EpiBeds: Data informed modelling of the COVID-19 hospital burden in England.

The first year of the COVID-19 pandemic put considerable strain on healthcare systems worldwide. In order to predict the effect of the local epidemic on hospital capacity in England, we used a variety of data streams to inform the construction and parameterisation of a hospital progression model, EpiBeds, which was coupled to a model of the generalised epidemic. In this model, individuals progress through different pathways (e.g. may recover, die, or progress to intensive care and recover or die) and data from a partially complete patient-pathway line-list was used to provide initial estimates of the mean duration that individuals spend in the different hospital compartments. We then fitted EpiBeds using complete data on hospital occupancy and hospital deaths, enabling estimation of the proportion of individuals that follow the different clinical pathways, the reproduction number of the generalised epidemic, and to make short-term predictions of hospital bed demand. The construction of EpiBeds makes it straightforward to adapt to different patient pathways and settings beyond England. As part of the UK response to the pandemic, EpiBeds provided weekly forecasts to the NHS for hospital bed occupancy and admissions in England, Wales, Scotland, and Northern Ireland at national and regional scales.

Quantification of protein abundance and interaction defines a mechanism for operation of the circadian clock.

The mammalian circadian clock exerts control of daily gene expression through cycles of DNA binding. Here, we develop a quantitative model of how a finite pool of BMAL1 protein can regulate thousands of target sites over daily time scales. We used quantitative imaging to track dynamic changes in endogenous labelled proteins across peripheral tissues and the SCN. We determine the contribution of multiple rhythmic processes coordinating BMAL1 DNA binding, including cycling molecular abundance, binding affinities, and repression. We find nuclear BMAL1 concentration determines corresponding CLOCK through heterodimerisation and define a DNA residence time of this complex. Repression of CLOCK:BMAL1 is achieved through rhythmic changes to BMAL1:CRY1 association and high-affinity interactions between PER2:CRY1 which mediates CLOCK:BMAL1 displacement from DNA. Finally, stochastic modelling reveals a dual role for PER:CRY complexes in which increasing concentrations of PER2:CRY1 promotes removal of BMAL1:CLOCK from genes consequently enhancing ability to move to new target sites.

Estimation of reproduction numbers in real time: Conceptual and statistical challenges.

The reproduction number R has been a central metric of the COVID-19 pandemic response, published weekly by the UK government and regularly reported in the media. Here, we provide a formal definition and discuss the advantages and most common misconceptions around this quantity. We consider the intuition behind different formulations of R , the complexities in its estimation (including the unavoidable lags involved), and its value compared to other indicators (e.g. the growth rate) that can be directly observed from aggregate surveillance data and react more promptly to changes in epidemic trend. As models become more sophisticated, with age and/or spatial structure, formulating R becomes increasingly complicated and inevitably model-dependent. We present some models currently used in the UK pandemic response as examples. Ultimately, limitations in the available data streams, data quality and time constraints force pragmatic choices to be made on a quantity that is an average across time, space, social structure and settings. Effectively communicating these challenges is important but often difficult in an emergency.

Challenges in control of COVID-19: short doubling time and long delay to effect of interventions.

Early assessments of the growth rate of COVID-19 were subject to significant uncertainty, as expected with limited data and difficulties in case ascertainment, but as cases were recorded in multiple countries, more robust inferences could be made. Using multiple countries, data streams and methods, we estimated that, when unconstrained, European COVID-19 confirmed cases doubled on average every 3 days (range 2.2-4.3 days) and Italian hospital and intensive care unit admissions every 2-3 days; values that are significantly lower than the 5-7 days dominating the early published literature. Furthermore, we showed that the impact of physical distancing interventions was typically not seen until at least 9 days after implementation, during which time confirmed cases could grow eightfold. We argue that such temporal patterns are more critical than precise estimates of the time-insensitive basic reproduction number R0 for initiating interventions, and that the combination of fast growth and long detection delays explains the struggle in countries' outbreak response better than large values of R0 alone. One year on from first reporting these results, reproduction numbers continue to dominate the media and public discourse, but robust estimates of unconstrained growth remain essential for planning worst-case scenarios, and detection delays are still key in informing the relaxation and re-implementation of interventions. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Vaccine Induced Herd Immunity for Control of Respiratory Syncytial Virus Disease in a Low-Income Country Setting.

BACKGROUND: Respiratory syncytial virus (RSV) is globally ubiquitous, and infection during the first six months of life is a major risk for severe disease and hospital admission; consequently RSV is the most important viral cause of respiratory morbidity and mortality in young children. Development of vaccines for young infants is complicated by the presence of maternal antibodies and immunological immaturity, but vaccines targeted at older children avoid these problems. Vaccine development for young infants has been unsuccessful, but this is not the case for older children (> 6 m). Would vaccinating older children have a significant public health impact? We developed a mathematical model to explore the benefits of a vaccine against RSV. METHODS AND FINDINGS: We have used a deterministic age structured model capturing the key epidemiological characteristics of RSV and performed a statistical maximum-likelihood fit to age-specific hospitalization data from a developing country setting. To explore the effects of vaccination under different mixing assumptions, we included two versions of contact matrices: one from a social contact diary study, and the second a synthesised construction based on demographic data. Vaccination is assumed to elicit an immune response equivalent to primary infection. Our results show that immunisation of young children (5-10 m) is likely to be a highly effective method of protection of infants (<6 m) against hospitalisation. The majority benefit is derived from indirect protection (herd immunity). A full sensitivity and uncertainty analysis using Latin Hypercube Sampling of the parameter space shows that our results are robust to model structure and model parameters. CONCLUSIONS: This result suggests that vaccinating older infants and children against RSV can have a major public health benefit.

Strategies for controlling non-transmissible infection outbreaks using a large human movement data set.

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.

Social encounter networks: characterizing Great Britain.

A major goal of infectious disease epidemiology is to understand and predict the spread of infections within human populations, with the intention of better informing decisions regarding control and intervention. However, the development of fully mechanistic models of transmission requires a quantitative understanding of social interactions and collective properties of social networks. We performed a cross-sectional study of the social contacts on given days for more than 5000 respondents in England, Scotland and Wales, through postal and online survey methods. The survey was designed to elicit detailed and previously unreported measures of the immediate social network of participants relevant to infection spread. Here, we describe individual-level contact patterns, focusing on the range of heterogeneity observed and discuss the correlations between contact patterns and other socio-demographic factors. We find that the distribution of the number of contacts approximates a power-law distribution, but postulate that total contact time (which has a shorter-tailed distribution) is more epidemiologically relevant. We observe that children, public-sector and healthcare workers have the highest number of total contact hours and are therefore most likely to catch and transmit infectious disease. Our study also quantifies the transitive connections made between an individual's contacts (or clustering); this is a key structural characteristic of social networks with important implications for disease transmission and control efficacy. Respondents' networks exhibit high levels of clustering, which varies across social settings and increases with duration, frequency of contact and distance from home. Finally, we discuss the implications of these findings for the transmission and control of pathogens spread through close contact.

Social encounter networks: collective properties and disease transmission.

A fundamental challenge of modern infectious disease epidemiology is to quantify the networks of social and physical contacts through which transmission can occur. Understanding the collective properties of these interactions is critical for both accurate prediction of the spread of infection and determining optimal control measures. However, even the basic properties of such networks are poorly quantified, forcing predictions to be made based on strong assumptions concerning network structure. Here, we report on the results of a large-scale survey of social encounters mainly conducted in Great Britain. First, we characterize the distribution of contacts, which possesses a lognormal body and a power-law tail with an exponent of -2.45; we provide a plausible mechanistic model that captures this form. Analysis of the high level of local clustering of contacts reveals additional structure within the network, implying that social contacts are degree assortative. Finally, we describe the epidemiological implications of this local network structure: these contradict the usual predictions from networks with heavy-tailed degree distributions and contain public-health messages about control. Our findings help us to determine the types of realistic network structure that should be assumed in future population level studies of infection transmission, leading to better interpretations of epidemiological data and more appropriate policy decisions.

Individual identity and movement networks for disease metapopulations.

The theory of networks has had a huge impact in both the physical and life sciences, shaping our understanding of the interaction between multiple elements in complex systems. In particular, networks have been extensively used in predicting the spread of infectious diseases where individuals, or populations of individuals, interact with a limited set of others-defining the network through which the disease can spread. Here for such disease models we consider three assumptions for capturing the network of movements between populations, and focus on two applied problems supported by detailed data from Great Britain: the commuter movement of workers between local areas (wards) and the permanent movement of cattle between farms. For such metapopulation networks, we show that the identity of individuals responsible for making network connections can have a significant impact on the infection dynamics, with clear implications for detailed public health and veterinary applications.

Impact of spatial clustering on disease transmission and optimal control.

Spatial heterogeneities and spatial separation of hosts are often seen as key factors when developing accurate predictive models of the spread of pathogens. The question we address in this paper is how coarse the resolution of the spatial data can be for a model to be a useful tool for informing control policies. We examine this problem using the specific case of foot-and-mouth disease spreading between farms using the formulation developed during the 2001 epidemic in the United Kingdom. We show that, if our model is carefully parameterized to match epidemic behavior, then using aggregate county-scale data from the United States is sufficient to closely determine optimal control measures (specifically ring culling). This result also holds when the approach is extended to theoretical distributions of farms where the spatial clustering can be manipulated to extremes. We have therefore shown that, although spatial structure can be critically important in allowing us to predict the emergent population-scale behavior from a knowledge of the individual-level dynamics, for this specific applied question, such structure is mostly subsumed in the parameterization allowing us to make policy predictions in the absence of high-quality spatial information. We believe that this approach will be of considerable benefit across a range of disciplines where data are only available at intermediate spatial scales.