Swiss Medical Weekly

The effective reproductive number Rt of COVID-19 is determined indirectly from data that are only incompletely known. Approaches based on reconstructing these data by sampling time lags from suitable distributions introduce noise effects that can result in distorted estimates of Rt. This, in turn, may lead to misleading interpretations of the efficacy of the various measures taken to limit COVID-19 transmission. We discuss in some detail a study used for real time monitoring of the reproductive number in Switzerland; see https://ncs-tf.ch/en/situation-report. We argue that the method used to derive the above curve is systematically flawed and leads to an underestimation of the efficacy of the lockdown. The method adopted by the Robert Koch Institute suffers from similar deficiencies, their impact is however smaller.

Following the rapid dissemination of COVID-19 cases in Switzerland, large-scale non-pharmaceutical interventions (NPIs) were implemented by the cantons and the federal government between February 28 and March 20. Estimates of the impact of these interventions on SARS-CoV-2 transmission are critical for decision making in this and future outbreaks. We here aim to assess the impact of these NPIs on disease transmission by estimating changes in the basic reproduction number (R0) at national and cantonal levels in relation to the timing of these NPIs. We estimate the time-varying R0 nationally and in twelve cantons by fitting a stochastic transmission model explicitly simulating within hospital dynamics. We use individual-level data of >1,000 hospitalized patients in Switzerland and public daily reports of hospitalizations and deaths. We estimate the national R0 was 3.15 (95% CI: 2.13-3.76) at the start of the epidemic. Starting from around March 6, we find a strong reduction in R0 with a 85% median decrease (95% quantile range, QR: 83%-90%) to a value of 0.44 (95% QR: 0.27-0.65) in the period of March 29-April 5. At the cantonal-level R0 decreased over the course of the epidemic between 71% and 94%. We found that reductions in R0 were synchronous with changes in mobility patterns as estimated through smartphone activity, which started before the official implementation of NPIs. We found that most of the reduction of transmission is due to behavioural changes as opposed to natural immunity, the latter accounting for only about 3% of the total reduction in effective transmission. As Switzerland considers relaxing some of the restrictions of social mixing, current estimates of R0 well below one are promising. However most of inferred transmission reduction was due to behaviour change (<3% due to natural immunity buildup), with an estimated 97% (95% QR: 96.6%-97.2%) of the Swiss population still susceptible to SARS-CoV-2 as of April 24. These results warrant a cautious relaxation of social distance practices and close monitoring of changes in both the basic and effective reproduction numbers.

The coronavirus disease 2019 (COVID-19) pandemic disrupted daily life and changes to routines were made in accordance with public health regulations. In 2020, nonpharmaceutical interventions were put in place to reduce exposure to and spread of the disease. The goal of this work was to quantify the effect of school closure during the first year of COVID-19 pandemic in Switzerland. This allowed us to determine the usefulness of school closures as a pandemic countermeasure for emerging coronaviruses in the absence of pharmaceutical interventions. The use of multivariate endemic-epidemic modelling enabled us to analyse disease spread between age groups which we believe is a necessary inclusion in any model seeking to achieve our goal. Sophisticated time-varying contact matrices encapsulating four different contact settings were included in our complex statistical modelling approach to reflect the amount of school closure in place on a given day. Using the model, we projected case counts under various transmission scenarios (driven by implemented social distancing policies). We compared these counterfactual scenarios against the true levels of social distancing policies implemented, where schools closed in the spring and reopened in the autumn. We found that if schools had been kept open, the vast majority of additional cases would be expected among primary school-aged children with a small fraction of cases percolating into other age groups following the contact matrix structure. Under this scenario where schools were kept open, the cases were highly concentrated among the youngest age group. In the scenario where schools had remained closed, most reduction would also be expected in the lowest age group with less effects seen in other groups.

Although long COVID in children exists, it is still unclear to what extent children are affected. The Ciao Corona study is a longitudinal cohort investigating SARS-CoV-2 seroprevalence and clustering of cases among around 2500 children and adolescents (hereafter referred to as children) from 55 randomly selected primary and secondary schools in the canton of Zurich in Switzerland. Between June 2020 and April 2021, we completed three testing phases where we collected venous blood for serological analysis and asked about symptoms with online questionnaires. We compared children who tested positive for SARS-CoV-2 antibodies in October/November 2020 with those who tested negative. Children who were seronegative in October/November 2020 and seroconverted or were not retested in March/April 2021 were excluded from the analysis (n=256). In March-May 2021 we assessed the presence of symptoms occurring since October 2020, lasting for at least 4 weeks, and persisting for either >4 weeks or >12 weeks. Overall, 1355 of 2503 children with a serology result in October/November 2020 and follow up questionnaire in March-May 2021 were included. Among seropositive and seronegative 6-to 16-year-old children, 9% versus 10% reported at least one symptom beyond 4 weeks, and 4% versus 2% at least one symptom beyond 12 weeks. None of the seropositive children reported hospitalization after October 2020. This study suggests a low prevalence of symptoms compatible with long COVID in a randomly selected population-based cohort of children followed over 6 months after serological testing.

BackgroundWhile the number of detected SARS-CoV-2 infections are widely available, an understanding of the extent of undetected cases is urgently needed for an effective tackling of the pandemic. The aim of this work is to estimate the true number of SARS-CoV-2 (detected and undetected) infections in several European Countries. The question being asked is: How many cases have actually occurred? MethodsWe propose an upper bound estimator under cumulative data distributions, in an open population, based on a day-wise estimator that allows for heterogeneity. The estimator is data-driven and can be easily computed from the distributions of daily cases and deaths. Uncertainty surrounding the estimates is obtained using bootstrap methods. ResultsWe focus on the ratio of the total estimated cases to the observed cases at April 17th. Differences arise at the Country level, and we get estimates ranging from the 3.93 times of Norway to the 7.94 times of France. Accurate estimates are obtained, as bootstrap-based intervals are rather narrow. ConclusionsMany parametric or semi-parametric models have been developed to estimate the population size from aggregated counts leading to an approximation of the missed population and/or to the estimate of the threshold under which the number of missed people cannot fall (i.e. a lower bound). Here, we provide a methodological contribution introducing an upper bound estimator and provide reliable estimates on the dark number, i.e. how many undetected cases are going around for several European Countries, where the epidemic spreads differently.

Recent studies assessing COVID-19 vaccine efficacy at the population level found counterintuitive results, such as positive associations between vaccination and infections or deaths. These ecological studies have limitations, including too short observation periods, focusing on infections, and not controlling for age groups and dominant variants. The current study addresses these limitations by investigating the relations between vaccination and COVID-19 cases, hospitalizations, and deaths over a longer period (9[1/2] months) while also considering age groups (from 10 to 80+ years old) and variants (Alpha and Delta), utilizing data from Switzerland. Results suggest that vaccination is negatively related to cases overall and in all cantons of Switzerland, and that vaccination is negatively related to hospitalizations and deaths from 50 years old. Furthermore, vaccination is a significant predictor of cases, hospitalizations, and deaths while holding the effects of age and dominant variant constant.

We investigate six scenarios spanning main parts of the decision space of non-medical interventions against the CoV-2 epidemic in Germany. Based on the notion of interventions-lifting we classify and evaluate the scenarios by five attributes (indicators): amount of interventions-lifting, death numbers, Public Health Care capacity, population immunity, peak dates of infections. For quantitative reasoning we use a simulated modified SEIR-model calibrated with actual data. We identify margins for intervention-liftings wrt. 13.05.2020 and discuss the relation to the effective reproduction number with a 6d-generation time. We show that, in order to constrain death numbers comparable to a strong Influenza epidemic, there is only a small corridor of 16% of possible liftings, with an additional 4% margin contributed by automated contact tracing. We show also that there is a much broader corridor of 50%+18%, though not overloading critical Public Health Care capacity, implying high death numbers.

AIMIn late February and early March 2020, Switzerland experienced rapid growth of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections with 30,243 confirmed cases and 1,860 deaths as of 10 May 2020. The sequential introduction of non-pharmaceutical interventions (NPIs) resulted in successful containment of the epidemic. A better understanding of how the timing of implementing NPIs influences the dynamics and outcome of SARS-CoV-2 epidemics will be crucial for the management of a potential resurgence in Switzerland. METHODSWe developed a dynamic transmission model that describes infection, hospitalization, recovery and death due to SARS-CoV-2 in Switzerland. Using a maximum likelihood framework, we fitted the model to aggregated daily numbers of hospitalized patients, ICU occupancy and death from 25 February to 10 May 2020. We estimated critical parameters of SARS-CoV-2 transmission in Switzerland and explored counterfactual scenarios of an earlier and later implementation of NPIs. RESULTSWe estimated the basic reproduction number R0 = 2.61 (95% compatibility interval, CI: 2.51-2.71) during the early exponential phase of the SARS-CoV-2 epidemic in Switzerland. After the implementation of NPIs, the effective reproduction number approached Re = 0.64 (95% CI: 0.61-0.66). Based on the observed doubling times of the epidemic before and after the implementation of NPIs, we estimated that one week of early exponential spread required 3.1 weeks (95% CI: 2.8-3.3 weeks) of lockdown to reduce the number of infections to the same level. Introducing the same sequence of NPIs one week earlier or later would have resulted in substantially lower (399, 95% prediction interval, PI: 347-458) and higher (8,683, 95% PI: 8,038-9,453) numbers of deaths, respectively. CONCLUSIONSThe introduction of NPIs in March 2020 prevented thousands of SARS-CoV-2-related deaths in Switzerland. Early implementation of NPIs during SARS-CoV-2 outbreaks can reduce the number of deaths and the necessary duration of strict control measures considerably.

The novel coronavirus (SARS-CoV-2), identified in China at the end of December 2019 and causing the disease COVID-19, has meanwhile led to outbreaks all over the globe with about 2.2 million confirmed cases and more than 150,000 deaths as of April 17, 2020 [37]. In view of most recent information on testing activity [32], we present here an update of our initial work [4]. In this work, mathematical models have been developed to study the spread of COVID-19 among the population in Germany and to asses the impact of non-pharmaceutical interventions. Systems of differential equations of SEIR type are extended here to account for undetected infections, as well as for stages of infections and age groups. The models are calibrated on data until April 5, data from April 6 to 14 are used for model validation. We simulate different possible strategies for the mitigation of the current outbreak, slowing down the spread of the virus and thus reducing the peak in daily diagnosed cases, the demand for hospitalization or intensive care units admissions, and eventually the number of fatalities. Our results suggest that a partial (and gradual) lifting of introduced control measures could soon be possible if accompanied by further increased testing activity, strict isolation of detected cases and reduced contact to risk groups.

Predictions about the further development of the Corona pandemic are widely diverging. Here, a simple yet powerful algorithm is introduced for extrapolating infection rate and number of total infections from available data. The calculation predicts that under present conditions the infection rate in Germany will culminate in a few weeks and decrease to low values by mid-June 2020. Total number of infections will reach several 100000 though. A refinement of the calculation is presented in the supplemental material and shows that the lock down in Germany has reduced the total number of infections from a target value of 338 000 to 184 000, corresponding to a decrease of about 45%.

Estimating the instantaneous reproduction number ([R]t) in near real-time is crucial for monitoring and responding to epidemic outbreaks on a daily basis. However, such estimates often suffer from bias due to reporting delays inherent in surveillance systems. A fast and flexible Bayesian methodology is proposed to overcome this challenge by estimating[R] t while taking into account reporting delays. Furthermore, the uncertainty associated with the nowcasting of cases is naturally taken into account to get a valid uncertainty estimation of the nowcasted reproduction number. The proposed methodology is evaluated through a simulation study and applied to COVID-19 incidence data in Belgium.

The case detection ratio of COVID-19 infections varies over time due to changing testing capacities, modified testing strategies and also, apparently, due to the dynamics in the number of infected itself. In this paper we investigate these dynamics by jointly looking at the reported number of detected COVID-19 infections with non-fatal and fatal outcomes in different age groups in Germany. We propose a statistical approach that allows us to spotlight the case detection ratio and quantify its changes over time. With this we can adjust the case counts reported at different time points so that they become comparable. Moreover we can explore the temporal development of the real number of infections, shedding light on the dark number. The results show that the case detection ratio has increased and, depending on the age group, is four to six times higher at the beginning of the second wave compared to what it was at the peak of the first wave. The true number of infection in Germany in October was considerably lower as during the peak of the first wave, where only a small fraction of COVID-19 infections were detected. Our modelling approach also allows quantifying the effects of different testing strategies on the case detection ratio. The analysis of the dynamics in the case detection rate and in the true infection figures enables a clearer picture of the course of the COVID-19 pandemic.

The officially reported daily Covid-19 fatality rate is modelled with a trend line based on a nominal day-to-day reproduction rate and a cosine to take account of weekly fluctuations. Although the time trajectories of officially reported infections and fatalities are pronouncedly different, the reproduction rates obtained therefrom are similar. The long-term effective reproduction rate is around 0.835 and the administrative measures to contain the pandemic seem not to have an immediate reducing effect but well the ease of restrictions an increasing one. The fatality trajectory represented by its trend line can be projected from the number of daily infections by assuming a time lapse between symptom onset and death between 17 and 19 days and a time-dependent nominal lethality. The time trajectory of this lethality increases from 2.5% at March 16 when public life was restricted to 6% within 20 days indicating relatively more infections of vulnerable people. After stipulating face mask wearing at April 27, the nominal lethality decreases down to 1% later in summer. A detailed analysis shows that mask wearing really reduces the number of fatal infections and the officially reported daily infections in May and June are less lethal than before.

The number of screening tests carried out in France and the methodology used to target the patients tested do not allow for a direct computation of the actual number of cases and the infection fatality ratio (IFR). The main objective of this work is to estimate the actual number of people infected with COVID-19 and to deduce the IFR during the observation window in France. We develop a mechanistic-statistical approach coupling a SIR epidemiological model describing the unobserved epidemiological dynamics, a probabilistic model describing the data acquisition process and a statistical inference method. The actual number of infected cases in France is probably higher than the observations: we find here a factor x8 (95%-CI: 5-12) which leads to an IFR in France of 0.5% (95%-CI: 0.3 - 0.8) based on hospital death counting data. Adjusting for the number of deaths in nursing homes, we obtain an IFR of 0.8% (95%-CI: 0.45 - 1.25). This IFR is consistent with previous findings in China (0.66%) and in the UK (0.9%) and lower than the value previously computed on the Diamond Princess cruise ship data (1.3%).

We propose an augmented version of the traditional SIRD epidemic model and we estimate its parameters using the SaRs-Cov-2 Italian open-data. The models parameters are estimated partly using numerical optimization and partly with ABC. Our estimation procedure provides a good fit to real data.

With a mathematical method based on linear algebra, from open access data (data.gouv.fr, google, apple) we produce forecasts for the number of patients in intensive care in France with an average error of 4% at 7 days, 7% at 14 days, 8% at 21 days, 10% at one month, 17% at 2 months, and 31% at 3 months. For the other epidemic indicators, the error is on average 6% at 7 days and 25% at 2 months.

The reproduction number (R0) is broadly considered as a key indicator for the spreading of the COVID-19 pandemic. The estimation of its value with respect to the key threshold of 1.0 is a measure of the need, and eventually effectiveness, of interventions imposed in various countries. Here we present an online tool for the data driven inference and quantification of uncertainties for R0 as well as the time points of interventions for 51 European countries. The study relies on the Bayesian calibration of the simple and well established SIR model with data from reported daily infections. The model is able to fit the data for most countries without individual tuning of parameters. We deploy an open source Bayesian inference framework and efficient sampling algorithms to present a publicly available GUI cse-lab.ethz.ch/coronavirus that allows the user to assess custom data and compare predictions for pairs of European countries. The results provide a ranking based on the rate of the diseases spread suggesting a metric for the effectiveness of social distancing measures. They also serve to demonstrate how geographic proximity and related times of interventions can lead to similarities in the progression of the epidemic.

For Germany it is predicted that the first wave of the corona pandemic disease reaches its maximum of new infections on April 11th, 2020 [Formula] days with 90 percent confidence. With a delay of about 7 days the maximum demand on breathing machines in hospitals occurs on April 18th, 2020 [Formula] days. The first pandemic wave ends in Germany end of May 2020. The predictions are based on the assumption of a Gaussian time evolution well justified by the central limit theorem of statistics. The width and the maximum time and thus the duration of this Gaussian distribution are determined from a statistical{chi} 2-fit to the observed doubling times before March 28, 2020.

We present a simple operational nowcasting/forecasting scheme based on a joint state/parameter estimate of the COVID-19 epidemic at national or regional scale, performed by assimilating the time series of reported daily death numbers into a simple SEIR model. This system generates estimates of the current reproductive rate, Rt, together with predictions of future daily deaths and clearly outperforms a number of alternative forecasting systems that have been presented recently. Our current (14th April 2020) estimates for Rt are, respectively, UK 0.49 (0.0 - 1.02), Spain 0.55 (0.33 - 0.77), Italy 0.90 (0.74 - 1.06) and France 0.67 (0.40 - 0.94) (mean and 95% credible intervals). Thus, we believe that the epidemics have been successfully suppressed in each of these countries, with high probability. Our approach is trivial to set up for any region and generates results in a few minutes on a laptop. We believe it would be straightforward to set up equivalent frameworks using more complex and realistic models, and hope that some experts in the field of epidemiological modelling will consider investigating this approach further.

Mobile contact tracing apps have been developed by many countries in response to the COVID-19 pandemic. Trials have focussed on unobserved population trials or staged scenarios aimed to simulate real life. No efficacy measure has been developed that assesses the fundamental ability of any proximity detection protocol to accurately detect, measure, and therefore assess the epidemiological risk that a mobile phone owner has been placed at. This paper provides a fair efficacy formula that can be applied to any mobile contact tracing app, using any technology, allowing its likely epidemiological effectiveness to be assessed. This paper defines such a formula and provides results for several simulated protocols as well as one real life protocol tested according to the standard methodology set out in this paper. The results presented show that protocols that use time windows greater than 30 seconds or that bucket their distance analogue (E.g. RSSI for Bluetooth) provide poor estimates of risk, showing an efficacy rating of less than 6%. The fair efficacy formula is shown in this paper to be able to be used to calculate the Efficacy of contact tracing variable value as used in two papers on using mobile applications for contact tracing [6]. The output from the formulae in this paper, therefore, can be used to directly assess the impact of technology on the spread of a disease outbreak. This formula can be used by nations developing contact tracing applications to assess the efficacy of their applications. This will allow them to reassure their populations and increase the uptake of contact tracing mobile apps, hopefully having an effect on slowing the spread of COVID-19 and future epidemics.