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

Emma Southall; Michael J. Tildesley; Louise Dyson

These findings support prior work on prevalence and initial work from O'Dea et al. 534 and Brett et al. with incidence-type data. Our analytical exploration of incidence has 535 indicated a new data source, RoI, which can be extracted from incidence timeseries. A 536 potential powerful tool would be to compute variance and CV indicators with different 537 types of data (incidence, rate of incidence and prevalence) and ensemble these. An 538 ensemble or combination of multiple statistical indicators was suggested by Drake & 539 Griffen [13] and has been applied to case studies with the same data-type and a 540 combination of EWS by Kefi et al. [30] to help interpret between different critical 541 transitions and also has successfully detected transitions using an ensemble of different 542 time series data [12] . This suggests a potential approach to achieve a single metric from 543 a combination of indicators calculated on multiple timeseries data with different trends, 544 such as we have observed with incidence and RoI, to achieve a more pronounced 545 indication of disease transitions. 546 Additionally, further work would be to include a heterogeneous ensemble as 547 suggested by O'Dea et al. [4] , whereby all parameters are sampled randomly for each 548 realisation rather than being equal. This will lead to more realistic results, as each 549 parameter sample represents time series data from different locations, as suggested by 550 studies on spatial statistics, a promising method for addressing limited data [8, 17, 18] . 551 Comparatively, we have shown here that computing the statistics on a homogeneous 552 ensemble although unrealistic, it returns exact stochastic behaviours of the system and 553 we used this to verify the simulated study with the theory.