Assessing the impact of non-pharmaceutical interventions on SARS-CoV-2 transmission in Switzerland

A modeling framework for the analysis of the SARS-CoV2 transmission dynamics

Despite the progress in medical data collection the actual burden of SARS-CoV-2 remains unknown due to under-ascertainment of cases. This was apparent in the acute phase of the pandemic and the use of reported deaths has been pointed out as a more reliable source of information, likely less prone to under-reporting. Since daily deaths occur from past infections weighted by their probability of death, one may infer the total number of infections accounting for their age distribution, using the data on reported deaths. We adopt this framework and assume that the dynamics generating the total number of infections can be described by a continuous time transmission model expressed through a system of nonlinear ordinary differential equations where the transmission rate is modeled as a diffusion process allowing to reveal both the effect of control strategies and the changes in individuals behavior. We develop this flexible Bayesian tool in Stan and study 3 pairs of European countries, estimating the time-varying reproduction number (R t $$ {R}_t $$ ) as well as the true cumulative number of infected individuals. As we estimate the true number of infections we offer a more accurate estimate ofR t $$ {R}_t $$ . We also provide an estimate of the daily reporting ratio and discuss the effects of changes in mobility and testing on the inferred quantities.

Interplay of Digital Proximity App Use and SARS-CoV-2 Vaccine Uptake in Switzerland: Analysis of Two Population-Based Cohort Studies

Objectives: Our study aims to evaluate developments in vaccine uptake and digital proximity tracing app use in a localized context of the SARS-CoV-2 pandemic. Methods: We report findings from two population-based longitudinal cohorts in Switzerland from January to December 2021. Failure time analyses and Cox proportional hazards regression models were conducted to assess vaccine uptake and digital proximity tracing app (SwissCovid) uninstalling outcomes. Results: We observed a dichotomy of individuals who did not use the SwissCovid app and did not get vaccinated, and who used the SwissCovid app and got vaccinated during the study period. Increased vaccine uptake was observed with SwissCovid app use (aHR, 1.51; 95% CI: 1.40-1.62 [CI-DFU]; aHR, 1.79; 95% CI: 1.62-1.99 [CSM]) compared to SwissCovid app non-use. Decreased SwissCovid uninstallation risk was observed for participants who got vaccinated (aHR, 0.55; 95% CI: 0.38-0.81 [CI-DFU]; aHR, 0.45; 95% CI: 0.27-0.78 [CSM]) compared to participants who did not get vaccinated. Conclusion: In evolving epidemic contexts, these findings underscore the need for communication strategies as well as flexible digital proximity tracing app adjustments that accommodate different preventive measures and their anticipated interactions.

Wastewater-based modeling, reconstruction, and prediction for COVID-19 outbreaks in Hungary caused by highly immune evasive variants

(MOTIVATION)

Wastewater-based epidemiology (WBE) has emerged as a promising approach for monitoring the COVID-19 pandemic, since the measurement process is cost-effective and is exposed to fewer potential errors compared to other indicators like hospitalization data or the number of detected cases. Consequently, WBE was gradually becoming a key tool for epidemic surveillance and often the most reliable data source, as the intensity of clinical testing for COVID-19 drastically decreased by the third year of the pandemic. Recent results suggests that the model-based fusion of wastewater measurements with clinical data and other indicators is essential in future epidemic surveillance.

(METHOD)

In this work, we developed a wastewater-based compartmental epidemic model with a two-phase vaccination dynamics and immune evasion. We proposed a multi-step optimization-based data assimilation method for epidemic state reconstruction, parameter estimation, and prediction. The computations make use of the measured viral load in wastewater, the available clinical data (hospital occupancy, delivered vaccine doses, and deaths), the stringency index of the official social distancing rules, and other measures. The current state assessment and the estimation of the current transmission rate and immunity loss allow a plausible prediction of the future progression of the pandemic.

(RESULTS)

Qualitative and quantitative evaluations revealed that the contribution of wastewater data in our computational epidemiological framework makes predictions more reliable. Predictions suggest that at least half of the Hungarian population has lost immunity during the epidemic outbreak caused by the BA.1 and BA.2 subvariants of Omicron in the first half of 2022. We obtained a similar result for the outbreaks caused by the subvariant BA.5 in the second half of 2022.

(APPLICABILITY)

The proposed approach has been used to support COVID management in Hungary and could be customized for other countries as well.

Joint Analysis of the Epidemic Evolution and Human Mobility During the First Wave of COVID-19 in Spain: Retrospective Study

BACKGROUND

The initial wave of the COVID-19 pandemic placed a tremendous strain on health care systems worldwide. To mitigate the spread of the virus, many countries implemented stringent nonpharmaceutical interventions (NPIs), which significantly altered human behavior both before and after their enactment. Despite these efforts, a precise assessment of the impact and efficacy of these NPIs, as well as the extent of human behavioral changes, remained elusive.

OBJECTIVE

In this study, we conducted a retrospective analysis of the initial wave of COVID-19 in Spain to better comprehend the influence of NPIs and their interaction with human behavior. Such investigations are vital for devising future mitigation strategies to combat COVID-19 and enhance epidemic preparedness more broadly.

METHODS

We used a combination of national and regional retrospective analyses of pandemic incidence alongside large-scale mobility data to assess the impact and timing of government-implemented NPIs in combating COVID-19. Additionally, we compared these findings with a model-based inference of hospitalizations and fatalities. This model-based approach enabled us to construct counterfactual scenarios that gauged the consequences of delayed initiation of epidemic response measures.

RESULTS

Our analysis demonstrated that the pre-national lockdown epidemic response, encompassing regional measures and heightened individual awareness, significantly contributed to reducing the disease burden in Spain. The mobility data indicated that people adjusted their behavior in response to the regional epidemiological situation before the nationwide lockdown was implemented. Counterfactual scenarios suggested that without this early epidemic response, there would have been an estimated 45,400 (95% CI 37,400-58,000) fatalities and 182,600 (95% CI 150,400-233,800) hospitalizations compared to the reported figures of 27,800 fatalities and 107,600 hospitalizations, respectively.

CONCLUSIONS

Our findings underscore the significance of self-implemented prevention measures by the population and regional NPIs before the national lockdown in Spain. The study also emphasizes the necessity for prompt and precise data quantification prior to enacting enforced measures. This highlights the critical interplay between NPIs, epidemic progression, and human behavior. This interdependence presents a challenge in predicting the impact of NPIs before they are implemented.

Health-related quality of life before and during the COVID-19 pandemic in Switzerland: a cross-sectional study

INTRODUCTION

The COVID-19 pandemic forced people to give up their daily routines and adjust to new circumstances. This might have affected health-related quality of life (HRQOL). We aimed to compare HRQOL during the first COVID-19 wave in 2020 to HRQOL before the pandemic and to identify determinants of HRQOL during the pandemic in Switzerland.

METHODS

We conducted a cross-sectional online survey during the pandemic (between May and July 2020; CoWELL sample; convenience sample). Before the pandemic (2015-2016), we had conducted a cross-sectional paper-based survey among a representative random sample of the Swiss general population (SGP sample). In both samples, we assessed physical and mental HRQOL (Short Form-36) and socio-demographic characteristics. In the CoWELL sample, we additionally assessed health- and COVID-19-related characteristics. Data were analysed using linear regressions.

RESULTS

The CoWELL sample included 1581 participants (76% women; mean age = 43 years, SD = 14 years) and the SGP sample 1209 participants (58% women, mean age = 49 years, SD = 15 years). Adjusted for sex, age, and education, the CoWELL sample reported higher physical HRQOL (PCS, +5.8 (95% CI: 5.1, 6.6), p < 0.001) and lower mental HRQOL (MCS, -6.9 (-7.8, -6.0), p < 0.001) than the SGP sample. In the CoWELL sample, especially persons with lower health literacy, who had no support network or who have had COVID-19, reported lower HRQOL.

DISCUSSION

Aspects unique to the COVID-19 pandemic affected HRQOL. Vulnerable persons such as those having had COVID-19, less support opportunities, and with lower health literacy are especially prone to impaired HRQOL during the COVID-19 pandemic.

Effectiveness of non-pharmaceutical interventions in nine fields of activity to decrease SARS-CoV-2 transmission (Spain, September 2020-May 2021)

Background

We estimated the association between the level of restriction in nine different fields of activity and SARS-CoV-2 transmissibility in Spain, from 15 September 2020 to 9 May 2021.

Methods

A stringency index (0-1) was created for each Spanish province (n = 50) daily. A hierarchical multiplicative model was fitted. The median of coefficients across provinces (95% bootstrap confidence intervals) quantified the effect of increasing one standard deviation in the stringency index over the logarithmic return of the weekly percentage variation of the 7-days SARS-CoV-2 cumulative incidence, lagged 12 days.

Results

Overall, increasing restrictions reduced SARS-CoV-2 transmission by 22% (RR = 0.78; one-sided 95%CI: 0, 0.82) in 1 week, with highest effects for culture and leisure 14% (0.86; 0, 0.98), social distancing 13% (0.87; 0, 0.95), indoor restaurants 10% (0.90; 0, 0.95) and indoor sports 6% (0.94; 0, 0.98). In a reduced model with seven fields, culture and leisure no longer had a significant effect while ceremonies decreased transmission by 5% (0.95; 0, 0.96). Models R ² was around 70%.

Conclusion

Increased restrictions decreased COVID-19 transmission. Limitations include remaining collinearity between fields, and somewhat artificial quantification of qualitative restrictions, so the exact attribution of the effect to specific areas must be done with caution.

Impact of cross-border-associated cases on the SARS-CoV-2 epidemic in Switzerland during summer 2020 and 2021

During the summers of 2020 and 2021, the number of confirmed cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections in Switzerland remained at relatively low levels, but grew steadily over time. It remains unclear to what extent epidemic growth during these periods was a result of the relaxation of local control measures or increased traveling and subsequent importation of cases. A better understanding of the role of cross-border-associated cases (imports) on the local epidemic dynamics will help to inform future surveillance strategies. We analyzed routine surveillance data of confirmed cases of SARS-CoV-2 in Switzerland from 1 June to 30 September 2020 and 2021. We used a stochastic branching process model that accounts for superspreading of SARS-CoV-2 to simulate epidemic trajectories in absence and in presence of imports during summer 2020 and 2021. The Swiss Federal Office of Public Health reported 22,919 and 145,840 confirmed cases of SARS-CoV-2 from 1 June to 30 September 2020 and 2021, respectively. Among cases with known place of exposure, 27% (3,276 of 12,088) and 25% (1,110 of 4,368) reported an exposure abroad in 2020 and 2021, respectively. Without considering the impact of imported cases, the steady growth of confirmed cases during summer periods would be consistent with a value of R_e that is significantly above the critical threshold of 1. In contrast, we estimated R_e at 0.84 (95% credible interval, CrI: 0.78-0.90) in 2020 and 0.82 (95% CrI: 0.74-0.90) in 2021 when imported cases were taken into account, indicating that the local R_e was below the critical threshold of 1 during summer. In Switzerland, cross-border-associated SARS-CoV-2 cases had a considerable impact on the local transmission dynamics and can explain the steady growth of the epidemic during the summers of 2020 and 2021.

Social Behavior and COVID-19: Analysis of the Social Factors behind Compliance with Interventions across the United States

Since its emergence, COVID-19 has caused a great impact in health and social terms. Governments and health authorities have attempted to minimize this impact by enforcing different mandates. Recent studies have addressed the relationship between various socioeconomic variables and compliance level to these interventions. However, little attention has been paid to what constitutes people's response and whether people behave differently when faced with different interventions. Data collected from different sources show very significant regional differences across the United States. In this paper, we attempt to shed light on the fact that a response may be different depending on the health system capacity and each individuals' social status. For that, we analyze the correlation between different societal (i.e., education, income levels, population density, etc.) and healthcare capacity-related variables (i.e., hospital occupancy rates, percentage of essential workers, etc.) in relation to people's level of compliance with three main governmental mandates in the United States: mobility restrictions, mask adoption, and vaccine participation. Our aim was to isolate the most influential variables impacting behavior in response to these policies. We found that there was a significant relationship between individuals' educational levels and political preferences with respect to compliance with each of these mandates.

The methodologies to assess the effectiveness of non-pharmaceutical interventions during COVID-19: a systematic review

Non-pharmaceutical interventions, such as school closures and stay-at-home orders, have been implemented around the world to control the spread of SARS-CoV-2. Their effectiveness in improving health-related outcomes has been the subject of numerous empirical studies. However, these studies show fairly large variation among methodologies in use, reflecting the absence of an established methodological framework. On the one hand, variation in methodologies may be desirable to assess the robustness of results; on the other hand, a lack of common standards can impede comparability among studies. To establish a comprehensive overview over the methodologies in use, we conducted a systematic review of studies assessing the effectiveness of non-pharmaceutical interventions between January 1, 2020 and January 12, 2021 (n = 248). We identified substantial variation in methodologies with respect to study setting, outcome, intervention, methodological approach, and effectiveness assessment. On this basis, we point to shortcomings of existing studies and make recommendations for the design of future studies.

Estimation and worldwide monitoring of the effective reproductive number of SARS-CoV-2

The effective reproductive number R_e is a key indicator of the growth of an epidemic. Since the start of the SARS-CoV-2 pandemic, many methods and online dashboards have sprung up to monitor this number through time. However, these methods are not always thoroughly tested, correctly placed in time, or are overly confident during high incidence periods. Here, we present a method for timely estimation of R_e, applied to COVID-19 epidemic data from 170 countries. We thoroughly evaluate the method on simulated data, and present an intuitive web interface for interactive data exploration. We show that, in early 2020, in the majority of countries the estimated R_e dropped below 1 only after the introduction of major non-pharmaceutical interventions. For Europe the implementation of non-pharmaceutical interventions was broadly associated with reductions in the estimated R_e. Globally though, relaxing non-pharmaceutical interventions had more varied effects on subsequent R_e estimates. Our framework is useful to inform governments and the general public on the status of epidemics in their country, and is used as the official source of R_e estimates for SARS-CoV-2 in Switzerland. It further allows detailed comparison between countries and in relation to covariates such as implemented public health policies, mobility, behaviour, or weather data.

Estimation and worldwide monitoring of the effective reproductive number of SARS-CoV-2

The effective reproductive number Re is a key indicator of the growth of an epidemic. Since the start of the SARS-CoV-2 pandemic, many methods and online dashboards have sprung up to monitor this number through time. However, these methods are not always thoroughly tested, correctly placed in time, or are overly confident during high incidence periods. Here, we present a method for timely estimation of Re, applied to COVID-19 epidemic data from 170 countries. We thoroughly evaluate the method on simulated data, and present an intuitive web interface for interactive data exploration. We show that, in early 2020, in the majority of countries the estimated Re dropped below 1 only after the introduction of major non-pharmaceutical interventions. For Europe the implementation of non-pharmaceutical interventions was broadly associated with reductions in the estimated Re. Globally though, relaxing non-pharmaceutical interventions had more varied effects on subsequent Re estimates. Our framework is useful to inform governments and the general public on the status of epidemics in their country, and is used as the official source of Re estimates for SARS-CoV-2 in Switzerland. It further allows detailed comparison between countries and in relation to covariates such as implemented public health policies, mobility, behaviour, or weather data.

Associations between components of household expenditures and the rate of change in the number of new confirmed cases of COVID-19 in Japan: Time-series analysis

Background

Social distancing measures to prevent the spread of COVID-19 included restrictions on retail services in many countries. In some countries, the governments also subsidized consumer spending on part of retail services to help struggling businesses. To evaluate the costs and benefits of government interventions in retail services, it is necessary to measure the infectiousness of each type of consumer activity.

Methods

This study regresses the log difference over seven days in the number of new confirmed cases of COVID-19 in Japan on lagged values of household expenditures per household on eating out, traveling, admissions to entertainment facilities, clothing and footwear, and the other items, as well as a measure of mobility in public transportation in the past 14 days. The sample period of the dependent variable is set from March 1, 2020, to February 1, 2021, in order to avoid a possible structural break due to the spread of mutant strains in 2021. The regression model is estimated by the Bayesian method with a non-informative (improper) prior. The estimated model is evaluated by out-of-sample forecast performance from February 2, 2021, onward.

Results

The out-of-sample forecasts of the regression by the posterior means of regression coefficients perform well before the spread of the Delta variant in Japan since June 2021. R² for the out-of-sample forecasts from February 2, 2021, to June 30, 2021, is 0.60. The dependent variable of the regression overshot the out-of-sample forecasts from mid-June to August 2021. Then, the out-of-sample forecasts overpredicted the dependent variable for the rest of 2021.

Conclusion

The estimated model can be potentially useful in simulating changes in the number of new confirmed cases due to household spending on retail services, if it can be adjusted to real-time developments of mutant strains and vaccinations. Such simulations would help in designing cost-efficient government interventions.

Effectiveness of different types and levels of social distancing measures: a scoping review of global evidence from earlier stage of COVID-19 pandemic

OBJECTIVE

Social distancing is one of the main non-pharmaceutical interventions used in the control of the COVID-19 pandemic. This scoping review aims to synthesise research findings on the effectiveness of different types and levels of social distancing measures in the earlier stage of COVID-19 pandemic without the confounding effect of mass vaccination.

DESIGN

Scoping review.

DATA SOURCES

MEDLINE, Embase, Global Health and four other databases were searched for eligible studies on social distancing for COVID-19 published from inception of the databases to 30 September 2020.

STUDY SELECTION AND DATA EXTRACTION

Effectiveness studies on social distancing between individuals, school closures, workplace/business closures, public transport restrictions and partial/full lockdown were included. Non-English articles, studies in healthcare settings or not based on empirical data were excluded.

RESULTS

After screening 1638 abstracts and 8 additional articles from other sources, 41 studies were included for synthesis of findings. The review found that the outcomes of social distancing measures were mainly indicated by changes in R_t , incidence and mortality, along with indirect indicators such as daily contact frequency and travel distance. There was adequate empirical evidence for the effect of social distancing at the individual level, and for partial or full lockdown at the community level. However, at the level of social settings, the evidence was moderate for school closure, and was limited for workplace/business closures as single targeted interventions. There was no evidence for a separate effect of public transport restriction.

CONCLUSIONS

In the community setting, there was stronger evidence for the combined effect of different social distancing interventions than for a single intervention. As fatigue of preventive behaviours is an issue in public health agenda, future studies should analyse the risks in specific settings such as eateries and entertainment to implement and evaluate measures which are proportionate to the risk.

Government Intervention, Human Mobility, and COVID-19: A Causal Pathway Analysis from 121 Countries

Based on data from 121 countries, the study assesses the dynamic effect and causality path of the government epidemic prevention policies and human mobility behaviors on the growth rates of COVID-19 new cases and deaths. Our results find that both policies and behaviors influenced COVID-19 cases and deaths. The direct effect of policies on COVID-19 was more than the indirect effect. Policies influence behaviors, and behaviors react spontaneously to information. Further, masks give people a false sense of security and increase mobility. The close public transport policy increased COVID-19 new cases. We also conducted sensitivity analysis and found that some policies hold robustly, such as the policies of school closing, restrictions on gatherings, stay-at-home requirements, international travel controls, facial coverings, and vaccination. The counterfactual tests suggest that, as of early March 2021, if governments had mandated masking policies early in the epidemic, the cases and deaths would have been reduced by 18% and 14% separately. If governments had implemented vaccination policies early in the pandemic, the cases and deaths would have been reduced by 93% and 62%, respectively. Without public transportation closures, cases and deaths would have been reduced by 40% and 10%, respectively.

A review on COVID-19 transmission, epidemiological features, prevention and vaccination

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused hundreds of millions of infections and millions of deaths over past two years. Currently, many countries have still not been able to take the pandemic under control. In this review, we systematically summarized what we have done to mitigate the COVID-19 pandemic, from the perspectives of virus transmission, public health control measures, to the development and vaccination of COVID-19 vaccines. As a virus most likely coming from bats, the SARS-CoV-2 may transmit among people via airborne, faecal-oral, vertical or foodborne routes. Our meta-analysis suggested that the R₀ of COVID-19 was 2.9 (95% CI: 2.7–3.1), and the estimates in Africa and Europe could be higher. The median R_t could decrease by 23–96% following the nonpharmacological interventions, including lockdown, isolation, social distance, and face mask, etc. Comprehensive intervention and lockdown were the most effective measures to control the pandemic. According to the pooled R₀ in our meta-analysis, there should be at least 93.3% (95% CI: 89.9–96.2%) people being vaccinated around the world. Limited amount of vaccines and the inequity issues in vaccine allocation call for more international cooperation to achieve the anti-epidemic goals and vaccination fairness.

Transmission dynamics model and the coronavirus disease 2019 epidemic: applications and challenges

Since late 2019, the beginning of coronavirus disease 2019 (COVID-19) pandemic, transmission dynamics models have achieved great development and were widely used in predicting and policy making. Here, we provided an introduction to the history of disease transmission, summarized transmission dynamics models into three main types: compartment extension, parameter extension and population-stratified extension models, highlight the key contribution of transmission dynamics models in COVID-19 pandemic: estimating epidemiological parameters, predicting the future trend, evaluating the effectiveness of control measures and exploring different possibilities/scenarios. Finally, we pointed out the limitations and challenges lie ahead of transmission dynamics models.

Reconstruction of Epidemiological Data in Hungary Using Stochastic Model Predictive Control

In this paper, we propose a model-based method for the reconstruction of not directly measured epidemiological data. To solve this task, we developed a generic optimization-based approach to compute unknown time-dependent quantities (such as states, inputs, and parameters) of discrete-time stochastic nonlinear models using a sequence of output measurements. The problem was reformulated as a stochastic nonlinear model predictive control computation, where the unknown inputs and parameters were searched as functions of the uncertain states, such that the model output followed the observations. The unknown data were approximated by Gaussian distributions. The predictive control problem was solved over a relatively long time window in three steps. First, we approximated the expected trajectories of the unknown quantities through a nonlinear deterministic problem. In the next step, we fixed the expected trajectories and computed the corresponding variances using closed-form expressions. Finally, the obtained mean and variance values were used as an initial guess to solve the stochastic problem. To reduce the estimated uncertainty of the computed states, a closed-loop input policy was considered during the optimization, where the state-dependent gain values were determined heuristically. The applicability of the approach is illustrated through the estimation of the epidemiological data of the COVID-19 pandemic in Hungary. To describe the epidemic spread, we used a slightly modified version of a previously published and validated compartmental model, in which the vaccination process was taken into account. The mean and the variance of the unknown data (e.g., the number of susceptible, infected, or recovered people) were estimated using only the daily number of hospitalized patients. The problem was reformulated as a finite-horizon predictive control problem, where the unknown time-dependent parameter, the daily transmission rate of the disease, was computed such that the expected value of the computed number of hospitalized patients fit the truly observed data as much as possible.

Remote Health Monitoring in the Workplace for Early Detection of COVID-19 Cases during the COVID-19 Pandemic Using a Mobile Health Application: COVIDApp

Background: COVIDApp is a platform created for management of COVID-19 in the workplace. Methods: COVIDApp was designed and implemented for the follow-up of 253 workers from seven companies in Catalonia. The assessment was based on two actions: first, the early detection and management of close contacts and potential cases of COVID-19, and second, the rapid remote activation of protocols. The main objectives of this strategy were to minimize the risk of transmission of COVID-19 infection in the work area through a new real-time communication channel and to avoid unnecessary sick leave. The parameters reported daily by workers were close contact with COVID cases and signs and/or symptoms of COVID-19. Results: Data were recorded between 1 May and 30 November 2020. A total of 765 alerts were activated by 76 workers: 127 green alarms (16.6%), 301 orange alarms (39.3%), and 337 red alarms (44.1%). Of all the red alarms activated, 274 (81.3%) were activated for symptoms potentially associated with COVID-19, and 63 (18.7%) for reporting close contact with COVID-19 cases. Only eight workers (3.1%) presented symptoms associated with COVID-19 infection. All of these workers underwent RT-PCR tests, which yielded negative results for SARS-CoV2. Three workers were considered to have had a risk contact with COVID-19 cases; only 1 (0.4%) asymptomatic worker had a positive RT-PCR test result, requiring the activation of protocols, isolation, and contact tracing. Conclusions: COVIDApp contributes to the early detection and rapid activation of protocols in the workplace, thus limiting the risk of spreading the virus and reducing the economic impact caused by COVID-19 in the productive sector. The platform shows the progression of infection in real time and can help design new strategies.

Code status documentation at admission in COVID-19 patients: a descriptive cohort study

OBJECTIVES

The COVID-19 pandemic pressurised healthcare with increased shortage of care. This resulted in an increase of awareness for code status documentation (ie, whether limitations to specific life-sustaining treatments are in place), both in the medical field and in public media. However, it is unknown whether the increased awareness changed the prevalence and content of code status documentation for COVID-19 patients. We aim to describe differences in code status documentation between infectious patients before the pandemic and COVID-19 patients.

SETTING

University Medical Centre of Utrecht, a tertiary care teaching academic hospital in the Netherlands.

PARTICIPANTS

A total of 1715 patients were included, 129 in the COVID-19 cohort (a cohort of COVID-19 patients, admitted from March 2020 to June 2020) and 1586 in the pre-COVID-19 cohort (a cohort of patients with (suspected) infections admitted between September 2016 to September 2018).

PRIMARY AND SECONDARY OUTCOME MEASURES

We described frequency of code status documentation, frequency of discussion of this code status with patient and/or family, and content of code status.

RESULTS

Frequencies of code status documentation (69.8% vs 72.7%, respectively) and discussion (75.6% vs 73.3%, respectively) were similar in both cohorts. More patients in the COVID-19 cohort than in the before COVID-19 cohort had any treatment limitation as opposed to full code (40% vs 25%). Within the treatment limitations, 'no intensive care admission' (81% vs 51%) and 'no intubation' (69% vs 40%) were more frequently documented in the COVID-19 cohort. A smaller difference was seen in 'other limitation' (17% vs 9%), while 'no resuscitation' (96% vs 92%) was comparable between both periods.

CONCLUSION

We observed no difference in the frequency of code status documentation or discussion in COVID-19 patients opposed to a pre-COVID-19 cohort. However, treatment limitations were more prevalent in patients with COVID-19, especially 'no intubation' and 'no intensive care admission'.

Regular testing of asymptomatic healthcare workers identifies cost-efficient SARS-CoV-2 preventive measures

Protecting healthcare professionals is crucial in maintaining a functioning healthcare system. The risk of infection and optimal preventive strategies for healthcare workers during the COVID-19 pandemic remain poorly understood. Here we report the results of a cohort study that included pre- and asymptomatic healthcare workers. A weekly testing regime has been performed in this cohort since the beginning of the COVID-19 pandemic to identify infected healthcare workers. Based on these observations we have developed a mathematical model of SARS-CoV-2 transmission that integrates the sources of infection from inside and outside the hospital. The data were used to study how regular testing and a desynchronisation protocol are effective in preventing transmission of COVID-19 infection at work, and compared both strategies in terms of workforce availability and cost-effectiveness. We showed that case incidence among healthcare workers is higher than would be explained solely by community infection. Furthermore, while testing and desynchronisation protocols are both effective in preventing nosocomial transmission, regular testing maintains work productivity with implementation costs.

A Mathematical Model of COVID-19 with Vaccination and Treatment

We formulate and theoretically analyze a mathematical model of COVID-19 transmission mechanism incorporating vital dynamics of the disease and two key therapeutic measures-vaccination of susceptible individuals and recovery/treatment of infected individuals. Both the disease-free and endemic equilibrium are globally asymptotically stable when the effective reproduction number R 0(v) is, respectively, less or greater than unity. The derived critical vaccination threshold is dependent on the vaccine efficacy for disease eradication whenever R 0(v) > 1, even if vaccine coverage is high. Pontryagin's maximum principle is applied to establish the existence of the optimal control problem and to derive the necessary conditions to optimally mitigate the spread of the disease. The model is fitted with cumulative daily Senegal data, with a basic reproduction number R 0 = 1.31 at the onset of the epidemic. Simulation results suggest that despite the effectiveness of COVID-19 vaccination and treatment to mitigate the spread of COVID-19, when R 0(v) > 1, additional efforts such as nonpharmaceutical public health interventions should continue to be implemented. Using partial rank correlation coefficients and Latin hypercube sampling, sensitivity analysis is carried out to determine the relative importance of model parameters to disease transmission. Results shown graphically could help to inform the process of prioritizing public health intervention measures to be implemented and which model parameter to focus on in order to mitigate the spread of the disease. The effective contact rate b, the vaccine efficacy ε, the vaccination rate v, the fraction of exposed individuals who develop symptoms, and, respectively, the exit rates from the exposed and the asymptomatic classes σ and ϕ are the most impactful parameters.

Post-lockdown infection rates of COVID-19 following the reopening of public businesses

Background

The Coronavirus Disease 2019 (COVID-19) pandemic warranted a myriad of government-ordered business closures across the USA in efforts to mitigate the spread of the virus. This study aims to discover the implications of government-enforced health policies of reopening public businesses amidst the pandemic and its effect on county-level infection rates.

Methods

Eighty-three US counties (n = 83) that reported at least 20 000 cases as of 4 November 2020 were selected for this study. The dates when businesses (restaurants, bars, retail, gyms, salons/barbers and public schools) partially and fully reopened, as well as infection rates on the 1st and 14th days following each businesses’ reopening, were recorded. Regression analysis was conducted to deduce potential associations between the 14-day change in infection rate and mask usage frequency, median household income, population density and social distancing.

Results

On average, infection rates rose significantly as businesses reopened. The average 14-day change in infection rate was higher for fully reopened businesses (infection rate = +0.100) compared to partially reopened businesses (infection rate = +0.0454). The P-value of the two distributions was 0.001692, indicating statistical significance (P < 0.01).

Conclusion

This research provides insight into the transmission of COVID-19 and promotes evidence-driven policymaking for disease prevention and community health.

Do school closures and school reopenings affect community transmission of COVID-19? A systematic review of observational studies

OBJECTIVES

To systematically reivew the observational evidence of the effect of school closures and school reopenings on SARS-CoV-2 community transmission.

SETTING

Schools (including early years settings, primary schools and secondary schools).

INTERVENTION

School closures and reopenings.

OUTCOME MEASURE

Community transmission of SARS-CoV-2 (including any measure of community infections rate, hospital admissions or mortality attributed to COVID-19).

METHODS

On 7 January 2021, we searched PubMed, Web of Science, Scopus, CINAHL, the WHO Global COVID-19 Research Database, ERIC, the British Education Index, the Australian Education Index and Google, searching title and abstracts for terms related to SARS-CoV-2 AND terms related to schools or non-pharmaceutical interventions (NPIs). We used the Cochrane Risk of Bias In Non-randomised Studies of Interventions tool to evaluate bias.

RESULTS

We identified 7474 articles, of which 40 were included, with data from 150 countries. Of these, 32 studies assessed school closures and 11 examined reopenings. There was substantial heterogeneity between school closure studies, with half of the studies at lower risk of bias reporting reduced community transmission by up to 60% and half reporting null findings. The majority (n=3 out of 4) of school reopening studies at lower risk of bias reported no associated increases in transmission.

CONCLUSIONS

School closure studies were at risk of confounding and collinearity from other non-pharmacological interventions implemented around the same time as school closures, and the effectiveness of closures remains uncertain. School reopenings, in areas of low transmission and with appropriate mitigation measures, were generally not accompanied by increasing community transmission. With such varied evidence on effectiveness, and the harmful effects, policymakers should take a measured approach before implementing school closures; and should look to reopen schools in times of low transmission, with appropriate mitigation measures.

The impact of school reopening on the spread of COVID-19 in England

By mid-May 2020, cases of COVID-19 in the UK had been declining for over a month; a multi-phase emergence from lockdown was planned, including a scheduled partial reopening of schools on 1 June 2020. Although evidence suggests that children generally display mild symptoms, the size of the school-age population means the total impact of reopening schools is unclear. Here, we present work from mid-May 2020 that focused on the imminent opening of schools and consider what these results imply for future policy. We compared eight strategies for reopening primary and secondary schools in England. Modifying a transmission model fitted to UK SARS-CoV-2 data, we assessed how reopening schools affects contact patterns, anticipated secondary infections and the relative change in the reproduction number, R. We determined the associated public health impact and its sensitivity to changes in social distancing within the wider community. We predicted that reopening schools with half-sized classes or focused on younger children was unlikely to push R above one. Older children generally have more social contacts, so reopening secondary schools results in more cases than reopening primary schools, while reopening both could have pushed R above one in some regions. Reductions in community social distancing were found to outweigh and exacerbate any impacts of reopening. In particular, opening schools when the reproduction number R is already above one generates the largest increase in cases. Our work indicates that while any school reopening will result in increased mixing and infection amongst children and the wider population, reopening schools alone in June 2020 was unlikely to push R above one. Ultimately, reopening decisions are a difficult trade-off between epidemiological consequences and the emotional, educational and developmental needs of children. Into the future, there are difficult questions about what controls can be instigated such that schools can remain open if cases increase. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Wastewater monitoring outperforms case numbers as a tool to track COVID-19 incidence dynamics when test positivity rates are high

Wastewater-based epidemiology (WBE) has been shown to coincide with, or anticipate, confirmed COVID-19 case numbers. During periods with high test positivity rates, however, case numbers may be underreported, whereas wastewater does not suffer from this limitation. Here we investigated how the dynamics of new COVID-19 infections estimated based on wastewater monitoring or confirmed cases compare to true COVID-19 incidence dynamics. We focused on the first pandemic wave in Switzerland (February to April, 2020), when test positivity ranged up to 26%. SARS-CoV-2 RNA loads were determined 2-4 times per week in three Swiss wastewater treatment plants (Lugano, Lausanne and Zurich). Wastewater and case data were combined with a shedding load distribution and an infection-to-case confirmation delay distribution, respectively, to estimate infection incidence dynamics. Finally, the estimates were compared to reference incidence dynamics determined by a validated compartmental model. Incidence dynamics estimated based on wastewater data were found to better track the timing and shape of the reference infection peak compared to estimates based on confirmed cases. In contrast, case confirmations provided a better estimate of the subsequent decline in infections. Under a regime of high-test positivity rates, WBE thus provides critical information that is complementary to clinical data to monitor the pandemic trajectory.

Wastewater monitoring outperforms case numbers as a tool to track COVID-19 incidence dynamics when test positivity rates are high

Wastewater-based epidemiology (WBE) has been shown to coincide with, or anticipate, confirmed COVID-19 case numbers. During periods with high test positivity rates, however, case numbers may be underreported, whereas wastewater does not suffer from this limitation. Here we investigated how the dynamics of new COVID-19 infections estimated based on wastewater monitoring or confirmed cases compare to true COVID-19 incidence dynamics. We focused on the first pandemic wave in Switzerland (February to April, 2020), when test positivity ranged up to 26%. SARS-CoV-2 RNA loads were determined 2-4 times per week in three Swiss wastewater treatment plants (Lugano, Lausanne and Zurich). Wastewater and case data were combined with a shedding load distribution and an infection-to-case confirmation delay distribution, respectively, to estimate infection incidence dynamics. Finally, the estimates were compared to reference incidence dynamics determined by a validated compartmental model. Incidence dynamics estimated based on wastewater data were found to better track the timing and shape of the reference infection peak compared to estimates based on confirmed cases. In contrast, case confirmations provided a better estimate of the subsequent decline in infections. Under a regime of high-test positivity rates, WBE thus provides critical information that is complementary to clinical data to monitor the pandemic trajectory.

Estimation of the reproduction number of influenza A(H1N1)pdm09 in South Korea using heterogeneous models

Background

The reproduction number is one of the most crucial parameters in determining disease dynamics, providing a summary measure of the transmission potential. However, estimating this value is particularly challenging owing to the characteristics of epidemic data, including non-reproducibility and incompleteness.

Methods

In this study, we propose mathematical models with different population structures; each of these models can produce data on the number of cases of the influenza A(H1N1)pdm09 epidemic in South Korea. These structured models incorporating the heterogeneity of age and region are used to estimate the reproduction numbers at various terminal times. Subsequently, the age- and region-specific reproduction numbers are also computed to analyze the differences illustrated in the incidence data.

Results

Incorporation of the age-structure or region-structure allows for robust estimation of parameters, while the basic SIR model provides estimated values beyond the reasonable range with severe fluctuation. The estimated duration of infectious period using age-structured model is around 3.8 and the reproduction number was estimated to be 1.6. The estimated duration of infectious period using region-structured model is around 2.1 and the reproduction number was estimated to be 1.4. The estimated age- and region-specific reproduction numbers are consistent with cumulative incidence for corresponding groups.

Conclusions

Numerical results reveal that the introduction of heterogeneity into the population to represent the general characteristics of dynamics is essential for the robust estimation of parameters.

A mechanistic and data-driven reconstruction of the time-varying reproduction number: Application to the COVID-19 epidemic

The effective reproduction number Reff is a critical epidemiological parameter that characterizes the transmissibility of a pathogen. However, this parameter is difficult to estimate in the presence of silent transmission and/or significant temporal variation in case reporting. This variation can occur due to the lack of timely or appropriate testing, public health interventions and/or changes in human behavior during an epidemic. This is exactly the situation we are confronted with during this COVID-19 pandemic. In this work, we propose to estimate Reff for the SARS-CoV-2 (the etiological agent of the COVID-19), based on a model of its propagation considering a time-varying transmission rate. This rate is modeled by a Brownian diffusion process embedded in a stochastic model. The model is then fitted by Bayesian inference (particle Markov Chain Monte Carlo method) using multiple well-documented hospital datasets from several regions in France and in Ireland. This mechanistic modeling framework enables us to reconstruct the temporal evolution of the transmission rate of the COVID-19 based only on the available data. Except for the specific model structure, it is non-specifically assumed that the transmission rate follows a basic stochastic process constrained by the observations. This approach allows us to follow both the course of the COVID-19 epidemic and the temporal evolution of its Reff(t). Besides, it allows to assess and to interpret the evolution of transmission with respect to the mitigation strategies implemented to control the epidemic waves in France and in Ireland. We can thus estimate a reduction of more than 80% for the first wave in all the studied regions but a smaller reduction for the second wave when the epidemic was less active, around 45% in France but just 20% in Ireland. For the third wave in Ireland the reduction was again significant (>70%).

Non-pharmaceutical interventions during the COVID-19 pandemic: A review

Infectious diseases and human behavior are intertwined. On one side, our movements and interactions are the engines of transmission. On the other, the unfolding of viruses might induce changes to our daily activities. While intuitive, our understanding of such feedback loop is still limited. Before COVID-19 the literature on the subject was mainly theoretical and largely missed validation. The main issue was the lack of empirical data capturing behavioral change induced by diseases. Things have dramatically changed in 2020. Non-pharmaceutical interventions (NPIs) have been the key weapon against the SARS-CoV-2 virus and affected virtually any societal process. Travel bans, events cancellation, social distancing, curfews, and lockdowns have become unfortunately very familiar. The scale of the emergency, the ease of survey as well as crowdsourcing deployment guaranteed by the latest technology, several Data for Good programs developed by tech giants, major mobile phone providers, and other companies have allowed unprecedented access to data describing behavioral changes induced by the pandemic. Here, I review some of the vast literature written on the subject of NPIs during the COVID-19 pandemic. In doing so, I analyze 348 articles written by more than 2518 authors in the first 12 months of the emergency. While the large majority of the sample was obtained by querying PubMed, it includes also a hand-curated list. Considering the focus, and methodology I have classified the sample into seven main categories: epidemic models, surveys, comments/perspectives, papers aiming to quantify the effects of NPIs, reviews, articles using data proxies to measure NPIs, and publicly available datasets describing NPIs. I summarize the methodology, data used, findings of the articles in each category and provide an outlook highlighting future challenges as well as opportunities.

Modelling strategies to organize healthcare workforce during pandemics: Application to COVID-19

Protection of the healthcare workforce is of paramount importance for the care of patients in the setting of a pandemic such as coronavirus disease 2019 (COVID-19). Healthcare workers are at increased risk of becoming infected. The ideal organisational strategy to protect the workforce in a situation in which social distancing cannot be maintained remains to be determined. In this study, we have mathematically modelled strategies for the employment of the hospital workforce with the goal of simulating the health and productivity of the workers. The models were designed to determine if desynchronization of medical teams by dichotomizing the workers may protect the workforce. Our studies model workforce productivity and the efficiency of home office applied to the case of COVID-19. The results reveal that a desynchronization strategy in which two medical teams work alternating for 7 days increases the available workforce.

The temporal association of introducing and lifting non-pharmaceutical interventions with the time-varying reproduction number (R) of SARS-CoV-2: a modelling study across 131 countries

BACKGROUND

Non-pharmaceutical interventions (NPIs) were implemented by many countries to reduce the transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the causal agent of COVID-19. A resurgence in COVID-19 cases has been reported in some countries that lifted some of these NPIs. We aimed to understand the association of introducing and lifting NPIs with the level of transmission of SARS-CoV-2, as measured by the time-varying reproduction number (R), from a broad perspective across 131 countries.

METHODS

In this modelling study, we linked data on daily country-level estimates of R from the London School of Hygiene & Tropical Medicine (London, UK) with data on country-specific policies on NPIs from the Oxford COVID-19 Government Response Tracker, available between Jan 1 and July 20, 2020. We defined a phase as a time period when all NPIs remained the same, and we divided the timeline of each country into individual phases based on the status of NPIs. We calculated the R ratio as the ratio between the daily R of each phase and the R from the last day of the previous phase (ie, before the NPI status changed) as a measure of the association between NPI status and transmission of SARS-CoV-2. We then modelled the R ratio using a log-linear regression with introduction and relaxation of each NPI as independent variables for each day of the first 28 days after the change in the corresponding NPI. In an ad-hoc analysis, we estimated the effect of reintroducing multiple NPIs with the greatest effects, and in the observed sequence, to tackle the possible resurgence of SARS-CoV-2.

FINDINGS

790 phases from 131 countries were included in the analysis. A decreasing trend over time in the R ratio was found following the introduction of school closure, workplace closure, public events ban, requirements to stay at home, and internal movement limits; the reduction in R ranged from 3% to 24% on day 28 following the introduction compared with the last day before introduction, although the reduction was significant only for public events ban (R ratio 0·76, 95% CI 0·58-1·00); for all other NPIs, the upper bound of the 95% CI was above 1. An increasing trend over time in the R ratio was found following the relaxation of school closure, bans on public events, bans on public gatherings of more than ten people, requirements to stay at home, and internal movement limits; the increase in R ranged from 11% to 25% on day 28 following the relaxation compared with the last day before relaxation, although the increase was significant only for school reopening (R ratio 1·24, 95% CI 1·00-1·52) and lifting bans on public gatherings of more than ten people (1·25, 1·03-1·51); for all other NPIs, the lower bound of the 95% CI was below 1. It took a median of 8 days (IQR 6-9) following the introduction of an NPI to observe 60% of the maximum reduction in R and even longer (17 days [14-20]) following relaxation to observe 60% of the maximum increase in R. In response to a possible resurgence of COVID-19, a control strategy of banning public events and public gatherings of more than ten people was estimated to reduce R, with an R ratio of 0·71 (95% CI 0·55-0·93) on day 28, decreasing to 0·62 (0·47-0·82) on day 28 if measures to close workplaces were added, 0·58 (0·41-0·81) if measures to close workplaces and internal movement restrictions were added, and 0·48 (0·32-0·71) if measures to close workplaces, internal movement restrictions, and requirements to stay at home were added.

INTERPRETATION

Individual NPIs, including school closure, workplace closure, public events ban, ban on gatherings of more than ten people, requirements to stay at home, and internal movement limits, are associated with reduced transmission of SARS-CoV-2, but the effect of introducing and lifting these NPIs is delayed by 1-3 weeks, with this delay being longer when lifting NPIs. These findings provide additional evidence that can inform policy-maker decisions on the timing of introducing and lifting different NPIs, although R should be interpreted in the context of its known limitations.

FUNDING

Wellcome Trust Institutional Strategic Support Fund and Data-Driven Innovation initiative.

Range of reproduction number estimates for COVID-19 spread

To monitor local and global COVID-19 outbreaks, and to plan containment measures, accessible and comprehensible decision-making tools need to be based on the growth rates of new confirmed infections, hospitalization or case fatality rates. Growth rates of new cases form the empirical basis for estimates of a variety of reproduction numbers, dimensionless numbers whose value, when larger than unity, describes surging infections and generally worsening epidemiological conditions. Typically, these determinations rely on noisy or incomplete data gained over limited periods of time, and on many parameters to estimate. This paper examines how estimates from data and models of time-evolving reproduction numbers of national COVID-19 infection spread change by using different techniques and assumptions. Given the importance acquired by reproduction numbers as diagnostic tools, assessing their range of possible variations obtainable from the same epidemiological data is relevant. We compute control reproduction numbers from Swiss and Italian COVID-19 time series adopting both data convolution (renewal equation) and a SEIR-type model. Within these two paradigms we run a comparative analysis of the possible inferences obtained through approximations of the distributions typically used to describe serial intervals, generation, latency and incubation times, and the delays between onset of symptoms and notification. Our results suggest that estimates of reproduction numbers under these different assumptions may show significant temporal differences, while the actual variability range of computed values is rather small.

An evaluation of COVID-19 transmission control in Wenzhou using a modified SEIR model

In December 2019, the first confirmed case of pneumonia caused by a novel coronavirus was reported. Coronavirus disease 2019 (COVID-19) is currently spreading around the world. The relationships among the pandemic and its associated travel restrictions, social distancing measures, contact tracing, mask-wearing habits and medical consultation efficiency have not yet been extensively assessed. Based on the epidemic data reported by the Health Commission of Wenzhou, we analysed the developmental characteristics of the epidemic and modified the Susceptible-Exposed-Infectious-Removed (SEIR) model in three discrete ways. (1) According to the implemented preventive measures, the epidemic was divided into three stages: initial, outbreak and controlled. (2) We added many factors, such as health protections, travel restrictions and social distancing, close-contact tracing and the time from symptom onset to hospitalisation (TSOH), to the model. (3) Exposed and infected people were subdivided into isolated and free-moving populations. For the parameter estimation of the model, the average TSOH and daily cured cases, deaths and imported cases can be obtained through individual data from epidemiological investigations. The changes in daily contacts are simulated using the intracity travel intensity (ICTI) from the Baidu Migration Big Data platform. The optimal values of the remaining parameters are calculated by the grid search method. With this model, we calculated the sensitivity of the control measures with regard to the prevention of the spread of the epidemic by simulating the number of infected people in various hypothetical situations. Simultaneously, through a simulation of a second epidemic, the challenges from the rebound of the epidemic were analysed, and prevention and control recommendations were made. The results show that the modified SEIR model can effectively simulate the spread of COVID-19 in Wenzhou. The policy of the lockdown of Wuhan, the launch of the first-level Public Health Emergency Preparedness measures on 23 January 2020 and the implementation of resident travel control measures on 31 January 2020 were crucial to COVID-19 control.

COVID-19 lockdown induces disease-mitigating structural changes in mobility networks

In the wake of the COVID-19 pandemic many countries implemented containment measures to reduce disease transmission. Studies using digital data sources show that the mobility of individuals was effectively reduced in multiple countries. However, it remains unclear whether these reductions caused deeper structural changes in mobility networks and how such changes may affect dynamic processes on the network. Here we use movement data of mobile phone users to show that mobility in Germany has not only been reduced considerably: Lockdown measures caused substantial and long-lasting structural changes in the mobility network. We find that long-distance travel was reduced disproportionately strongly. The trimming of long-range network connectivity leads to a more local, clustered network and a moderation of the "small-world" effect. We demonstrate that these structural changes have a considerable effect on epidemic spreading processes by "flattening" the epidemic curve and delaying the spread to geographically distant regions.

Practical considerations for measuring the effective reproductive number, Rt

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.

Practical considerations for measuring the effective reproductive number, R t

Estimation of the effective reproductive number, R t , is important for detecting changes in disease transmission over time. During the COVID-19 pandemic, policymakers and public health officials are using R t to assess the effectiveness of interventions and to inform policy. However, estimation of R t 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 R t , we recommend the approach of Cori et al. (2013), 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 (2004), 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 spread. We advise against using methods derived from Bettencourt and Ribeiro (2008), as the resulting R t 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 R t estimation.

Key questions for modelling COVID-19 exit strategies

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

Future scenarios for the SARS-CoV-2 epidemic in Switzerland: an age-structured model

The recent lifting of COVID-19 related restrictions in Switzerland causes uncertainty about the future of the epidemic. We developed a compartmental model for SARS-CoV-2 transmission in Switzerland and projected the course of the epidemic until the end of year 2020 under various scenarios. The model was age-structured with three categories: children (0-17), adults (18-64) and seniors (65- years). Lifting all restrictions according to the plans disclosed by the Swiss federal authorities by mid-May resulted in a rapid rebound in the epidemic, with the peak expected in July. Measures equivalent to at least 76% reduction in all contacts were able to eradicate the epidemic; a 54% reduction in contacts could keep the intensive care unit occupancy under the critical level and delay the next wave until October. In scenarios where strong contact reductions were only applied in selected age groups, the epidemic could not be suppressed, resulting in an increased risk of a rebound in July, and another stronger wave in September. Future interventions need to cover all age groups to keep the SARS-CoV-2 epidemic under control.