Detecting critical slowing down in high-dimensional epidemiological systems

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. Emerging and re-emerging infectious diseases, such as Ebola and measles, present urgent public health challenges and threaten the progress made towards eliminating the global burden of disease. Consequently, a crucial activity in modern epidemiology is developing methods of anticipating (re-)emerging disease outbreaks. Early-warning signals (EWS) are a proposed method for detecting disease (re-)emergence, based on critical slowing down (CSD), a dynamical phenomenon present in systems approaching transition points. The presence of CSD preceding disease (re-)emergence has been comprehensively demonstrated in a range of low-dimensional epidemiological models. For EWS to be useful, however, CSD needs to be a generic feature of (re-)emerging disease transmission dynamics, rather than being limited to specific models. 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. In addition, we studied seven candidate EWS, and found that four are strong candidates for use in monitoring systems to detect disease (re-)emergence.