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

Emma Southall; Michael J. Tildesley; Louise Dyson

Rate of incidence 350 We have observed that incidence data does not approach a critical transition as 351 described by critical slowing down theory. Consequently we demonstrated in Figure 1 352 that the variance of incidence does not necessarily increase on the approach to a critical 353 transition. A new approach for working with incidence-type data is to consider the rate 354 of incidence, λ(t) = T (I + 1|I), which for each model we have derived the dynamical The copyright holder for this preprint (which was not peer-reviewed) is the .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 Variance (RoI) 357 The analytical variance in the rate of incidence is presented in Fig. 2 (orange line) . We 358 find that the theoretical analysis supports the simulation studies and provides us with 359 an understanding of how statistical indicators calculated in RoI data change on the 360 approach to a critical transition. We observe an increasing variance in the rate of 361 incidence before a critical transition; a time series trend which if exhibited in real-world 362 data could be used to anticipate disease tipping points. 363 We present results calculated in RoI simulations using the two methods: "true" and 364 "approximated" RoI, in Fig. 2 . The first method uses prevalence data ("true", purple 365 line) and corresponds well with the analytical solution (orange line) for all models and 366 the latter method (smoothing incidence data "approximated", blue line) fits particularly 367 well for Model 3 (Fig. 2(c) ). However it does not follow as closely to some time-varying 368 properties of the variance for Model 1 & 2 ( Fig. 2(a) and (b) ) respectively. Although increasing variance on the approach to the critical transition. In particular, 371 "approximated" RoI can be implemented in practice from incidence type data (blue line), 372 captures this property in all models.