Prospects for detecting early warning signals in discrete event sequence data: Application to epidemiological incidence data

Abstract

Early warning signals (EWS) identify systems approaching a critical transition, where the system undergoes a sudden change in state. For example, monitoring changes in variance or autocorrelation offers a computationally inexpensive method which can be used in real-time to assess when an infectious disease transitions to elimination. EWS have a promising potential to not only be used to monitor infectious diseases, but also to inform control policies to aid disease elimination. Previously, potential EWS have been identified for prevalence data, however the prevalence of a disease is often not known directly. In this work we identify EWS for incidence data, the standard data type collected by the Centers for Disease Control and Prevention (CDC) or World Health Organization (WHO). We show, through several examples, that EWS calculated on simulated incidence time series data exhibit vastly different behaviours to those previously studied on prevalence data. In particular, the variance displays a decreasing trend on the approach to disease elimination, contrary to that expected from critical slowing down theory; this could lead to unreliable indicators of elimination when calculated on real-world data. We derive analytical predictions which can be generalised for many epidemiological systems, and we support our theory with simulated studies of disease incidence. Additionally, we explore EWS calculated on the rate of incidence over time, a property which can be extracted directly from incidence data. We find that although incidence might not exhibit typical critical slowing down properties before a critical transition, the rate of incidence does, presenting a promising new data type for the application of statistical indicators.

Fig 1. Comparing predictions to simulations for variance.

For each model (SIS with social distancing; SIS with vaccination; SIS emergence) we calculate the variance between 500 homogeneous realisations at every time step (daily). Each figure shows: Poisson process distribution (green line); dynamic predictions (red line) and Gillespie simulations (blue line). The bottom left panel also shows the dynamical prediction from O’Dea et al. which was derived for this specific system (lilac line).

Fig 2. Variance calculated on the rate of incidence.

For each model (SIS with social distancing (panel a); SIS with vaccination (panel b); SIS emergence(panel c)) we calculate the variance on the rate of incidence, RoI between 500 homogeneous realisations at every time step (daily). Each figure shows: dynamic solution (orange line); rolling RoI calculated from new cases n_c (blue line) and true RoI calculated from the production of prevalence, susceptible and effective contact rate ($\lambda \left(t\right)=\frac{\beta SI}{N}$, purple line).

Fig 3. AUC scores for different EWS.

We compare the performance of 5 common statistical indicators for SIS with social distancing (a) for disease elimination and SIS emergence (b). The Rate of Incidence is taken to be the “rolling” RoI.