Estimation of the effective reproductive number Rt is important for detecting changes in disease transmission over time. During the Coronavirus Disease 2019 (COVID-19) pandemic, policy makers and ...public health officials are using Rt to assess the effectiveness of interventions and to inform policy. However, estimation of Rt from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation of Rt, we recommend the approach of Cori and colleagues, which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, such as Wallinga and Teunis, are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to the spread. We advise caution when using methods derived from the approach of Bettencourt and Ribeiro, as the resulting Rt estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in Rt estimation.
Isolation of cases and contact tracing is used to control outbreaks of infectious diseases, and has been used for coronavirus disease 2019 (COVID-19). Whether this strategy will achieve control ...depends on characteristics of both the pathogen and the response. Here we use a mathematical model to assess if isolation and contact tracing are able to control onwards transmission from imported cases of COVID-19.
We developed a stochastic transmission model, parameterised to the COVID-19 outbreak. We used the model to quantify the potential effectiveness of contact tracing and isolation of cases at controlling a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-like pathogen. We considered scenarios that varied in the number of initial cases, the basic reproduction number (R0), the delay from symptom onset to isolation, the probability that contacts were traced, the proportion of transmission that occurred before symptom onset, and the proportion of subclinical infections. We assumed isolation prevented all further transmission in the model. Outbreaks were deemed controlled if transmission ended within 12 weeks or before 5000 cases in total. We measured the success of controlling outbreaks using isolation and contact tracing, and quantified the weekly maximum number of cases traced to measure feasibility of public health effort.
Simulated outbreaks starting with five initial cases, an R0 of 1·5, and 0% transmission before symptom onset could be controlled even with low contact tracing probability; however, the probability of controlling an outbreak decreased with the number of initial cases, when R0 was 2·5 or 3·5 and with more transmission before symptom onset. Across different initial numbers of cases, the majority of scenarios with an R0 of 1·5 were controllable with less than 50% of contacts successfully traced. To control the majority of outbreaks, for R0 of 2·5 more than 70% of contacts had to be traced, and for an R0 of 3·5 more than 90% of contacts had to be traced. The delay between symptom onset and isolation had the largest role in determining whether an outbreak was controllable when R0 was 1·5. For R0 values of 2·5 or 3·5, if there were 40 initial cases, contact tracing and isolation were only potentially feasible when less than 1% of transmission occurred before symptom onset.
In most scenarios, highly effective contact tracing and case isolation is enough to control a new outbreak of COVID-19 within 3 months. The probability of control decreases with long delays from symptom onset to isolation, fewer cases ascertained by contact tracing, and increasing transmission before symptoms. This model can be modified to reflect updated transmission characteristics and more specific definitions of outbreak control to assess the potential success of local response efforts.
Wellcome Trust, Global Challenges Research Fund, and Health Data Research UK.
A severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variant, VOC 202012/01 (lineage B.1.1.7), emerged in southeast England in September 2020 and is rapidly spreading toward fixation. Using ...a variety of statistical and dynamic modeling approaches, we estimate that this variant has a 43 to 90% (range of 95% credible intervals, 38 to 130%) higher reproduction number than preexisting variants. A fitted two-strain dynamic transmission model shows that VOC 202012/01 will lead to large resurgences of COVID-19 cases. Without stringent control measures, including limited closure of educational institutions and a greatly accelerated vaccine rollout, COVID-19 hospitalizations and deaths across England in the first 6 months of 2021 were projected to exceed those in 2020. VOC 202012/01 has spread globally and exhibits a similar transmission increase (59 to 74%) in Denmark, Switzerland, and the United States.
Case isolation and contact tracing can contribute to the control of COVID-19 outbreaks
. However, it remains unclear how real-world social networks could influence the effectiveness and efficiency of ...such approaches. To address this issue, we simulated control strategies for SARS-CoV-2 transmission in a real-world social network generated from high-resolution GPS data that were gathered in the course of a citizen-science experiment
. We found that tracing the contacts of contacts reduced the size of simulated outbreaks more than tracing of only contacts, but this strategy also resulted in almost half of the local population being quarantined at a single point in time. Testing and releasing non-infectious individuals from quarantine led to increases in outbreak size, suggesting that contact tracing and quarantine might be most effective as a 'local lockdown' strategy when contact rates are high. Finally, we estimated that combining physical distancing with contact tracing could enable epidemic control while reducing the number of quarantined individuals. Our findings suggest that targeted tracing and quarantine strategies would be most efficient when combined with other control measures such as physical distancing.
Mathematical and statistical models can be used to make predictions of how epidemics may progress in the near future and form a central part of outbreak mitigation and control. Renewal equation based ...models allow inference of epidemiological parameters from historical data and forecast future epidemic dynamics without requiring complex mechanistic assumptions. However, these models typically ignore interaction between age groups, partly due to challenges in parameterising a time varying interaction matrix. Social contact data collected regularly during the COVID-19 epidemic provide a means to inform interaction between age groups in real-time. We developed an age-specific forecasting framework and applied it to two age-stratified time-series: incidence of SARS-CoV-2 infection, estimated from a national infection and antibody prevalence survey; and, reported cases according to the UK national COVID-19 dashboard. Jointly fitting our model to social contact data from the CoMix study, we inferred a time-varying next generation matrix which we used to project infections and cases in the four weeks following each of 29 forecast dates between October 2020 and November 2021. We evaluated the forecasts using proper scoring rules and compared performance with three other models with alternative data and specifications alongside two naive baseline models. Overall, incorporating age interaction improved forecasts of infections and the CoMix-data-informed model was the best performing model at time horizons between two and four weeks. However, this was not true when forecasting cases. We found that age group interaction was most important for predicting cases in children and older adults. The contact-data-informed models performed best during the winter months of 2020–2021, but performed comparatively poorly in other periods. We highlight challenges regarding the incorporation of contact data in forecasting and offer proposals as to how to extend and adapt our approach, which may lead to more successful forecasts in future.
The COVID-19 pandemic has shown a markedly low proportion of cases among children
. Age disparities in observed cases could be explained by children having lower susceptibility to infection, lower ...propensity to show clinical symptoms or both. We evaluate these possibilities by fitting an age-structured mathematical model to epidemic data from China, Italy, Japan, Singapore, Canada and South Korea. We estimate that susceptibility to infection in individuals under 20 years of age is approximately half that of adults aged over 20 years, and that clinical symptoms manifest in 21% (95% credible interval: 12-31%) of infections in 10- to 19-year-olds, rising to 69% (57-82%) of infections in people aged over 70 years. Accordingly, we find that interventions aimed at children might have a relatively small impact on reducing SARS-CoV-2 transmission, particularly if the transmissibility of subclinical infections is low. Our age-specific clinical fraction and susceptibility estimates have implications for the expected global burden of COVID-19, as a result of demographic differences across settings. In countries with younger population structures-such as many low-income countries-the expected per capita incidence of clinical cases would be lower than in countries with older population structures, although it is likely that comorbidities in low-income countries will also influence disease severity. Without effective control measures, regions with relatively older populations could see disproportionally more cases of COVID-19, particularly in the later stages of an unmitigated epidemic.
In December, 2019, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), a novel coronavirus, emerged in Wuhan, China. Since then, the city of Wuhan has taken unprecedented measures in ...response to the outbreak, including extended school and workplace closures. We aimed to estimate the effects of physical distancing measures on the progression of the COVID-19 epidemic, hoping to provide some insights for the rest of the world.
To examine how changes in population mixing have affected outbreak progression in Wuhan, we used synthetic location-specific contact patterns in Wuhan and adapted these in the presence of school closures, extended workplace closures, and a reduction in mixing in the general community. Using these matrices and the latest estimates of the epidemiological parameters of the Wuhan outbreak, we simulated the ongoing trajectory of an outbreak in Wuhan using an age-structured susceptible-exposed-infected-removed (SEIR) model for several physical distancing measures. We fitted the latest estimates of epidemic parameters from a transmission model to data on local and internationally exported cases from Wuhan in an age-structured epidemic framework and investigated the age distribution of cases. We also simulated lifting of the control measures by allowing people to return to work in a phased-in way and looked at the effects of returning to work at different stages of the underlying outbreak (at the beginning of March or April).
Our projections show that physical distancing measures were most effective if the staggered return to work was at the beginning of April; this reduced the median number of infections by more than 92% (IQR 66–97) and 24% (13–90) in mid-2020 and end-2020, respectively. There are benefits to sustaining these measures until April in terms of delaying and reducing the height of the peak, median epidemic size at end-2020, and affording health-care systems more time to expand and respond. However, the modelled effects of physical distancing measures vary by the duration of infectiousness and the role school children have in the epidemic.
Restrictions on activities in Wuhan, if maintained until April, would probably help to delay the epidemic peak. Our projections suggest that premature and sudden lifting of interventions could lead to an earlier secondary peak, which could be flattened by relaxing the interventions gradually. However, there are limitations to our analysis, including large uncertainties around estimates of R0 and the duration of infectiousness.
Bill & Melinda Gates Foundation, National Institute for Health Research, Wellcome Trust, and Health Data Research UK.
During the Coronavirus Disease 2019 (COVID-19) pandemic, the United Kingdom government imposed public health policies in England to reduce social contacts in hopes of curbing virus transmission. We ...conducted a repeated cross-sectional study to measure contact patterns weekly from March 2020 to March 2021 to estimate the impact of these policies, covering 3 national lockdowns interspersed by periods of less restrictive policies.
The repeated cross-sectional survey data were collected using online surveys of representative samples of the UK population by age and gender. Survey participants were recruited by the online market research company Ipsos MORI through internet-based banner and social media ads and email campaigns. The participant data used for this analysis are restricted to those who reported living in England. We calculated the mean daily contacts reported using a (clustered) bootstrap and fitted a censored negative binomial model to estimate age-stratified contact matrices and estimate proportional changes to the basic reproduction number under controlled conditions using the change in contacts as a scaling factor. To put the findings in perspective, we discuss contact rates recorded throughout the year in terms of previously recorded rates from the POLYMOD study social contact study. The survey recorded 101,350 observations from 19,914 participants who reported 466,710 contacts over 53 weeks. We observed changes in social contact patterns in England over time and by participants' age, personal risk factors, and perception of risk. The mean reported contacts for adults 18 to 59 years old ranged between 2.39 (95% confidence interval CI 2.20 to 2.60) contacts and 4.93 (95% CI 4.65 to 5.19) contacts during the study period. The mean contacts for school-age children (5 to 17 years old) ranged from 3.07 (95% CI 2.89 to 3.27) to 15.11 (95% CI 13.87 to 16.41). This demonstrates a sustained decrease in social contacts compared to a mean of 11.08 (95% CI 10.54 to 11.57) contacts per participant in all age groups combined as measured by the POLYMOD social contact study in 2005 to 2006. Contacts measured during periods of lockdowns were lower than in periods of eased social restrictions. The use of face coverings outside the home has remained high since the government mandated use in some settings in July 2020. The main limitations of this analysis are the potential for selection bias, as participants are recruited through internet-based campaigns, and recall bias, in which participants may under- or overreport the number of contacts they have made.
In this study, we observed that recorded contacts reduced dramatically compared to prepandemic levels (as measured in the POLYMOD study), with changes in reported contacts correlated with government interventions throughout the pandemic. Despite easing of restrictions in the summer of 2020, the mean number of reported contacts only returned to about half of that observed prepandemic at its highest recorded level. The CoMix survey provides a unique repeated cross-sectional data set for a full year in England, from the first day of the first lockdown, for use in statistical analyses and mathematical modelling of COVID-19 and other diseases.
The time-varying reproduction number (
: the average number of secondary infections caused by each infected person) may be used to assess changes in transmission potential during an epidemic. While ...new infections are not usually observed directly, they can be estimated from data. However, data may be delayed and potentially biased. We investigated the sensitivity of
estimates to different data sources representing COVID-19 in England, and we explored how this sensitivity could track epidemic dynamics in population sub-groups. We sourced public data on test-positive cases, hospital admissions and deaths with confirmed COVID-19 in seven regions of England over March through August 2020. We estimated
using a model that mapped unobserved infections to each data source. We then compared differences in
with the demographic and social context of surveillance data over time. Our estimates of transmission potential varied for each data source, with the relative inconsistency of estimates varying across regions and over time.
estimates based on hospital admissions and deaths were more spatio-temporally synchronous than when compared to estimates from all test positives. We found these differences may be linked to biased representations of subpopulations in each data source. These included spatially clustered testing, and where outbreaks in hospitals, care homes, and young age groups reflected the link between age and severity of the disease. We highlight that policy makers could better target interventions by considering the source populations of
estimates. Further work should clarify the best way to combine and interpret
estimates from different data sources based on the desired use. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.
The risk of severe COVID-19 if an individual becomes infected is known to be higher in older individuals and those with underlying health conditions. Understanding the number of individuals at ...increased risk of severe COVID-19 and how this varies between countries should inform the design of possible strategies to shield or vaccinate those at highest risk.
We estimated the number of individuals at increased risk of severe disease (defined as those with at least one condition listed as “at increased risk of severe COVID-19” in current guidelines) by age (5-year age groups), sex, and country for 188 countries using prevalence data from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017 and UN population estimates for 2020. The list of underlying conditions relevant to COVID-19 was determined by mapping the conditions listed in GBD 2017 to those listed in guidelines published by WHO and public health agencies in the UK and the USA. We analysed data from two large multimorbidity studies to determine appropriate adjustment factors for clustering and multimorbidity. To help interpretation of the degree of risk among those at increased risk, we also estimated the number of individuals at high risk (defined as those that would require hospital admission if infected) using age-specific infection–hospitalisation ratios for COVID-19 estimated for mainland China and making adjustments to reflect country-specific differences in the prevalence of underlying conditions and frailty. We assumed males were twice at likely as females to be at high risk. We also calculated the number of individuals without an underlying condition that could be considered at increased risk because of their age, using minimum ages from 50 to 70 years. We generated uncertainty intervals (UIs) for our estimates by running low and high scenarios using the lower and upper 95% confidence limits for country population size, disease prevalences, multimorbidity fractions, and infection–hospitalisation ratios, and plausible low and high estimates for the degree of clustering, informed by multimorbidity studies.
We estimated that 1·7 billion (UI 1·0–2·4) people, comprising 22% (UI 15–28) of the global population, have at least one underlying condition that puts them at increased risk of severe COVID-19 if infected (ranging from <5% of those younger than 20 years to >66% of those aged 70 years or older). We estimated that 349 million (186–787) people (4% 3–9 of the global population) are at high risk of severe COVID-19 and would require hospital admission if infected (ranging from <1% of those younger than 20 years to approximately 20% of those aged 70 years or older). We estimated 6% (3–12) of males to be at high risk compared with 3% (2–7) of females. The share of the population at increased risk was highest in countries with older populations, African countries with high HIV/AIDS prevalence, and small island nations with high diabetes prevalence. Estimates of the number of individuals at increased risk were most sensitive to the prevalence of chronic kidney disease, diabetes, cardiovascular disease, and chronic respiratory disease.
About one in five individuals worldwide could be at increased risk of severe COVID-19, should they become infected, due to underlying health conditions, but this risk varies considerably by age. Our estimates are uncertain, and focus on underlying conditions rather than other risk factors such as ethnicity, socioeconomic deprivation, and obesity, but provide a starting point for considering the number of individuals that might need to be shielded or vaccinated as the global pandemic unfolds.
UK Department for International Development, Wellcome Trust, Health Data Research UK, Medical Research Council, and National Institute for Health Research.
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