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

Emma Southall; Michael J. Tildesley; Louise Dyson

Derivations of the analytical results and calculations of each statistic can be found in 123 the supporting text (S1 Appendix). We present our analysis for incidence data and 124 derive the corresponding statistical indicators. We exploit the well known fact that a 125 counting process can be described by a Poisson process. We apply this result to the 126 field of EWS to incorporate statistical signatures of a Poisson distributed variable to 127 describe the behaviour of the number of new infectious cases in epidemiology. 128 We verify our analytical results for prevalence and incidence with simulated studies, 129 and compare the contrasting results between prevalence and incidence. We measure the 130 change in trend of multiple statistical indicators using the Kendall's Tau score which 131 gives an indication of an increasing or decreasing trend. We begin with a simple example of a system that is approaching elimination from an 135 existing endemic state of I. We consider an SIS model where the effective contact rate 136 β acts as the control parameter. Effective reduction of β can be induced by public 137 health campaigns (such as washing hands or improving food hygiene) and through 138 social distancing (such as school closure). By decreasing β(t) in time, it slowly forces