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

Emma Southall; Michael J. Tildesley; Louise Dyson

Therefore, it is highly recommended to understand analytically how EWS change on 488 the approach to a critical transition in order to avoid misleading results. The 489 generalised theory of a counting process can be applied to many other systems outside 490 of the scope of epidemiology where we would expect a decreasing variance preceding a 491 critical transition. Potential applications include the observation of animals through 492 camera traps, disease surveillance sampling in wildlife or movements in stock prices, 493 which are all examples of incidence-type data. Notably, a substantial number of studies 494 on ecosystem data, climate data and financial data have observed inconsistencies in 495 statistical indicators [16, 22, 23, 29] . Although we found the Poisson process to be 496 overdispersed in the context of epidemiology, it provides a broad framework which can 497 be extended to many other infectious disease systems using the incoming transition 498 probabilities into the infectious class. 499 We proposed extracting the rate of incidence (RoI) or intensity of Poisson process 500 from incidence-type data to illustrate that to utilising CSD, such as observing an 501 increasing variance, requires suitable data which undergoes a bifurcation. In particular, 502 we have shown that the critical threshold in the RoI corresponds with that of 503 prevalence; and as expected we demonstrated that the trend in variance in RoI does 504 increase before an imminent epidemiological transition. 505 We applied five early warning signals to simulated datasets comprising of the three 506 discussed types: prevalence, incidence and rate of incidence. The simulated data we 507 have investigated represents perfect reporting or the "best case scenario". Often is the 508 case that there is underreporting that may reduce the detectability of signals in 509 real-world data. The work we have presented here can be extended to include a gamma 510 distributed intensity λ. Using a gamma distributed rate of incidence will account for 511 reporting errors as described by O'Dea et al.