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

Emma Southall; Michael J. Tildesley; Louise Dyson

In this paper, we advance the current literature to describe generalised signatures of 86 statistical indicators for incidence data, on the approach to a threshold, highlighting the 87 differences between EWS descriptors of incidence and prevalence. Strikingly, our results 88 demonstrate that although EWS of emergence exhibit an increasing variance, a trait demonstrate that variance instead decreases on the approach to a disease elimination 91 transition. We find that although incidence data does not undergo the transcritical 92 bifurcation traditionally considered by CSD theory, nevertheless time series trends are 93 still a valuable tool to predict disease elimination. The discrepancy between prevalence 94 and incidence on the one hand, and elimination and emergence on the other, could lead 95 to potential problems in detecting thresholds if the differences are not clearly 96 understood. 97 We introduce an analytical theory from stochastic processes to address why variance 98 in incidence decreases for disease elimination. We study multiple other indicators of disease elimination predicted by this theory, and compare their responses with 100 stochastic simulations. We also consider the rate of incidence as a measurement that 101 can be extracted from incidence data. Notably, we find that on the approach to a 102 critical transition the rate of incidence exhibits typical CSD signatures which 103 correspond with prevalence data, such as an increasing variance. We present a broad 104 analytical framework for EWS of incidence and rate of incidence for a variety of 105 different disease systems. We explore more intricate systems where elimination is driven 106 by different factors to understand the robustness of this theory. This simple generalised 107 result can be applied to many infectious diseases undergoing emergence or elimination, 108 a promising development for EWS of infectious diseases.