A flexible method for optimising sharing of healthcare resources and demand in the context of the COVID-19 pandemic.

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

Exploring the effects of BCG vaccination in patients diagnosed with tuberculosis: Observational study using the Enhanced Tuberculosis Surveillance system.

BACKGROUND: Bacillus Calmette-Guérin (BCG) is one of the most widely-used vaccines worldwide. BCG primarily reduces the progression from infection to disease, however there is evidence that BCG may provide additional benefits. We aimed to investigate whether there is evidence in routinely-collected surveillance data that BCG vaccination impacts outcomes for tuberculosis (TB) cases in England. METHODS: We obtained all TB notifications for 2009-2015 in England from the Enhanced Tuberculosis surveillance system. We considered five outcomes: All-cause mortality, death due to TB (in those who died), recurrent TB, pulmonary disease, and sputum smear status. We used logistic regression, with complete case analysis, to investigate each outcome with BCG vaccination, years since vaccination and age at vaccination, adjusting for potential confounders. All analyses were repeated using multiply imputed data. RESULTS: We found evidence of an association between BCG vaccination and reduced all-cause mortality (aOR:0.76 (95%CI 0.64-0.89), P:0.001) and weak evidence of an association with reduced recurrent TB (aOR:0.90 (95%CI 0.81-1.00), P:0.056). Analyses using multiple imputation suggested that the benefits of vaccination for all-cause mortality were reduced after 10 years. CONCLUSIONS: We found that BCG vaccination was associated with reduced all-cause mortality in people with TB although this benefit was less pronounced more than 10 years after vaccination. There was weak evidence of an association with reduced recurrent TB

Meta-analysis of the severe acute respiratory syndrome coronavirus 2 serial intervals and the impact of parameter uncertainty on the coronavirus disease 2019 reproduction number

This is the final version. Available on open access from SAGE Publications via the DOI in this recordThe serial interval of an infectious disease, commonly interpreted as the time between the onset of symptoms in sequentially infected individuals within a chain of transmission, is a key epidemiological quantity involved in estimating the reproduction number. The serial interval is closely related to other key quantities, including the incubation period, the generation interval (the time between sequential infections), and time delays between infection and the observations associated with monitoring an outbreak such as confirmed cases, hospital admissions, and deaths. Estimates of these quantities are often based on small data sets from early contact tracing and are subject to considerable uncertainty, which is especially true for early coronavirus disease 2019 data. In this paper, we estimate these key quantities in the context of coronavirus disease 2019 for the UK, including a meta-analysis of early estimates of the serial interval. We estimate distributions for the serial interval with a mean of 5.9 (95% CI 5.2; 6.7) and SD 4.1 (95% CI 3.8; 4.7) days (empirical distribution), the generation interval with a mean of 4.9 (95% CI 4.2; 5.5) and SD 2.0 (95% CI 0.5; 3.2) days (fitted gamma distribution), and the incubation period with a mean 5.2 (95% CI 4.9; 5.5) and SD 5.5 (95% CI 5.1; 5.9) days (fitted log-normal distribution). We quantify the impact of the uncertainty surrounding the serial interval, generation interval, incubation period, and time delays, on the subsequent estimation of the reproduction number, when pragmatic and more formal approaches are taken. These estimates place empirical bounds on the estimates of most relevant model parameters and are expected to contribute to modeling coronavirus disease 2019 transmission.Engineering and Physical Sciences Research Council (EPSRC)NHS EnglandAlan Turing InstituteMedical Research Council (MRC)National Institute for Health Research (NIHR

Path integral Monte Carlo simulation of helium at negative pressures

Path integral Monte Carlo (PIMC) simulations of liquid helium at negative pressure have been carried out for a temperature range from the critical temperature to below the superfluid transition. We have calculated the temperature dependence of the spinodal line as well as the pressure dependence of the isothermal sound velocity in the region of the spinodal. We discuss the slope of the superfluid transition line and the shape of the dispersion curve at negative pressures.Comment: 6 pages, 7 figures, submitted to Physical Review B Revised: new reference, replaced figure

Estimates of regional infectivity of COVID-19 in the United Kingdom following imposition of social distancing measures

This is the final version. Available from The Royal Society via the DOI in this record. Data and code supporting this article can be accessed on GitHub at the following link: https://github.com/terminological/uk-covid-datatools/tree/master/vignettes/current-rt.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’.Engineering and Physical Sciences Research Council (EPSRC)Engineering and Physical Sciences Research Council (EPSRC)Engineering and Physical Sciences Research Council (EPSRC)Medical Research Council (MRC)National Institute for Health Research (NIHR

MetaWards: A flexible metapopulation framework for modelling disease spread

This is the final version. Available on open access from Open Journals via the DOI in this recordThe software is available at https://github.com/metawards/MetaWardsUnderstanding how disease spreads through populations is important when designing and implementing control measures. MetaWards implements a stochastic metapopulation model of disease transmission that enables geographical modelling of disease spread that can scale all the way from modelling local transmission up to full national-or international-scale outbreaks. It is built in Python and has a flexible plugin architecture to support complex scenario modelling. This enables the code to be adapted to model new situations and new control measures as they arise, e.g. emergence of new variants of disease, enaction of different types of movement restrictions, availability of different types of vaccines etc. It implements a userdefinable compartmental transmission model, such as an SIR model, that can be extended multi-dimensionally via multiple demographics or sub-populations, and multiple geographical regions. Models can be constructed from the various sources of movement and demographic data that are available, and are accelerated via Cython (Behnel et al., 2020), OpenMP, Scoop (Hold & Gagnon, 2019) and MPI4Py (Dalcin & Fang, 2021) to scale efficiently from running on personal laptops to large supercomputers. Python, R and command line interfaces and a complete set of tutorials empower researchers to adapt their models to a variety of scenarios.Engineering and Physical Sciences Research Council (EPSRC)Medical Research Council (MRC)Alan Turing InstitutePfize

Commentary on the use of the reproduction number R during the COVID-19 pandemic

Since the beginning of the COVID-19 pandemic, the reproduction number R has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, R is defined as the average number of secondary infections caused by one primary infected individual. R seems convenient, because the epidemic is expanding if R>1 and contracting if R<1. The magnitude of R indicates by how much transmission needs to be reduced to control the epidemic. Using R in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of R but many, and the precise definition of R affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined R, there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate R vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when R is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of R, and the data and methods used to estimate it, can make R a more useful metric for future management of the epidemic

A novel approach for evaluating contact patterns and risk mitigation strategies for COVID-19 in English primary schools with application of structured expert judgement

Personal contacts drive COVID-19 infections. After being closed (23 March 2020) UK primary schools partially re-opened on 1 June 2020 with social distancing and new risk mitigation strategies. We conducted a structured expert elicitation of teachers to quantify primary school contact patterns and how contact rates changed upon re-opening with risk mitigation measures in place. These rates, with uncertainties, were determined using a performance-based algorithm. We report mean number of contacts per day for four cohorts within schools, with associated 90% confidence ranges. Prior to lockdown, younger children (Reception and Year 1) made 15 contacts per day [range 8.35] within school, older children (Year 6) 18 contacts [range 5.55], teaching staff 25 contacts [range 4.55] and non-classroom staff 11 contacts [range 2.27]. After re-opening, the mean number of contacts was reduced by 53% for young children, 62% for older children, 60% for classroom staff and 64% for other staff. Contacts between teaching and non-teaching staff reduced by 80%. The distributions of contacts per person are asymmetric with heavy tail reflecting a few individuals with high contact numbers. Questions on risk mitigation and supplementary structured interviews elucidated how new measures reduced daily contacts in-school and contribute to infection risk reduction

Measured Dynamic Social Contact Patterns Explain the Spread of H1N1v Influenza

Patterns of social mixing are key determinants of epidemic spread. Here we present the results of an internet-based social contact survey completed by a cohort of participants over 9,000 times between July 2009 and March 2010, during the 2009 H1N1v influenza epidemic. We quantify the changes in social contact patterns over time, finding that school children make 40% fewer contacts during holiday periods than during term time. We use these dynamically varying contact patterns to parameterise an age-structured model of influenza spread, capturing well the observed patterns of incidence; the changing contact patterns resulted in a fall of approximately 35% in the reproduction number of influenza during the holidays. This work illustrates the importance of including changing mixing patterns in epidemic models. We conclude that changes in contact patterns explain changes in disease incidence, and that the timing of school terms drove the 2009 H1N1v epidemic in the UK. Changes in social mixing patterns can be usefully measured through simple internet-based surveys