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

Emma Southall; Michael J. Tildesley; Louise Dyson

In Fig. 2(c) we observe that both measurements of the variance of λ t calculated on 410 stochastic simulations of Model 3 have closely followed the analytical solution of 411 variance. As expected the true stochastic simulations (Fig. 2(c) purple line) follow 412 closely to the theory, supporting that this derivation of ω is correct. More interestingly, 413 calculating the variance of the rate of incidence directly from simulations of new cases 414 (N t , Fig. 2(c) blue line) has performed far better than when presented in Model 1 (Fig. 415 2(a) ). For Model 3, we observe that the variance of the rate of incidence increases 416 before the critical threshold, where the infectious disease emerges with outbreaking 417 dynamics similar to prevalence for this model. We further found that the early 418 dynamics of the "approximated" RoI simulations represent the true behaviour of the 419 variance. This result may be due to R 0 increasing more slowly in Model 3 than the rate 420 it decreases at in Model 1, satisfying the ergodic condition. In this section, we investigate the potential of identifying an epidemiological transition 423 using five commonly implemented early-warning signals: variance, coefficient of 424 variation (CV), skewness, kurtosis and lag-1 autocorrelation (AC(1)). Exploration of 425 each EWS follows similarly to variance, as analysed above theoretically and numerically 426 for prevalence, incidence and rate of incidence. In the supporting text, time series analyses for these indicators (S1 Appendix).