Short-term forecasts to inform the response to the COVID-19 epidemic in the UK (preprint)

Background: Short-term forecasts of infectious disease can create situational awareness and inform planning for outbreak response. Here, we report on multi-model forecasts of Covid-19 in the UK that were generated at regular intervals starting at the end of March 2020, in order to monitor expected healthcare utilisation and population impacts in real time. Methods: We evaluated the performance of individual model forecasts generated between 24 March and 14 July 2020, using a variety of metrics including the weighted interval score as well as metrics that assess the calibration, sharpness, bias and absolute error of forecasts separately. We further combined the predictions from individual models to ensemble forecasts using a simple mean as well as a quantile regression average that aimed to maximise performance. We further compared model performance to a null model of no change. Results: In most cases, individual models performed better than the null model, and ensembles models were well calibrated and performed comparatively to the best individual models. The quantile regression average did not noticeably outperform the mean ensemble. Conclusions: Ensembles of multi-model forecasts can inform the policy response to the Covid-19 pandemic by assessing future resource needs and expected population impact of morbidity and mortality.

Precautionary breaks: planned, limited duration circuit breaks to control the prevalence of COVID-19 (preprint)

The COVID-19 pandemic in the UK has been characterised by periods of exponential growth and decline, as different non-pharmaceutical interventions (NPIs) are brought into play. During the early uncontrolled phase of the outbreak (early March 2020) there was a period of prolonged exponential growth with epidemiological observations such as hospitalisation doubling every 3-4 days (growth rate r{approx}0.2). The enforcement of strict lockdown measures led to a noticeable decline in all epidemic quantities (r{approx}-0.06) that slowed during the summer as control measures were relaxed (r{approx}-0.02). Since August, infections, hospitalisations and deaths have been rising (precise estimation of the cur-rent growth rate is difficult due to extreme regional heterogeneity and temporal lags between the different epidemiological observations) and various NPIs have been applied locally throughout the UK in response. Controlling any rise in infection is a compromise between public health and societal costs, with more stringent NPIs reducing cases but damaging the economy and restricting freedoms. Currently, NPI imposition is made in response to the epidemiological state, are of indefinite length and are often imposed at short notice, greatly increasing the negative impact. An alternative approach is to consider planned, limited duration periods of strict NPIs aiming to purposefully reduce prevalence before such emergency NPIs are required. These 'precautionary breaks' may offer a means of keeping control of the epidemic, while their fixed duration and the forewarning may limit their society impact. Here, using simple analysis and age-structured models matched to the unfolding UK epidemic, we investigate the action of precautionary breaks. In particular we consider their impact on the prevalence of infection, as well as the total number of predicted hospitalisations and deaths. We find that precautionary breaks provide the biggest gains when the growth rate is low, but offer a much needed brake on increasing infection when the growth rate is higher, potentially allowing other measures (such as contact tracing)to regain control.

Fitting models to the COVID-19 outbreak and estimating R (preprint)

The COVID-19 pandemic has brought to the fore the need for policy makers to receive timely and ongoing scientific guidance in response to this recently emerged human infectious disease. Fitting mathematical models of infectious disease transmission to the available epidemiological data provides a key statistical tool for understanding the many quantities of interest that are not explicit in the underlying epidemiological data streams. Of these, the basic reproductive ratio, $R$, has taken on special significance in terms of the general understanding of whether the epidemic is under control ($R<1$). Unfortunately, none of the epidemiological data streams are designed for modelling, hence assimilating information from multiple (often changing) sources of data is a major challenge that is particularly stark in novel disease outbreaks. Here, we present in some detail the inference scheme employed for calibrating the Warwick COVID-19 model to the available public health data streams, which span hospitalisations, critical care occupancy, mortality and serological testing. We then perform computational simulations, making use of the acquired parameter posterior distributions, to assess how the accuracy of short-term predictions varied over the timecourse of the outbreak. To conclude, we compare how refinements to data streams and model structure impact estimates of epidemiological measures, including the estimated growth rate and daily incidence.

The impact of school reopening on the spread of COVID-19 in England (preprint)

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.

Predictions of COVID-19 dynamics in the UK: short-term forecasting and analysis of potential exit strategies (preprint)

BackgroundEfforts to suppress transmission of SARS-CoV-2 in the UK have seen non-pharmaceutical interventions being invoked. The most severe measures to date include all restaurants, pubs and cafes being ordered to close on 20th March, followed by a "stay at home" order on the 23rd March and the closure of all non-essential retail outlets for an indefinite period. Government agencies are presently analysing how best to develop an exit strategy from these measures and to determine how the epidemic may progress once measures are lifted. Mathematical models are currently providing short and long term forecasts regarding the future course of the COVID-19 outbreak in the UK to support evidence-based policymaking. MethodsWe present a deterministic, age-structured transmission model that uses real-time data on confirmed cases requiring hospital care and mortality to provide up-to-date predictions on epidemic spread in ten regions of the UK. The model captures a range of age-dependent heterogeneities, reduced transmission from asymptomatic infections and produces a good fit to the key epidemic features over time. We simulated a suite of scenarios to assess the impact of differing approaches to relaxing social distancing measures from 7th May 2020, on the estimated number of patients requiring inpatient and critical care treatment, and deaths. With regard to future epidemic outcomes, we investigated the impact of reducing compliance, ongoing shielding of elder age groups, reapplying stringent social distancing measures using region based triggers and the role of asymptomatic transmission. FindingsWe find that significant relaxation of social distancing measures from 7th May onwards can lead to a rapid resurgence of COVID-19 disease and the health system being quickly overwhelmed by a sizeable, second epidemic wave. In all considered age-shielding based strategies, we projected serious demand on critical care resources during the course of the pandemic. The reintroduction and release of strict measures on a regional basis, based on ICU bed occupancy, results in a long epidemic tail, until the second half of 2021, but ensures that the health service is protected by reintroducing social distancing measures for all individuals in a region when required. DiscussionOur work confirms the effectiveness of stringent non-pharmaceutical measures in March 2020 to suppress the epidemic. It also provides strong evidence to support the need for a cautious, measured approach to relaxation of lockdown measures, to protect the most vulnerable members of society and support the health service through subduing demand on hospital beds, in particular bed occupancy in intensive care units.