Theory of early warning signals of disease emergenceand leading indicators of elimination

Abstract

Anticipating infectious disease emergence and documenting progress in disease elimination are important applications for the theory of critical transitions. A key problem is the development of theory relating the dynamical processes of transmission to observable phenomena. In this paper, we consider compartmental susceptibleinfectious-susceptible (SIS) and susceptible-infectiousrecovered (SIR) models that are slowly forced through a critical transition. We derive expressions for the behavior of several candidate indicators, including the autocorrelation coefficient, variance, coefficient of variation, and power spectra of SIS and SIR epidemics during the approach to emergence or elimination. We validated these expressions using individual-based simulations. We further showed that moving-window estimates of these quantities may be used for anticipating critical transitions in infectious disease systems. Although leading indicators of elimination were highly predictive, we found the approach to emergence to be much more difficult to detect. It is hoped that these results, which show the anticipation of critical transitions in infectious disease systems to be theoretically possible, may be used to guide the construction of online algorithms for processing surveillance data.

Criticality and Information Dynamics in Epidemiological Models

“…A maladapted pathogen with R 0 < 1 can cause an epidemic if its R 0 exceeds 1 (due to, for instance, mutations or changes in the host population), which is how new pathogens can emerge by crossing the species barrier [13]. From a phase transition point-of-view, Reference [14] have studied the change in epidemiological quantities while approaching the critical point, in order to see if they can be used for anticipating the emergence of criticality and potential elimination of such dynamics. Their results suggest that theoretically, we can predict critical thresholds in epidemics [14], which could be of a substantial value in health care.…”

“…From a phase transition point-of-view, Reference [14] have studied the change in epidemiological quantities while approaching the critical point, in order to see if they can be used for anticipating the emergence of criticality and potential elimination of such dynamics. Their results suggest that theoretically, we can predict critical thresholds in epidemics [14], which could be of a substantial value in health care. In practice, one of the challenges lies in pinpointing such critical thresholds in finite-size systems, where a precise identification of phase transitions requires an estimation of the rate of change of the order parameter, often from finite and/or distributed data [15,16].…”

Waiting time to infectious disease emergence

“…This critical transition becomes possible when the average number of infections caused by a single infectious individual in an entirely susceptible population (called R 0 ) becomes greater than 1-at this point the population is often referred to as supercritical [15,16]. Forecasting this critical transition is the goal of earlywarning systems [17 -19] of disease emergence [12]. In addition to knowing when a population will become supercritical [12], accurate forecasting also requires estimating the time of the first major outbreak or epidemic of a newly emerging or re-emerging disease.…”

Spores and soil from six sides: interdisciplinarity and the environmental biology of anthrax (Bacillus anthracis)

“…However, ENMs operate on a broader temporal scale than required for short‐term outbreak anticipation efforts. Early warning systems (EWSs), based on leading indicators (O'Regan & Drake, ; Brett, Drake & Rohani, ) or on climatic covariates (Thomson et al ., ; Semenza et al ., ), address the problem of outbreak prediction on a shorter timescale, and are a high priority for development for many diseases – but to our knowledge, these models have yet to be developed and deployed for anthrax. The existence of long‐term outbreak data sets from long‐term research sites like Etosha or Kruger could likely support the development of these tools, but the transferability of these models to other regions would be limited both by the selection of statistical fitting procedures, and by differences in the underlying eco‐epidemiological process across systems.…”