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.

Voluntary risk mitigation behaviour can reduce impact of SARS-CoV-2: a real-time modelling study of the January 2022 Omicron wave in England.

BACKGROUND: Predicting the likely size of future SARS-CoV-2 waves is necessary for public health planning. In England, voluntary "plan B" mitigation measures were introduced in December 2021 including increased home working and face coverings in shops but stopped short of restrictions on social contacts. The impact of voluntary risk mitigation behaviours on future SARS-CoV-2 burden is unknown. METHODS: We developed a rapid online survey of risk mitigation behaviours ahead of the winter 2021 festive period and deployed in two longitudinal cohort studies in the UK (Avon Longitudinal Study of Parents and Children (ALSPAC) and TwinsUK/COVID Symptom Study (CSS) Biobank) in December 2021. Using an individual-based, probabilistic model of COVID-19 transmission between social contacts with SARS-CoV-2 Omicron variant parameters and realistic vaccine coverage in England, we predicted the potential impact of the SARS-CoV-2 Omicron wave in England in terms of the effective reproduction number and cumulative infections, hospital admissions and deaths. Using survey results, we estimated in real-time the impact of voluntary risk mitigation behaviours on the Omicron wave in England, if implemented for the entire epidemic wave. RESULTS: Over 95% of survey respondents (NALSPAC = 2686 and NTwins = 6155) reported some risk mitigation behaviours, with vaccination and using home testing kits reported most frequently. Less than half of those respondents reported that their behaviour was due to "plan B". We estimate that without risk mitigation behaviours, the Omicron variant is consistent with an effective reproduction number between 2.5 and 3.5. Due to the reduced vaccine effectiveness against infection with the Omicron variant, our modelled estimates suggest that between 55% and 60% of the English population could be infected during the current wave, translating into between 12,000 and 46,000 cumulative deaths, depending on assumptions about severity and vaccine effectiveness. The actual number of deaths was 15,208 (26 November 2021-1 March 2022). We estimate that voluntary risk reduction measures could reduce the effective reproduction number to between 1.8 and 2.2 and reduce the cumulative number of deaths by up to 24%. CONCLUSIONS: Predicting future infection burden is affected by uncertainty in disease severity and vaccine effectiveness estimates. In addition to biological uncertainty, we show that voluntary measures substantially reduce the projected impact of the SARS-CoV-2 Omicron variant but that voluntary measures alone would be unlikely to completely control transmission.

Effectiveness of BNT162b2 COVID-19 vaccination in prevention of hospitalisations and severe disease in adults with SARS-CoV-2 Delta (B.1.617.2) and Omicron (B.1.1.529) variant between June 2021 and July 2022: A prospective test negative case–control study

Summary Background Whilst other studies have reported the effectiveness of mRNA vaccination against hospitalisation, including emergency department or intensive care admission, few have assessed effectiveness against other more clinically robust indices of COVID-19 severity. Methods A prospective single-centre test-negative design case–control study of adults hospitalised with COVID-19 disease or other acute respiratory disease between 1 June 2021 and 20 July 2022. We assessed VE (vaccine effectiveness) against hospitalisation, length of stay [LOS] >3 days, WHO COVID Score >5 and supplementary oxygen FiO2 (fraction inspired oxygen) >28%, conducting regression analyses controlling for age, gender, index of multiple deprivation, Charlson comorbidity index, time, and community infection prevalence. Findings 935 controls and 546 cases were hospitalised during the Delta period, with 721 controls and 372 cases hospitalised during the Omicron study period. Two-dose BNT162b2 was associated with VE 82.5% [95% confidence interval 76.2%–87.2%] against hospitalisation following Delta infection, 63.3% [26.9–81.8%], 58.5% [24.8–77.3%], and 51.5% [16.7–72.1%] against LOS >3 days, WHO COVID Score >5, and requirement for FiO2 >28% respectively. Three-dose BNT162b2 protection against hospitalisation with Omicron infection was 30.9% [5.9–49.3%], with sensitivity analyses ranging from 28.8–72.6%. Protection against LOS >3 days, WHO COVID Score >5 and requirement for FiO2 >28% was 56.1% [20.6–76.5%], 58.8% [31.2–75.8%], and 41.5% [−0.4–66.3%], respectively. In the UK, BNT162b2 was prioritised for high-risk individuals and those aged >75 years. In the latter group we found a higher estimate of VE against hospitalisation of 47.2% [16.8–66.6%]. Interpretation BNT162b2 vaccination results in risk reductions for hospitalisation and multiple patient outcomes following Delta and Omicron COVID-19 infection, particularly in older adults. BNT162b2 remains effective against severe SARS-CoV-2 disease. Funding AvonCAP is an investigator-led project funded under a collaborative agreement by 10.13039/100004319Pfizer.

Severity of Omicron (B.1.1.529) and Delta (B.1.617.2) SARS-CoV-2 infection among hospitalised adults: A prospective cohort study in Bristol, United Kingdom.

Background: There is an urgent public health need to evaluate disease severity in adults hospitalised with Delta and Omicron SARS-CoV-2 variant infections. However, limited data exist assessing severity of disease in adults hospitalised with Omicron SARS-CoV-2 infections, and to what extent patient-factors, including vaccination, age, frailty and pre-existing disease, affect variant-dependent disease severity. Methods: A prospective cohort study of adults (≥18 years of age) hospitalised with acute lower respiratory tract disease at acute care hospitals in Bristol, UK conducted over 10-months. Delta or Omicron SARS-CoV-2 infection was defined by positive SARS-CoV-2 PCR and variant identification or inferred by dominant circulating variant. We constructed adjusted regression analyses to assess disease severity using three different measures: FiO2 >28% (fraction inspired oxygen), World Health Organization (WHO) outcome score >5 (assessing need for ventilatory support), and hospital length of stay (LOS) >3 days following admission for Omicron or Delta infection. Findings: Independent of other variables, including vaccination, Omicron variant infection in hospitalised adults was associated with lower severity than Delta. Risk reductions were 58%, 67%, and 16% for supplementary oxygen with >28% FiO2 [Relative Risk (RR) = 0.42 (95%CI: 0.34-0.52), P < 0.001], WHO outcome score >5 [RR = 0.33 (95%CI: 0.21-0.50), P < 0.001], and to have had a LOS > 3 days [RR = 0.84 (95%CI: 0.76-0.92), P < 0.001]. Younger age and vaccination with two or three doses were also independently associated with lower COVID-19 severity. Interpretation: We provide reassuring evidence that Omicron infection results in less serious adverse outcomes than Delta in hospitalised patients. Despite lower severity relative to Delta, Omicron infection still resulted in substantial patient and public health burden and an increased admission rate of older patients with Omicron which counteracts some of the benefit arising from less severe disease. Funding: AvonCAP is an investigator-led project funded under a collaborative agreement by Pfizer.

Effectiveness of BNT162b2 COVID-19 vaccination in prevention of hospitalisations and severe disease in adults with SARS-CoV-2 Delta (B.1.617.2) and Omicron (B.1.1.529) variant between June 2021 and July 2022: A prospective test negative case-control study.

Background: Whilst other studies have reported the effectiveness of mRNA vaccination against hospitalisation, including emergency department or intensive care admission, few have assessed effectiveness against other more clinically robust indices of COVID-19 severity. Methods: A prospective single-centre test-negative design case-control study of adults hospitalised with COVID-19 disease or other acute respiratory disease between 1 June 2021 and 20 July 2022. We assessed VE (vaccine effectiveness) against hospitalisation, length of stay [LOS] >3 days, WHO COVID Score >5 and supplementary oxygen FiO2 (fraction inspired oxygen) >28%, conducting regression analyses controlling for age, gender, index of multiple deprivation, Charlson comorbidity index, time, and community infection prevalence. Findings: 935 controls and 546 cases were hospitalised during the Delta period, with 721 controls and 372 cases hospitalised during the Omicron study period. Two-dose BNT162b2 was associated with VE 82.5% [95% confidence interval 76.2%-87.2%] against hospitalisation following Delta infection, 63.3% [26.9-81.8%], 58.5% [24.8-77.3%], and 51.5% [16.7-72.1%] against LOS >3 days, WHO COVID Score >5, and requirement for FiO2 >28% respectively. Three-dose BNT162b2 protection against hospitalisation with Omicron infection was 30.9% [5.9-49.3%], with sensitivity analyses ranging from 28.8-72.6%. Protection against LOS >3 days, WHO COVID Score >5 and requirement for FiO2 >28% was 56.1% [20.6-76.5%], 58.8% [31.2-75.8%], and 41.5% [-0.4-66.3%], respectively. In the UK, BNT162b2 was prioritised for high-risk individuals and those aged >75 years. In the latter group we found a higher estimate of VE against hospitalisation of 47.2% [16.8-66.6%]. Interpretation: BNT162b2 vaccination results in risk reductions for hospitalisation and multiple patient outcomes following Delta and Omicron COVID-19 infection, particularly in older adults. BNT162b2 remains effective against severe SARS-CoV-2 disease. Funding: AvonCAP is an investigator-led project funded under a collaborative agreement by Pfizer.

Population disruption: observational study of changes in the population distribution of the UK during the COVID-19 pandemic

Background: Mobility data have demonstrated major changes in human movement patterns in response to COVID-19 and associated interventions in many countries. This involves sub-national redistribution, short-term relocations, and international migration. Aggregated mobile phone location data combined with small-area census population data allow changes in the population distribution of the UK to be quantified with high spatial and temporal granularity. Methods: In this paper, we combine detailed data from Facebook, measuring the location of approximately 6 million daily active Facebook users in 5km 2 tiles in the UK with census-derived population estimates to measure population mobility and redistribution. We provide time-varying population estimates and assess spatial population changes with respect to population density and four key reference dates in 2020 (first UK lockdown, end of term, beginning of term, Christmas). Results: We show how population estimates derived from Facebook data vary compared to mid-2020 small area population estimates by UK national statistics agencies. We also estimate that between March 2020 and March 2021, the total population of the UK declined and we identify important spatial variations in this population change, showing that low-density areas have experienced lower population decreases than urban areas. We estimate that, for the top 10% highest population tiles, the population has decreased by 6.6%. Finally, we provide evidence that geographic redistributions of population within the UK coincide with dates of non-pharmaceutical interventions including lockdowns and movement restrictions, as well as seasonal patterns of migration around holiday dates. Conclusions: The methods used in this study reveal significant changes in population distribution at high spatial and temporal resolutions that have not previously been quantified by available demographic surveys in the UK. We found early indicators of potential longer-term changes in the population distribution of the UK although it is not clear if these changes will persist after the COVID-19 pandemic.

Incidence of community acquired lower respiratory tract disease in Bristol, UK during the COVID-19 pandemic: A prospective cohort study.

Background: The emergence of COVID-19 and public health measures implemented to reduce SARS-CoV-2 infections have both affected acute lower respiratory tract disease (aLRTD) epidemiology and incidence trends. The severity of COVID-19 and non-SARS-CoV-2 aLRTD during this period have not been compared in detail. Methods: We conducted a prospective cohort study of adults age ≥18 years admitted to either of two acute care hospitals in Bristol, UK, from August 2020 to November 2021. Patients were included if they presented with signs or symptoms of aLRTD (e.g., cough, pleurisy), or a clinical or radiological aLRTD diagnosis. Findings: 12,557 adult aLRTD hospitalisations occurred: 10,087 were associated with infection (pneumonia or non-pneumonic lower respiratory tract infection [NP-LRTI]), 2161 with no infective cause, with 306 providing a minimal surveillance dataset. Confirmed SARS-CoV-2 infection accounted for 32% (3178/10,087) of respiratory infections. Annual incidences of overall, COVID-19, and non- SARS-CoV-2 pneumonia were 714.1, 264.2, and 449.9, and NP-LRTI were 346.2, 43.8, and 302.4 per 100,000 adults, respectively. Weekly incidence trends in COVID-19 aLRTD showed large surges (median 6.5 [IQR 0.7-10.2] admissions per 100,000 adults per week), while other infective aLRTD events were more stable (median 14.3 [IQR 12.8-16.4] admissions per 100,000 adults per week) as were non-infective aLRTD events (median 4.4 [IQR 3.5-5.5] admissions per 100,000 adults per week). Interpretation: While COVID-19 disease was a large component of total aLRTD during this pandemic period, non- SARS-CoV-2 infection still caused the majority of respiratory infection hospitalisations. COVID-19 disease showed significant temporal fluctuations in frequency, which were less apparent in non-SARS-CoV-2 infection. Despite public health interventions to reduce respiratory infection, disease incidence remains high. Funding: AvonCAP is an investigator-led project funded under a collaborative agreement by Pfizer.

An analysis of 45 large-scale wastewater sites in England to estimate SARS-CoV-2 community prevalence.

Accurate surveillance of the COVID-19 pandemic can be weakened by under-reporting of cases, particularly due to asymptomatic or pre-symptomatic infections, resulting in bias. Quantification of SARS-CoV-2 RNA in wastewater can be used to infer infection prevalence, but uncertainty in sensitivity and considerable variability has meant that accurate measurement remains elusive. Here, we use data from 45 sewage sites in England, covering 31% of the population, and estimate SARS-CoV-2 prevalence to within 1.1% of estimates from representative prevalence surveys (with 95% confidence). Using machine learning and phenomenological models, we show that differences between sampled sites, particularly the wastewater flow rate, influence prevalence estimation and require careful interpretation. We find that SARS-CoV-2 signals in wastewater appear 4-5 days earlier in comparison to clinical testing data but are coincident with prevalence surveys suggesting that wastewater surveillance can be a leading indicator for symptomatic viral infections. Surveillance for viruses in wastewater complements and strengthens clinical surveillance, with significant implications for public health.

Safety and immunogenicity of the inactivated whole-virus adjuvanted COVID-19 vaccine VLA2001: A randomized, dose escalation, double-blind phase 1/2 clinical trial in healthy adults.

OBJECTIVES: We aimed to evaluate the safety and optimal dose of a novel inactivated whole-virus adjuvanted vaccine against SARS-CoV-2: VLA2001. METHODS: We conducted an open-label, dose-escalation study followed by a double-blind randomized trial using low, medium and high doses of VLA2001 (1:1:1). The primary safety outcome was the frequency and severity of solicited local and systemic reactions within 7 days after vaccination. The primary immunogenicity outcome was the geometric mean titre (GMT) of neutralizing antibodies against SARS-CoV-2 two weeks after the second vaccination. The study is registered as NCT04671017. RESULTS: Between December 16, 2020, and June 3, 2021, 153 healthy adults aged 18-55 years were recruited in the UK. Overall, 81.7% of the participants reported a solicited AE, with injection site tenderness (58.2%) and headache (46.4%) being the most frequent. Only 2 participants reported a severe solicited event. Up to day 106, 131 (85.6%) participants had reported any AE. All observed incidents were transient and non-life threatening in nature. Immunogenicity measured at 2 weeks after completion of the two-dose priming schedule, showed significantly higher GMTs of SARS-CoV-2 neutralizing antibody titres in the highest dose group (GMT 545.6; 95% CI: 428.1, 695.4) which were similar to a panel of convalescent sera (GMT 526.9; 95% CI: 336.5, 825.1). Seroconversion rates of neutralizing antibodies were also significantly higher in the high-dose group (>90%) compared to the other dose groups. In the high dose group, antigen-specific IFN-γ expressing T-cells reactive against the S, M and N proteins were observed in 76, 36 and 49%, respectively. CONCLUSIONS: VLA2001 was well tolerated in all tested dose groups, and no safety signal of concern was identified. The highest dose group showed statistically significantly stronger immunogenicity with similar tolerability and safety, and was selected for phase 3 clinical development.

Effectiveness of BNT162b2 and ChAdOx1 nCoV-19 COVID-19 vaccination at preventing hospitalisations in people aged at least 80 years: a test-negative, case-control study.

BACKGROUND: On Dec 8, 2020, deployment of the first SARS-CoV-2 vaccination authorised for UK use (BNT162b2 mRNA vaccine) began, followed by an adenoviral vector vaccine ChAdOx1 nCoV-19 on Jan 4, 2021. Care home residents and staff, frontline health-care workers, and adults aged 80 years and older were vaccinated first. However, few data exist regarding the effectiveness of these vaccines in older people with many comorbidities. In this post-implementation evaluation of two COVID-19 vaccines, we aimed to determine the effectiveness of one dose in reducing COVID-19-related admissions to hospital in people of advanced age. METHODS: This prospective test-negative case-control study included adults aged at least 80 years who were admitted to hospital in two NHS trusts in Bristol, UK with signs and symptoms of respiratory disease. Patients who developed symptoms before receiving their vaccine or those who received their vaccine after admission to hospital were excluded, as were those with symptoms that started more than 10 days before hospital admission. We did logistic regression analysis, controlling for time (week), sex, index of multiple deprivations, and care residency status, and sensitivity analyses matched for time and sex using a conditional logistic model adjusting for index of multiple deprivations and care residency status. This study is registered with ISRCTN, number 39557. FINDINGS: Between Dec 18, 2020, and Feb 26, 2021, 466 adults were eligible (144 test-positive and 322 test-negative). 18 (13%) of 135 people with SARS-CoV-2 infection and 90 (34%) of 269 controls received one dose of BNT162b2. The adjusted vaccine effectiveness was 71·4% (95% CI 46·5-90·6). Nine (25%) of 36 people with COVID-19 infection and 53 (59%) of 90 controls received one dose of ChAdOx1 nCoV-19. The adjusted vaccine effectiveness was 80·4% (95% CI 36·4-94·5). When BNT162b2 effectiveness analysis was restricted to the period covered by ChAdOx1 nCoV-19, the estimate was 79·3% (95% CI 47·0-92·5). INTERPRETATION: One dose of either BNT162b2 or ChAdOx1 nCoV-19 resulted in substantial risk reductions of COVID-19-related hospitalisation in people aged at least 80 years. FUNDING: Pfizer.

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.

The 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.

Seroprevalencia de SARS-CoV-2 en niños y adolescentes mexicanos en edad escolar.

Objetivo. Estimar la seroprevalencia de SARS-CoV-2 en población de edad escolar en México. Material y métodos. Se categorizaron a niños y adolescentes que participaron en la Encuesta Nacional de Salud y Nutrición 2020 sobre Covid-19 (Ensanut 2020 Covid-19) por edad escolar y nivel educativo. En participantes seropositivos, se identificó la proporción de infecciones asintomáticas. Se estimaron razones de prevalencia usando un modelo de regresión log-binomial. Resultados. La seroprevalencia en educación básica y media fue de 18.7% (IC95%: 14.9, 22.5) y 26.7% (IC95%: 22.1, 31.3), respectivamente. La infección asintomática fue más frecuente en educación básica (88.5% [IC95%: 80.5, 93.5]). Conclusiones. En población de educación básica la infección por SARS-CoV-2 es baja y usualmente asintomática.

High COVID-19 transmission potential associated with re-opening universities can be mitigated with layered interventions.

Controlling COVID-19 transmission in universities poses challenges due to the complex social networks and potential for asymptomatic spread. We developed a stochastic transmission model based on realistic mixing patterns and evaluated alternative mitigation strategies. We predict, for plausible model parameters, that if asymptomatic cases are half as infectious as symptomatic cases, then 15% (98% Prediction Interval: 6-35%) of students could be infected during the first term without additional control measures. First year students are the main drivers of transmission with the highest infection rates, largely due to communal residences. In isolation, reducing face-to-face teaching is the most effective intervention considered, however layering multiple interventions could reduce infection rates by 75%. Fortnightly or more frequent mass testing is required to impact transmission and was not the most effective option considered. Our findings suggest that additional outbreak control measures should be considered for university settings.

University students and staff able to maintain low daily contact numbers during various COVID-19 guideline periods

UK universities re-opened in September 2020, amidst the coronavirus epidemic. During the first term, various national social distancing measures were introduced, including banning groups of >6 people and the second lockdown in November;however, outbreaks among university students occurred. We aimed to measure the University of Bristol staff and student contact patterns via an online, longitudinal survey capturing self-reported contacts on the previous day. We investigated the change in contacts associated with COVID-19 guidance periods: post-first lockdown (23/06/2020–03/07/2020), relaxed guidance period (04/07/2020–13/09/2020), ‘rule-of-six’ period (14/09/2020–04/11/2020) and the second lockdown (05/11/2020–25/11/2020). In total, 722 staff (4199 responses) and 738 students (1906 responses) were included in the study. For staff, daily contacts were higher in the relaxed guidance and ‘rule-of-six’ periods than the post-first lockdown and second lockdown. Mean student contacts dropped between the ‘rule-of-six’ and second lockdown periods. For both staff and students, the proportion meeting with groups larger than six dropped between the ‘rule-of-six’ period and the second lockdown period, although was higher for students than for staff. Our results suggest university staff and students responded to national guidance by altering their social contacts. Most contacts during the second lockdown were household contacts. The response in staff and students was similar, suggesting that students can adhere to social distancing guidance while at university. The number of contacts recorded for both staff and students were much lower than those recorded by previous surveys in the UK conducted before the COVID-19 pandemic.

Vaccine escape in a heterogeneous population: insights for SARS-CoV-2 from a simple model.

As a countermeasure to the SARS-CoV-2 pandemic, there has been swift development and clinical trial assessment of candidate vaccines, with subsequent deployment as part of mass vaccination campaigns. However, the SARS-CoV-2 virus has demonstrated the ability to mutate and develop variants, which can modify epidemiological properties and potentially also the effectiveness of vaccines. The widespread deployment of highly effective vaccines may rapidly exert selection pressure on the SARS-CoV-2 virus directed towards mutations that escape the vaccine-induced immune response. This is particularly concerning while infection is widespread. By developing and analysing a mathematical model of two population groupings with differing vulnerability and contact rates, we explore the impact of the deployment of vaccines among the population on the reproduction ratio, cases, disease abundance and vaccine escape pressure. The results from this model illustrate two insights: (i) vaccination aimed at reducing prevalence could be more effective at reducing disease than directly vaccinating the vulnerable; (ii) the highest risk for vaccine escape can occur at intermediate levels of vaccination. This work demonstrates a key principle: the careful targeting of vaccines towards particular population groups could reduce disease as much as possible while limiting the risk of vaccine escape.

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

[This corrects the article DOI: 10.1371/journal.pone.0241027.].

Household bubbles and COVID-19 transmission: insights from percolation theory.

In the era of social distancing to curb the spread of COVID-19, bubbling is the combining of two or more households to create an exclusive larger group. The impact of bubbling on COVID-19 transmission is challenging to quantify because of the complex social structures involved. We developed a network description of households in the UK, using the configuration model to link households. We explored the impact of bubbling scenarios by joining together households of various sizes. For each bubbling scenario, we calculated the percolation threshold, that is, the number of connections per individual required for a giant component to form, numerically and theoretically. We related the percolation threshold to the household reproduction number. We find that bubbling scenarios in which single-person households join with another household have a minimal impact on network connectivity and transmission potential. Ubiquitous scenarios where all households form a bubble are likely to lead to an extensive transmission that is hard to control. The impact of plausible scenarios, with variable uptake and heterogeneous bubble sizes, can be mitigated with reduced numbers of contacts outside the household. Bubbling of households comes at an increased risk of transmission; however, under certain circumstances risks can be modest and could be balanced by other changes in behaviours. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

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

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'.

Mapping social distancing measures to the reproduction number for COVID-19.

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 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'.