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

Emma Southall; Michael J. Tildesley; Louise Dyson

An area that still needs to be addressed with this methodology of smoothing new 383 case data is determining a suitable window size. This could result to misleading EWS 384 when used in practice. In the supporting text S1 Fig, we demonstrate that if the disease 385 is approaching elimination at a slower rate, both methods ("true" and "approximated") 386 converge to the analytical solution. We chose parameters such that Model 1 approaches 387 disease elimination at the same rate as Model 3 approaches disease emergence (R 0 388 changes from 1.2 to 0, β {1} 0 = 0.24). As the system changes slowly enough then the 389 system will be approximately ergodic, such that the moving average resembles the mean 390 incidence. Thus the "approximated" method will be closer to the "true" solution. In 391 comparison, the faster a system changes over time, will correspond to a wider range in 392 incidence cases across the moving window. Resulting in a lower mean over the window 393 which can be seen in Fig. 2(a),(b) ; although the statistic will be more pronounced at 394 the threshold. 395 We find that for Model 2 (Fig. 2(b) ) the general trend of the variance is less 396 pronounced at the critical transition than observed for Model 1. We observe that the 397 analytical solution (Fig. 2(b) orange line) and true stochastic simulations (Fig. 2(b) 398 purple) only slightly increase before the critical transition, implying this trend would be 399 difficult to detect in real-world data. In particular, the Kendall-tau score which can be 400 an indication of an increasing trend, is negative (decreasing, τ = −1) for Model 2, 401 whilst for Model 1 and 3 we find that τ = 0.987 and τ = 1 respectively. Although, we 402 observe that the "approximated" simulations of the rate of incidence (Fig. 2(b) blue 403 line) exhibit similar properties as Model 1. We observe that the early stage dynamics of 404 this method have not predicted the expected behaviour of the analytical solution. It can 405 be noted that R 0 decreases at the same rate as Model 1, suggesting that this can be a 406 result of the approximation when R 0 is not slowly changing. Due to this approximation, 407 it can be observed that the variance of new cases does therefore increase before the The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.04.02.021576 doi: bioRxiv preprint critical transition (blue line).