Analyzing epidemic trends of SARS-CoV-2 in Switzerland

Nanina Anderegg, Julien Riou, Christian L. Althaus

Institute of Social and Preventive Medicine, Universität Bern, Switzerland

Quantifying the impact of quarantine duration on COVID-19 transmission

Peter Ashcroft, Sonja Lehtinen, Daniel Angst, Nicola Low and Sebastian Bonhoeffer

ETH Zurich & ISPM Universität Bern

Effectiveness of TTIQ

Peter Ashcroft, Sonja Lehtinen, and Sebastian Bonhoeffer

Institute of Integrative Biology, ETH Zurich, Switzerland

Time Series

Chaoran Chen, Timothy Vaughan, Tanja Stadler

Computational Evolution Group, D-BSSE, ETH Zurich, Switzerland


Re Estimation

Jérémie Scire, Jana S. Huisman et al.

ETH Zürich, D-BSSE & D-USYS

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nextstrain: Phylogenetic analysis of Swiss SARS-CoV-2 genomes in their international context

maintained by Emma Hodcroft, Richard Neher, Sarah Nadeau and Tanja Stadler.

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icumonitoring.ch

Cheng Zhao, Nicola Criscuolo, Burcu Tepekule, Monica Golumbeanu, Melissa Penny, Peter Ashcroft, Matthias Hilty, Thierry Fumeaux, Thomas Van Boeckel

ETH Zürich, Swiss TPH, Universitätsspital Zürich, Swiss Society for Intensive Care Medicine

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Parameter
Filter
Time series
The number of positive tests from the recent 2 days and the number of hospitalisation and deaths from the recent 5 days might be incomplete due to reporting delays.
Data last updated on Data Source: Swiss Federal Office of Public Health
Display options
Normalisation
The normalisation calculates the positive case numbers if the hospitalisation rate per age group is assumed to be constant. It aims to improve the comparability of the numbers between different months. If this field is activated, the shown plot does not present the actual numbers.
Assumption
The hospitalisation rate per age group is constant and equals the value in
.
Method

Due to changing testing capacities and regimes, it is difficult to compare the numbers of different points in time. The normalisation mode assumes that the true hospitalisation rate per age group did not change and calculates the normalized number of positive cases using the following formula:

$$\#PositiveCases = \sum_{i\in \{AgeGroups\}}\#Hospitalisations_i \times \frac{\#PositiveTestsInSelectedMonths_i}{\#HospitalisaionsInSelectedMonths_i} $$

Frequently Asked Questions (FAQ)

What does the dashboard show?

The dashboard presents three types of information:

  • In the default case - when neither “Clinical event probability given” nor the normalisation is selected - absolute numbers are displayed. Depending on the selected clinical event that is selected in the top-left panel of the website, the plot shows the number of positive tests taken on a particular day, the number of confirmed COVID-19 patients hospatalised or died on a day,, or the total number of tested persons on a day.
  • When “Clinical event probability given” is checked, estimated probabilities or relative numbers are shown. For example, if “Hospitalisation given Positive test” is chosen, the dashboard plots the hospitalisation probability of patients who were positively tested on a particular day. In other words, the number of hospitalised persons who had taken their test on a day is divided by the number of all positive tests on that day.
  • When “Activate normalisation” is selected, the plot does not show the true number of cases but the theoretical number of cases under the (strong) assumption that the hospitalisation probability per age group did not change throughout the pandemic. More information can be found in the above box.

How are the confidence intervals calculated?

Let's take the hospitalisation probability (“Hospitalisation given Positive test”) as an example.

If the “Clinical event probability given” option is selected, the shown numbers can be interpreted as probabilities. This means that we get the estimated probability of a person being hospitalised when the person was tested positively on a specific day. The certainty of the estimation depends on the sample size: when many people had a positive test on a day, the certainty is higher.

The binomial distribution is used as the underlying model. We set the “number of trials” n = number of positive cases, “the number of successes” k = number of hospitalisations. The maximum likelihood estimate of the probability is p = k/n . The confidence interval is calculated with the Clopper-Pearson method.

When a sliding window is selected, all hospitalisations and positive tests in the chosen time window are taken into account (the values are summed up in the chosen time window).

Analyzing epidemic trends of SARS-CoV-2 in Switzerland


Nanina Anderegg, Julien Riou, Christian L. Althaus (Institute of Social and Preventive Medicine, University of Bern)

This tool estimates national trends in daily confirmed cases, hospitalizations, ICU occupancy and deaths using a negative binomial generalized linear model. The model uses reported numbers as the response and date and weekend (0: work day, 1: weekend) as predictors. Confirmed cases and hospitalizations are further stratified by canton and age groups. Due to reporting delays, the last 3 and 5 days of confirmed cases and hospitalizations/deaths are removed, respectively. Lines and ribbons show the maximum likelihood estimate of the exponential increase/decrease and the 95% prediction intervals of the model fit, respectively.

Parameter
Cantonal trends
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Ranking
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Cantonal trends
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Ranking
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Data Tables

A collection of indicator values for Switzerland

Quantifying the impact of quarantine duration on COVID-19 transmission


Peter Ashcroft1, Sonja Lehtinen1, Daniel Angst1, Nicola Low2 and Sebastian Bonhoeffer1
1Institute of Integrative Biology, ETH Zurich, Switzerland, 2Institute of Social and Preventive Medicine, University of Bern, Bern, Switzerland

The large number of individuals placed into quarantine because of possible SARS-CoV-2 exposure has high societal and economic costs. There is ongoing debate about the appropriate duration of quarantine, particularly since the fraction of individuals who eventually test positive is perceived as being low. We use empirically-determined distributions of incubation period, infectivity, and generation time to quantify how the duration of quarantine affects onward transmission from traced contacts of confirmed SARS-CoV-2 cases and from returning travellers. We also consider the roles of testing followed by release if negative (test-and-release), reinforced hygiene, adherence, and symptoms in calculating quarantine efficacy. We show that there are quarantine strategies based on a test-and-release protocol that, from an epidemiological viewpoint, perform almost as well as a 10 day quarantine, but with fewer person days spent in quarantine. The findings apply to both travellers and contacts, but the specifics depend on the context.

Read the full preprint on medRxiv.

Empirical distributions
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Weibull distribution.
Ferretti et al., medRxiv 2020.09.04.20188516
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Shifted Student's t-distribution.
Ferretti et al., medRxiv 2020.09.04.20188516
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The distribution of incubation times follows a meta-distribution constructed from the average of seven reported log-normal distributions. Ferretti et al., medRxiv 2020.09.04.20188516
Test-and-release parameters
tE=0 time of exposure is fixed to zero *tests are subject to time-dependent false-negative results: Kucirka et al., Ann. Intern. Med. 2020 173:262-267

Additional Hygiene & Social Distancing Measures
Quantifying the impact of quarantine for traced contacts
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Quarantine duration parameters
Quantifying the effect of duration and delay for the standard quarantine protocol (no test) for traced contacts.
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Further considerations
Adherence: Changing the duration of quarantine could affect how many people adhere to the guidelines. Here we show the fold-change in adherence required to offset the change in quarantine efficacy if the duration is changed.
Symptoms: Individuals who develop symptoms should isolate independent of quarantine. Here we deduct these cases once they develop symptoms from the transmission prevented by quarantine.
Adherence and symptoms
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Test-and-release parameters
tQ=0 travellers enter quarantine immediately upon arrival *tests are subject to time-dependent false-negative results: Kucirka et al., Ann. Intern. Med. 2020 173:262-267
Normalisationnormalise to local transmission or total transmission

Additional Hygiene & Social Distancing Measures
Quantifying the impact of quarantine for returning travellers
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Quarantine duration parameters
Normalisationnormalise to local transmission or total transmission
Quantifying the effect of travel duration and quarantine duration for the standard quarantine protocol (no test) for returning travellers
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Further considerations
Adherence: Changing the duration of quarantine could affect how many people adhere to the guidelines. Here we show the fold-change in adherence required to offset the change in quarantine efficacy if the duration is changed.
Symptoms: Individuals who develop symptoms should isolate independent of quarantine. Here we deduct these cases once they develop symptoms from the transmission prevented by quarantine.
Adherence and symptoms
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Quantifying the impact of test-trace-isolate-quarantine (TTIQ) strategies on COVID-19 transmission


Peter Ashcroft1, Sonja Lehtinen1 and Sebastian Bonhoeffer1
1Institute of Integrative Biology, ETH Zurich, Switzerland

We present a mathematical model that leverages empirically determined distributions of incubation period, infectivity, and generation time to quantify how test-trace-isolate-quarantine (TTIQ) strategies can reduce the transmission of SARS-CoV-2. The TTIQ strategy is determined by five independent parameters:

  1. f : Probability that a symptomatic individual is isolated from the population;
  2. Δ1 : Time delay between symptom onset and isolation;
  3. τ : Duration prior to symptom onset in which contacts are identifiable;
  4. g : Fraction of identifiable contacts that are successfully traced and quarantined per isolated index case;
  5. Δ2 : Time delay between isolation of the index case and the start of quarantine for the secondary contacts.

We have two further parameters describing the epidemic situation without TTIQ measures:

  1. R : the expected number of infections caused by a single infected;
  2. α : the fraction of transmission that is attributable to asymptomatic cases.

This is work in progress. This has not yet been peer-reviewed. Read the full preprint on medRxiv.

Empirical distributions
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Weibull distribution.
Ferretti et al., medRxiv 2020.09.04.20188516
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Shifted Student's t-distribution.
Ferretti et al., medRxiv 2020.09.04.20188516
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The distribution of incubation times follows a meta-distribution constructed from the average of seven reported log-normal distributions. Ferretti et al., medRxiv 2020.09.04.20188516
TTIQ parameters

Epidemic parameters

Focal TTIQ parameter set

Reproductive number under TTIQ
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Testing & isolation parameters
We set g=0 to eliminate contact tracing.
Reproductive number under testing & isolation only
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CH Covid-19 Dashboard

Covid-19 Dashboard for Switzerland. A collection of exploratory data bites.

Data Sources

Please see individual modules for specifics.

Code

Source Code for this site is available on GitHub License: GPL v3

Bug reports, issues or other reports and suggestions are always welcome on out GitHub Issue Tracker!

Contributors

in no particular order.

  • Timothy Vaughan, Computational Evolution, D-BSSE, ETH Zürich
  • Chaoran Chen, Computational Evolution, D-BSSE, ETH Zürich
  • Peter Ashcroft, Theoretical Biology, D-USYS, ETH Zürich
  • Sonja Lethinen, Theoretical Biology, D-USYS, ETH Zürich
  • Daniel Angst, Theoretical Biology, D-USYS, ETH Zürich
  • Sebastian Bonhoeffer, Theoretical Biology, D-USYS, ETH Zürich
  • Tanja Stadler, Computational Evolution, D-BSSE, ETH Zürich
  • Monica Golumbeanu, Swiss Tropical and Public Health Institute and University of Basel
  • Melissa Penny, Swiss Tropical and Public Health Institute and University of Basel
  • Nanina Anderegg, Institute of Social and Preventive Medicine, University of Bern
  • Christian L. Althaus, Institute of Social and Preventive Medicine, University of Bern
  • Julien Riou, Institute of Social and Preventive Medicine, University of Bern