Background: In the UK, cases of COVID-19 have been declining since mid-April and there is good evidence to suggest that the effective reproduction number has dropped below 1, leading to a multi-phase relaxation plan for the country to emerge from lockdown. As part of this staggered process, primary schools are scheduled to partially reopen on 1st June. Evidence from a range of sources suggests that children are, in general, only mildly affected by the disease and have low mortality rates, though there is less certainty regarding children's role in transmission. Therefore, there is wide discussion on the impact of reopening schools. Methods: We compare eight strategies for reopening primary and secondary schools in England from 1st June, focusing on the return of particular year groups and the associated epidemic consequences. This is assessed through model simulation, modifying a previously developed dynamic transmission model for SARS-CoV-2. We quantify how the process of reopening schools affected contact patterns and anticipated secondary infections, the relative change in R according to the extent of school reopening, and determine the public health impact via estimated change in clinical cases and its sensitivity to decreases in adherence post strict lockdown. Findings: Whilst reopening schools, in any form, results in more mixing between children, an increase in R and hence transmission of the disease, the magnitude of that increase can be low dependent upon the age-groups that return to school and the behaviour of the remaining population. We predict that reopening schools in a way that allows half class sizes or that is focused on younger children is unlikely to push R above one, although there is noticeable variation between the regions of the country. Given that older children have a greater number of social contacts and hence a greater potential for transmission, our findings suggest reopening secondary schools results in larger increases in case burden than only reopening primary schools; reopening both generates the largest increase and could push R above one in some regions. The impact of less social-distancing in the rest of the population, generally has far larger effects than reopening schools and exacerbates the impacts of reopening. Discussion: Our work indicates that any reopening of schools will result in increased mixing and infection amongst children and the wider population, although the opening of schools alone is unlikely to push the value of R above one. However, impacts of other recent relaxations of lockdown measures are yet to be quantified, suggesting some regions may be closer to the critical threshold that would lead to a growth in cases. Given the uncertainties, in part due to limited data on COVID-19 in children, school reopening should be carefully monitored. Ultimately, the decision about reopening classrooms is a difficult trade-off between increased epidemiological consequences and the emotional, educational and developmental needs of children.

HighlightsWe derive indicators of disease eradication so that control efforts may cease.Detrending is necessary to analyse single timeseries data and is difficult to achieve.Detrending using the mean of even a few simulations of the same process works well.Metapopulation models suggest a promising solution to the problem of detrending.

Early warning signals (EWS) identify systems approaching a critical transition, where the system undergoes a sudden change in state. For example, monitoring changes in variance or autocorrelation offers a computationally inexpensive method which can be used in real-time to assess when an infectious disease transitions to elimination. EWS have a promising potential to not only be used to monitor infectious diseases, but also to inform control policies to aid disease elimination. Previously, potential EWS have been identified for prevalence data, however the prevalence of a disease is often not known directly. In this work we identify EWS for incidence data, the standard data type collected by the Centers for Disease Control and Prevention (CDC) or World Health Organization (WHO). We show, through several examples, that EWS calculated on simulated incidence time series data exhibit vastly different behaviours to those previously studied on prevalence data. In particular, the variance displays a decreasing trend on the approach to disease elimination, contrary to that expected from critical slowing down theory; this could lead to unreliable indicators of elimination when calculated on real-world data. We derive analytical predictions which can be generalised for many epidemiological systems, and we support our theory with simulated studies of disease incidence. Additionally, we explore EWS calculated on the rate of incidence over time, a property which can be extracted directly from incidence data. We find that although incidence might not exhibit typical critical slowing down properties before a critical transition, the rate of incidence does, presenting a promising new data type for the application of statistical indicators. Author summaryThe threat posed by infectious diseases has a huge impact on our global society. It is therefore critical to monitor infectious diseases as new data become available during control campaigns. One obstacle in observing disease emergence or elimination is understanding what influences noise in the data and how this fluctuates when near to zero cases. The standard data type collected is the number of new cases per day/month/year but mathematical modellers often focus on data such as the total number of infectious people, due to its analytical properties. We have developed a methodology to monitor the standard type of data to inform whether a disease is approaching emergence or disease elimination. We have shown computationally how

Early warning signals (EWS) identify systems approaching a critical transition, where the system undergoes a sudden change in state. For example, monitoring changes in variance or autocorrelation offers a computationally inexpensive method which can be used in realtime to assess when an infectious disease transitions to elimination. EWS have a promising potential to not only be used to monitor infectious diseases, but also to inform control policies to aid disease elimination. Previously, potential EWS have been identified for prevalence data, however the prevalence of a disease is often not known directly. In this work we identify EWS for incidence data, the standard data type collected by the Centers for Disease Control and Prevention (CDC) or World Health Organization (WHO). We show, through several examples, that EWS calculated on simulated incidence time series data exhibit vastly different behaviours to those previously studied on prevalence data. In particular, the variance displays a decreasing trend on the approach to disease elimination, contrary to that expected from critical slowing down theory; this could lead to unreliable indicators of elimination when calculated on real-world data. We derive analytical predictions which can be generalised for many epidemiological systems, and we support our theory with simulated studies of disease incidence. Additionally, we explore EWS calculated on the rate of incidence over time, a property which can be extracted directly from incidence data. We find that although incidence might not exhibit typical critical slowing down properties before a critical transition, the rate of incidence does, presenting a promising new data type for the application of statistical indicators.