signals (EWS), which are statistical moments estimated from time series data. For EWS to be useful at detecting future (re-)emergence, CSD needs to be a generic (model-independent) feature of epidemiological dynamics irrespective of system complexity. Currently, it is unclear whether the predictions of CSD—derived from simple, low-dimensional systems—pertain to real systems, which are high-dimensional. To assess the generality of CSD, we carried out a simulation study of a hierarchy of models, with increasing structural complexity and dimensionality, for a measles-like infectious disease. Our five models included: i) a nonseasonal homogeneous Susceptible-Exposed-Infectious-Recovered (SEIR) model, ii) a homogeneous SEIR model with seasonality in transmission, iii) an age-structured SEIR model, iv) a multiplex network-based model (Mplex) and v) an agent-based simulator (FRED). All models were parameterised to have a herd-immunity immunization threshold of around 90% coverage, and underwent a linear decrease in vaccine uptake, from 92% to 70% over 15 years. We found evidence of CSD prior to disease re-emergence in all models. We also evaluated the performance of seven EWS: the autocorrelation, coefficient of variation, index of dispersion, kurtosis, mean, skewness, variance. Performance was scored using the Area Under the ROC Curve (AUC) statistic. The best performing EWS were the mean and variance, with AUC > 0.75 one year before the estimated transition time. These two, along with the autocorrelation and index of dispersion, are promising candidate EWS for detecting disease emergence.

Highlights

Critical slowing down (CSD) is a dynamical feature of systems approaching phase transitions, and has been investigated both theoretically [1,2,3,4,5,6,7] and experimentally [8,9,10,11,12,13,14] across the natural sciences
To assess the generality of CSD, we carried out a simulation study of a hierarchy of models of a re-emerging measles-like infectious disease
We found that CSD is present in the dynamics of all the models studied, supporting its generality

Summary

Introduction

Critical slowing down (CSD) is a dynamical feature of systems approaching phase transitions, and has been investigated both theoretically [1,2,3,4,5,6,7] and experimentally [8,9,10,11,12,13,14] across the natural sciences. The ubiquity of CSD has led to suggestions that the phenomenon may be exploited to develop mechanism-independent methods of anticipating impending transitions [5] This has spurred the examination of various summary statistics that can detect the presence of CSD in time series data and may serve as early-warning signals (EWS) [5,6,7, 9,10,11,12,13,14]. The existence of CSD as Reff approaches 1 has been comprehensively demonstrated in a range in low-dimensional epidemiological models (see for instance Fig 1c), including those with: seasonality in transmission [27], imperfectly reported data [28, 29], declining vaccine uptake [6] and vector-borne transmission [30].

Objectives

Methods

Results

Discussion

Conclusion