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

Emma Southall; Michael J. Tildesley; Louise Dyson

One of the greatest challenges in society today is the burden of infectious diseases, 2 affecting public health and economic stability all over the world. Infectious diseases 3 disproportionately affect individuals in poverty, with millions of those suffering daily 4 from diseases that are considered eradicable. The potential for eradicating diseases such 5 as polio, guinea worm, measles, mumps or rubella is immense (International Task Force 6 for Disease Elimination, [31] ). Even where effective vaccines or treatments exist, disease it was later abandoned in 1969 due to funding shortages and drug resistance [26] , 10 leading to re-emergence of disease in Europe [27] . Assessing when a disease is close 11 enough to elimination to die out without further intervention, thus prompting the end 12 of a control campaign, is a problem of global economic importance. If campaigns are 13 stopped prematurely it can result in disease resurgence and subsequently put control 14 efforts back by decades. Conversely, the threat posed by newly emerging diseases such 15 as SARs, Ebola or the recent corona-virus outbreak COVID-2019 strains available 16 resources, places restrictions on global movement and disrupts the worlds most 17 vulnerable societies. Identifying which newly-emerging diseases will present a global 18 threat, and which will never cause a widespread epidemic is of critical importance. 19 To overcome the challenges identifying disease elimination or emergence, numerous 20 studies have suggested the use of early warning signals (EWS) [3] [4] [5] [6] [7] [8] . EWS are statistics 21 that may be derived from data that change in a predictable way on the approach to a 22 critical threshold. In epidemiology this threshold is commonly described as the point at 23 which the basic reproduction number, R 0 , passes through R 0 = 1. A system with R 0 24 increasing through 1 describes an emerging or endemic disease whereas R 0 decreasing 25 through 1 results in disease elimination. We seek to find EWS to identify when a 26 disease is approaching such a transition. We may identify such statistics using critical 27 slowing down (CSD) theory, which indicates the imminent approach of a threshold, 28 arising from increasing recovery times of perturbations as a system approaches a critical 29 transition [1, 2] . This increase in recovery time occurs because, as the stability of a 30 steady state changes, such as from a disease free state to emergence or from endemic 31 state to elimination, the dominant eigenvalue of the steady state passes through zero. 32 Since the eigenvalue also determines the relaxation time of the system, this recovery 33 time therefore increases as we approach a critical transition. 34 EWS offer the ability to anticipate a critical transition indirectly in real world noisy 35 time series data, by observing, for example, increasing variance or autocorrelation in the 36 fluctuations around the steady-state [2, 9] . Statistical indicators offer a computationally 37 inexpensive and efficient method for assessing the status of an infectious disease, 38 presenting a simple mechanism for disease surveillance and monitoring of control 39 policies. 40 The development of EWS is an active area of research in many fields, identifying the 41 statistical signatures of abrupt shifts in many dynamical systems. Studies have applied 42 EWS to historical data or laboratory experiments where a tipping point is 43 known [1, 13, 23] ; developed methods for