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.

Omicron-associated changes in SARS-CoV-2 symptoms in the United Kingdom.

BACKGROUND: The SARS-CoV-2 Delta variant has been replaced by the highly transmissible Omicron BA.1 variant, and subsequently by Omicron BA.2. It is important to understand how these changes in dominant variants affect reported symptoms, while also accounting for symptoms arising from other co-circulating respiratory viruses. METHODS: In a nationally representative UK community study, the COVID-19 Infection Survey, we investigated symptoms in PCR-positive infection episodes vs. PCR-negative study visits over calendar time, by age and vaccination status, comparing periods when the Delta, Omicron BA.1 and BA.2 variants were dominant. RESULTS: Between October-2020 and April-2022, 120,995 SARS-CoV-2 PCR-positive episodes occurred in 115,886 participants, with 70,683 (58%) reporting symptoms. The comparator comprised 4,766,366 PCR-negative study visits (483,894 participants); 203,422 (4%) reporting symptoms. Symptom reporting in PCR-positives varied over time, with a marked reduction in loss of taste/smell as Omicron BA.1 dominated, maintained with BA.2 (44%/45% 17 October 2021, 16%/13% 2 January 2022, 15%/12% 27 March 2022). Cough, fever, shortness of breath, myalgia, fatigue/weakness and headache also decreased after Omicron BA.1 dominated, but sore throat increased, the latter to a greater degree than concurrent increases in PCR-negatives. Fatigue/weakness increased again after BA.2 dominated, although to a similar degree to concurrent increases in PCR-negatives. Symptoms were consistently more common in adults aged 18-65 years than in children or older adults. CONCLUSIONS: Increases in sore throat (also common in the general community), and a marked reduction in loss of taste/smell, make Omicron harder to detect with symptom-based testing algorithms, with implications for institutional and national testing policies.

Inferring risks of coronavirus transmission from community household data.

The response of many governments to the COVID-19 pandemic has involved measures to control within- and between-household transmission, providing motivation to improve understanding of the absolute and relative risks in these contexts. Here, we perform exploratory, residual-based, and transmission-dynamic household analysis of the Office for National Statistics COVID-19 Infection Survey data from 26 April 2020 to 15 July 2021 in England. This provides evidence for: (i) temporally varying rates of introduction of infection into households broadly following the trajectory of the overall epidemic and vaccination programme; (ii) susceptible-Infectious transmission probabilities of within-household transmission in the 15-35% range; (iii) the emergence of the Alpha and Delta variants, with the former being around 50% more infectious than wildtype and 35% less infectious than Delta within households; (iv) significantly (in the range of 25-300%) more risk of bringing infection into the household for workers in patient-facing roles pre-vaccine; (v) increased risk for secondary school-age children of bringing the infection into the household when schools are open; (vi) increased risk for primary school-age children of bringing the infection into the household when schools were open since the emergence of new variants.

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.

A computational framework for modelling infectious disease policy based on age and household structure with applications to the COVID-19 pandemic.

The widespread, and in many countries unprecedented, use of non-pharmaceutical interventions (NPIs) during the COVID-19 pandemic has highlighted the need for mathematical models which can estimate the impact of these measures while accounting for the highly heterogeneous risk profile of COVID-19. Models accounting either for age structure or the household structure necessary to explicitly model many NPIs are commonly used in infectious disease modelling, but models incorporating both levels of structure present substantial computational and mathematical challenges due to their high dimensionality. Here we present a modelling framework for the spread of an epidemic that includes explicit representation of age structure and household structure. Our model is formulated in terms of tractable systems of ordinary differential equations for which we provide an open-source Python implementation. Such tractability leads to significant benefits for model calibration, exhaustive evaluation of possible parameter values, and interpretability of results. We demonstrate the flexibility of our model through four policy case studies, where we quantify the likely benefits of the following measures which were either considered or implemented in the UK during the current COVID-19 pandemic: control of within- and between-household mixing through NPIs; formation of support bubbles during lockdown periods; out-of-household isolation (OOHI); and temporary relaxation of NPIs during holiday periods. Our ordinary differential equation formulation and associated analysis demonstrate that multiple dimensions of risk stratification and social structure can be incorporated into infectious disease models without sacrificing mathematical tractability. This model and its software implementation expand the range of tools available to infectious disease policy analysts.

Association between household composition and severe COVID-19 outcomes in older people by ethnicity: an observational cohort study using the OpenSAFELY platform.

BACKGROUND: Ethnic differences in the risk of severe COVID-19 may be linked to household composition. We quantified the association between household composition and risk of severe COVID-19 by ethnicity for older individuals. METHODS: With the approval of NHS England, we analysed ethnic differences in the association between household composition and severe COVID-19 in people aged 67 or over in England. We defined households by number of age-based generations living together, and used multivariable Cox regression stratified by location and wave of the pandemic and accounted for age, sex, comorbidities, smoking, obesity, housing density and deprivation. We included 2 692 223 people over 67 years in Wave 1 (1 February 2020-31 August 2020) and 2 731 427 in Wave 2 (1 September 2020-31 January 2021). RESULTS: Multigenerational living was associated with increased risk of severe COVID-19 for White and South Asian older people in both waves [e.g. Wave 2, 67+ living with three other generations vs 67+-year-olds only: White hazard ratio (HR) 1.61 95% CI 1.38-1.87, South Asian HR 1.76 95% CI 1.48-2.10], with a trend for increased risks of severe COVID-19 with increasing generations in Wave 2. There was also an increased risk of severe COVID-19 in Wave 1 associated with living alone for White (HR 1.35 95% CI 1.30-1.41), South Asian (HR 1.47 95% CI 1.18-1.84) and Other (HR 1.72 95% CI 0.99-2.97) ethnicities, an effect that persisted for White older people in Wave 2. CONCLUSIONS: Both multigenerational living and living alone were associated with severe COVID-19 in older adults. Older South Asian people are over-represented within multigenerational households in England, especially in the most deprived settings, whereas a substantial proportion of White older people live alone. The number of generations in a household, number of occupants, ethnicity and deprivation status are important considerations in the continued roll-out of COVID-19 vaccination and targeting of interventions for future pandemics.

Transmission dynamics of SARS-CoV-2 in a strictly-Orthodox Jewish community in the UK.

Some social settings such as households and workplaces, have been identified as high risk for SARS-CoV-2 transmission. Identifying and quantifying the importance of these settings is critical for designing interventions. A tightly-knit religious community in the UK experienced a very large COVID-19 epidemic in 2020, reaching 64.3% seroprevalence within 10 months, and we surveyed this community both for serological status and individual-level attendance at particular settings. Using these data, and a network model of people and places represented as a stochastic graph rewriting system, we estimated the relative contribution of transmission in households, schools and religious institutions to the epidemic, and the relative risk of infection in each of these settings. All congregate settings were important for transmission, with some such as primary schools and places of worship having a higher share of transmission than others. We found that the model needed a higher general-community transmission rate for women (3.3-fold), and lower susceptibility to infection in children to recreate the observed serological data. The precise share of transmission in each place was related to assumptions about the internal structure of those places. Identification of key settings of transmission can allow public health interventions to be targeted at these locations.

Symptoms and Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) Positivity in the General Population in the United Kingdom.

BACKGROUND: "Classic" symptoms (cough, fever, loss of taste/smell) prompt severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) polymerase chain reaction (PCR) testing in the United Kingdom. Studies have assessed the ability of different symptoms to identify infection, but few have compared symptoms over time (reflecting variants) and by vaccination status. METHODS: Using the COVID-19 Infection Survey, sampling households across the United Kingdom, we compared symptoms in PCR-positives vs PCR-negatives, evaluating sensitivity of combinations of 12 symptoms (percentage symptomatic PCR-positives reporting specific symptoms) and tests per case (TPC) (PCR-positives or PCR-negatives reporting specific symptoms/ PCR-positives reporting specific symptoms). RESULTS: Between April 2020 and August 2021, 27 869 SARS-CoV-2 PCR-positive episodes occurred in 27 692 participants (median 42 years), of whom 13 427 (48%) self-reported symptoms ("symptomatic PCR-positives"). The comparator comprised 3 806 692 test-negative visits (457 215 participants); 130 612 (3%) self-reported symptoms ("symptomatic PCR-negatives"). Symptom reporting in PCR-positives varied by age, sex, and ethnicity, and over time, reflecting changes in prevalence of viral variants, incidental changes (eg, seasonal pathogens (with sore throat increasing in PCR-positives and PCR-negatives from April 2021), schools reopening) and vaccination rollout. After May 2021 when Delta emerged, headache and fever substantially increased in PCR-positives, but not PCR-negatives. Sensitivity of symptom-based detection increased from 74% using "classic" symptoms, to 81% adding fatigue/weakness, and 90% including all 8 additional symptoms. However, this increased TPC from 4.6 to 5.3 to 8.7. CONCLUSIONS: Expanded symptom combinations may provide modest benefits for sensitivity of PCR-based case detection, but this will vary between settings and over time, and increases tests/case. Large-scale changes to targeted PCR-testing approaches require careful evaluation given substantial resource and infrastructure implications.

Monitoring populations at increased risk for SARS-CoV-2 infection in the community using population-level demographic and behavioural surveillance.

BACKGROUND: The COVID-19 pandemic is rapidly evolving, with emerging variants and fluctuating control policies. Real-time population screening and identification of groups in whom positivity is highest could help monitor spread and inform public health messaging and strategy. METHODS: To develop a real-time screening process, we included results from nose and throat swabs and questionnaires taken 19 July 2020-17 July 2021 in the UK's national COVID-19 Infection Survey. Fortnightly, associations between SARS-CoV-2 positivity and 60 demographic and behavioural characteristics were estimated using logistic regression models adjusted for potential confounders, considering multiple testing, collinearity, and reverse causality. FINDINGS: Of 4,091,537 RT-PCR results from 482,677 individuals, 29,903 (0·73%) were positive. As positivity rose September-November 2020, rates were independently higher in younger ages, and those living in Northern England, major urban conurbations, more deprived areas, and larger households. Rates were also higher in those returning from abroad, and working in healthcare or outside of home. When positivity peaked December 2020-January 2021 (Alpha), high positivity shifted to southern geographical regions. With national vaccine roll-out from December 2020, positivity reduced in vaccinated individuals. Associations attenuated as rates decreased between February-May 2021. Rising positivity rates in June-July 2021 (Delta) were independently higher in younger, male, and unvaccinated groups. Few factors were consistently associated with positivity. 25/45 (56%) confirmed associations would have been detected later using 28-day rather than 14-day periods. INTERPRETATION: Population-level demographic and behavioural surveillance can be a valuable tool in identifying the varying characteristics driving current SARS-CoV-2 positivity, allowing monitoring to inform public health policy. FUNDING: Department of Health and Social Care (UK), Welsh Government, Department of Health (on behalf of the Northern Ireland Government), Scottish Government, National Institute for Health Research.

Effect of Delta variant on viral burden and vaccine effectiveness against new SARS-CoV-2 infections in the UK.

The effectiveness of the BNT162b2 and ChAdOx1 vaccines against new severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections requires continuous re-evaluation, given the increasingly dominant B.1.617.2 (Delta) variant. In this study, we investigated the effectiveness of these vaccines in a large, community-based survey of randomly selected households across the United Kingdom. We found that the effectiveness of BNT162b2 and ChAdOx1 against infections (new polymerase chain reaction (PCR)-positive cases) with symptoms or high viral burden is reduced with the B.1.617.2 variant (absolute difference of 10-13% for BNT162b2 and 16% for ChAdOx1) compared to the B.1.1.7 (Alpha) variant. The effectiveness of two doses remains at least as great as protection afforded by prior natural infection. The dynamics of immunity after second doses differed significantly between BNT162b2 and ChAdOx1, with greater initial effectiveness against new PCR-positive cases but faster declines in protection against high viral burden and symptomatic infection with BNT162b2. There was no evidence that effectiveness varied by dosing interval, but protection was higher in vaccinated individuals after a prior infection and in younger adults. With B.1.617.2, infections occurring after two vaccinations had similar peak viral burden as those in unvaccinated individuals. SARS-CoV-2 vaccination still reduces new infections, but effectiveness and attenuation of peak viral burden are reduced with B.1.617.2.

Possible future waves of SARS-CoV-2 infection generated by variants of concern with a range of characteristics.

Viral reproduction of SARS-CoV-2 provides opportunities for the acquisition of advantageous mutations, altering viral transmissibility, disease severity, and/or allowing escape from natural or vaccine-derived immunity. We use three mathematical models: a parsimonious deterministic model with homogeneous mixing; an age-structured model; and a stochastic importation model to investigate the effect of potential variants of concern (VOCs). Calibrating to the situation in England in May 2021, we find epidemiological trajectories for putative VOCs are wide-ranging and dependent on their transmissibility, immune escape capability, and the introduction timing of a postulated VOC-targeted vaccine. We demonstrate that a VOC with a substantial transmission advantage over resident variants, or with immune escape properties, can generate a wave of infections and hospitalisations comparable to the winter 2020-2021 wave. Moreover, a variant that is less transmissible, but shows partial immune-escape could provoke a wave of infection that would not be revealed until control measures are further relaxed.

Hospital length of stay for COVID-19 patients: Data-driven methods for forward planning.

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.

The population attributable fraction of cases due to gatherings and groups with relevance to COVID-19 mitigation strategies.

Many countries have banned groups and gatherings as part of their response to the pandemic caused by the coronavirus, SARS-CoV-2. Although there are outbreak reports involving mass gatherings, the contribution to overall transmission is unknown. We used data from a survey of social contact behaviour that specifically asked about contact with groups to estimate the population attributable fraction (PAF) due to groups as the relative change in the basic reproduction number when groups are prevented. Groups of 50+ individuals accounted for 0.5% of reported contact events, and we estimate that the PAF due to groups of 50+ people is 5.4% (95% confidence interval 1.4%, 11.5%). The PAF due to groups of 20+ people is 18.9% (12.7%, 25.7%) and the PAF due to groups of 10+ is 25.2% (19.4%, 31.4%). Under normal circumstances with pre-COVID-19 contact patterns, large groups of individuals have a relatively small epidemiological impact; small- and medium-sized groups between 10 and 50 people have a larger impact on an epidemic. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Outbreaks in care homes may lead to substantial disease burden if not mitigated.

The number of COVID-19 outbreaks reported in UK care homes rose rapidly in early March of 2020. Owing to the increased co-morbidities and therefore worse COVID-19 outcomes for care home residents, it is important that we understand this increase and its future implications. We demonstrate the use of an SIS model where each nursing home is an infective unit capable of either being susceptible to an outbreak (S) or in an active outbreak (I). We use a generalized additive model to approximate the trend in growth rate of outbreaks in care homes and find the fit to be improved in a model where the growth rate is proportional to the number of current care home outbreaks compared with a model with a constant growth rate. Using parameters found from the outbreak-dependent growth rate, we predict a 73% prevalence of outbreaks in UK care homes without intervention as a reasonable worst-case planning assumption. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Using a household-structured branching process to analyse contact tracing in the SARS-CoV-2 pandemic.

We explore strategies of contact tracing, case isolation and quarantine of exposed contacts to control the SARS-CoV-2 epidemic using a branching process model with household structure. This structure reflects higher transmission risks among household members than among non-household members. We explore strategic implementation choices that make use of household structure, and investigate strategies including two-step tracing, backwards tracing, smartphone tracing and tracing upon symptom report rather than test results. The primary model outcome is the effect of contact tracing, in combination with different levels of physical distancing, on the growth rate of the epidemic. Furthermore, we investigate epidemic extinction times to indicate the time period over which interventions must be sustained. We consider effects of non-uptake of isolation/quarantine, non-adherence, and declining recall of contacts over time. Our results find that, compared to self-isolation of cases without contact tracing, a contact tracing strategy designed to take advantage of household structure allows for some relaxation of physical distancing measures but cannot completely control the epidemic absent of other measures. Even assuming no imported cases and sustainment of moderate physical distancing, testing and tracing efforts, the time to bring the epidemic to extinction could be in the order of months to years. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

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'.

Ct threshold values, a proxy for viral load in community SARS-CoV-2 cases, demonstrate wide variation across populations and over time.

Background: Information on SARS-CoV-2 in representative community surveillance is limited, particularly cycle threshold (Ct) values (a proxy for viral load). Methods: We included all positive nose and throat swabs 26 April 2020 to 13 March 2021 from the UK's national COVID-19 Infection Survey, tested by RT-PCR for the N, S, and ORF1ab genes. We investigated predictors of median Ct value using quantile regression. Results: Of 3,312,159 nose and throat swabs, 27,902 (0.83%) were RT-PCR-positive, 10,317 (37%), 11,012 (40%), and 6550 (23%) for 3, 2, or 1 of the N, S, and ORF1ab genes, respectively, with median Ct = 29.2 (~215 copies/ml; IQR Ct = 21.9-32.8, 14-56,400 copies/ml). Independent predictors of lower Cts (i.e. higher viral load) included self-reported symptoms and more genes detected, with at most small effects of sex, ethnicity, and age. Single-gene positives almost invariably had Ct > 30, but Cts varied widely in triple-gene positives, including without symptoms. Population-level Cts changed over time, with declining Ct preceding increasing SARS-CoV-2 positivity. Of 6189 participants with IgG S-antibody tests post-first RT-PCR-positive, 4808 (78%) were ever antibody-positive; Cts were significantly higher in those remaining antibody negative. Conclusions: Marked variation in community SARS-CoV-2 Ct values suggests that they could be a useful epidemiological early-warning indicator. Funding: Department of Health and Social Care, National Institutes of Health Research, Huo Family Foundation, Medical Research Council UK; Wellcome Trust.