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Purpose In this work, the authors present some of the key results found during early efforts to model the COVID-19 outbreak inside a UK prison. In particular, this study describes outputs from an idealised disease model that simulates the dynamics of a COVID-19 outbreak in a prison setting when varying levels of social interventions are in place, and a Monte Carlo-based model that assesses the reduction in risk of case importation, resulting from a process that requires incoming prisoners to undergo a period of self-isolation prior to admission into the general prison population. Design/methodology/approach Prisons, typically containing large populations confined in a small space with high degrees of mixing, have long been known to be especially susceptible to disease outbreaks. In an attempt to meet rising pressures from the emerging COVID-19 situation in early 2020, modellers for Public Health England’s Joint Modelling Cell were asked to produce some rapid response work that sought to inform the approaches that Her Majesty’s Prison and Probation Service (HMPPS) might take to reduce the risk of case importation and sustained transmission in prison environments. Findings Key results show that deploying social interventions has the potential to considerably reduce the total number of infections, while such actions could also reduce the probability that an initial infection will propagate into a prison-wide outbreak. For example, modelling showed that a 50% reduction in the risk of transmission (compared to an unmitigated outbreak) could deliver a 98% decrease in total number of cases, while this reduction could also result in 86.8% of outbreaks subsiding before more than five persons have become infected. Furthermore, this study also found that requiring new arrivals to self-isolate for 10 and 14 days prior to admission could detect up to 98% and 99% of incoming infections, respectively. Research limitations/implications In this paper we have presented models which allow for the studying of COVID-19 in a prison scenario, while also allowing for the assessment of proposed social interventions. By publishing these works, the authors hope these methods might aid in the management of prisoners across additional scenarios and even during subsequent disease outbreaks. Such methods as described may also be readily applied use in other closed community settings. Originality/value These works went towards informing HMPPS on the impacts that the described strategies might have during COVID-19 outbreaks inside UK prisons. The works described herein are readily amendable to the study of a range of addition outbreak scenarios. There is also room for these methods to be further developed and built upon which the timeliness of the original project did not permit.

Background Predicting hospital length of stay (LoS) for patients with COVID-19 infection is essential to ensure that adequate bed capacity can be provided without unnecessarily restricting care for patients with other conditions. Here, we demonstrate the utility of three complementary methods for predicting LoS using UK national- and hospital-level data. Method On a national scale, relevant patients were identified from the COVID-19 Hospitalisation in England Surveillance System (CHESS) reports. An Accelerated Failure Time (AFT) survival model and a truncation corrected method (TC), both with underlying Weibull distributions, were fitted to the data to estimate LoS from hospital admission date to an outcome (death or discharge) and from hospital admission date to Intensive Care Unit (ICU) admission date. In a second approach we fit a multi-state (MS) survival model to data directly from the Manchester University NHS Foundation Trust (MFT). We develop a planning tool that uses LoS estimates from these models to predict bed occupancy. Results All methods produced similar overall estimates of LoS for overall hospital stay, given a patient is not admitted to ICU (8.4, 9.1 and 8.0 days for AFT, TC and MS, respectively). Estimates differ more significantly between the local and national level when considering ICU. National estimates for ICU LoS from AFT and TC were 12.4 and 13.4 days, whereas in local data the MS method produced estimates of 18.9 days. Conclusions Given the complexity and partiality of different data sources and the rapidly evolving nature of the COVID-19 pandemic, it is most appropriate to use multiple analysis methods on multiple datasets. The AFT method accounts for censored cases, but does not allow for simultaneous consideration of different outcomes. The TC method does not include censored cases, instead correcting for truncation in the data, but does consider these different outcomes. The MS method can model complex pathways to different outcomes whilst accounting for censoring, but cannot handle non-random case missingness. Overall, we conclude that data-driven modelling approaches of LoS using these methods is useful in epidemic planning and management, and should be considered for widespread adoption throughout healthcare systems internationally where similar data resources exist.

During an infectious disease outbreak, biases in the data and complexities of the underlying dynamics pose significant challenges in mathematically modelling the outbreak and designing policy. Motivated by the ongoing response to COVID-19, we provide a toolkit of statistical and mathematical models beyond the simple SIR-type differential equation models for analysing the early stages of an outbreak and assessing interventions. In particular, we focus on parameter estimation in the presence of known biases in the data, and the effect of non-pharmaceutical interventions in enclosed subpopulations, such as households and care homes. We illustrate these methods by applying them to the COVID-19 pandemic.

Early assessments of the spreading rate of COVID-19 were subject to significant uncertainty, as expected with limited data and difficulties in case ascertainment, but more reliable inferences can now be made. Here, we estimate from European data that COVID-19 cases are expected to double initially every three days, until social distancing interventions slow this growth, and that the impact of such measures is typically only seen nine days - i.e. three doubling times - after their implementation. We argue that such temporal patterns are more critical than precise estimates of the basic reproduction number for initiating interventions. This observation has particular implications for the low- and middle-income countries currently in the early stages of their local epidemics., Main text: 13 pages (1-13), 3 figures, 1 table; Supplementary Information: 9 pages (14-22), 4 figures, 1 table