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In the absence of a vaccine, severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) transmission has been controlled by preventing person-to-person interactions via social distancing measures. In order to re-open parts of society, policy-makers need to consider how combinations of measures will affect transmission and understand the trade-offs between them. We use age-specific social contact data, together with epidemiological data, to quantify the components of the COVID-19 reproduction number. We estimate the impact of social distancing policies on the reproduction number by turning contacts on and off based on context and age. We focus on the impact of re-opening schools against a background of wider social distancing measures. We demonstrate that pre-collected social contact data can be used to provide a time-varying estimate of the reproduction number ( R ). We find that following lockdown (when R = 0.7, 95% CI 0.6, 0.8), opening primary schools has a modest impact on transmission ( R = 0.89, 95% CI 0.82-0.97) as long as other social interactions are not increased. Opening secondary and primary schools is predicted to have a larger impact ( R = 1.22, 95% CI 1.02-1.53). Contact tracing and COVID security can be used to mitigate the impact of increased social mixing to some extent; however, social distancing measures are still required to control transmission. Our approach has been widely used by policy-makers to project the impact of social distancing measures and assess the trade-offs between them. Effective social distancing, contact tracing and COVID security are required if all age groups are to return to school while controlling transmission. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) reproduction number has become an essential parameter for monitoring disease transmission across settings and guiding interventions. The UK published weekly estimates of the reproduction number in the UK starting in May 2020 which are formed from multiple independent estimates. In this paper, we describe methods used to estimate the time-varying SARS-CoV-2 reproduction number for the UK. We used multiple data sources and estimated a serial interval distribution from published studies. We describe regional variability and how estimates evolved during the early phases of the outbreak, until the relaxing of social distancing measures began to be introduced in early July. Our analysis is able to guide localized control and provides a longitudinal example of applying these methods over long timescales. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

As the number of cases of COVID-19 continues to grow, local health services are at risk of being overwhelmed with patients requiring intensive care. We develop and implement an algorithm to provide optimal re-routing strategies to either transfer patients requiring Intensive Care Units (ICU) or ventilators, constrained by feasibility of transfer. We validate our approach with realistic data from the United Kingdom and Spain. In the UK, we consider the National Health Service at the level of trusts and define a 4-regular geometric graph which indicates the four nearest neighbours of any given trust. In Spain we coarse-grain the healthcare system at the level of autonomous communities, and extract similar contact networks. Through random search optimisation we identify the best load sharing strategy, where the cost function to minimise is based on the total number of ICU units above capacity. Our framework is general and flexible allowing for additional criteria, alternative cost functions, and can be extended to other resources beyond ICU units or ventilators. Assuming a uniform ICU demand, we show that it is possible to enable access to ICU for up to 1000 additional cases in the UK in a single step of the algorithm. Under a more realistic and heterogeneous demand, our method is able to balance about 600 beds per step in the Spanish system only using local sharing, and over 1300 using countrywide sharing, potentially saving a large percentage of these lives that would otherwise not have access to ICU., Competing Interests: The authors have declared that no competing interests exist.

Prediction and control of the spread of infectious disease in human populations benefits greatly from our growing capacity to quantify human movement behavior. Here we develop a mathematical model for non-transmissible infections contracted from a localized environmental source, informed by a detailed description of movement patterns of the population of Great Britain. The model is applied to outbreaks of Legionnaires' disease, a potentially life-threatening form of pneumonia caused by the bacteria Legionella pneumophilia. We use case-report data from three recent outbreaks that have occurred in Great Britain where the source has already been identified by public health agencies. We first demonstrate that the amount of individual-level heterogeneity incorporated in the movement data greatly influences our ability to predict the source location. The most accurate predictions were obtained using reported travel histories to describe movements of infected individuals, but using detailed simulation models to estimate movement patterns offers an effective fast alternative. Secondly, once the source is identified, we show that our model can be used to accurately determine the population likely to have been exposed to the pathogen, and hence predict the residential locations of infected individuals. The results give rise to an effective control strategy that can be implemented rapidly in response to an outbreak.