Updated 2020-04-24

Joseph Lemaitre (École Polytechnique Fédérale de Lausanne, EPFL), Javier Perez-Saez (Johns Hopkins University, JHU), Andrew Azman (JHU), Andrea Rinaldo (EPFL), Jacques Fellay (EPFL).

FOR PLANNING PURPOSES ONLY: NOT A FORECAST

EDIT as of June 4, 2020: This report is currently outdated and has not been updated since April 24, 2020. Older versions of this report are available on github. R0 estimations (see Inference tab) has been published here. Another group provide updated R0 estimation on the NCS-TF website

Scenarios

This report compares the health impact and surge capacity needs for the COVID-19 epidemic in Switzerland. The underlying model is based on our best understanding of SARS-CoV-2 natural history and transmission, and uses current demographic and epidemiologic data from Switzerland and other locations. We project the number of hospitalizations, ICU admissions, and deaths in both the short and long term under different public-health intervention scenarios.

EDIT June 4, 2020: This report is currently outdated, and up to now none of

Scenario definition

We compared 3 intervention scenarios for model simulations from January 31, 2020 through October 01, 2020:

We consider three planning scenarios:

  • Current Measures Stopped May 1st, which assumes measures instituted in Switzerland:
    • School closure on March 14,
    • Physical distancing measures progressively established from March 14 to March 20.

are held up until May 1st. We inferred the impact of these moderately restrictive non-pharmaceutical interventions (NPIs) in Switzerland using data on hospitalizations and deaths (see Inference tab above). For May 1st on, we assume a return to baseline, early epidemic level transmissibility for the foreseeable future.

  • R0 around 1.2, which assumes that current measures are replaced from May 1st on by a combination of measures that keeps the \(R_0\) around 1.2

  • R0 around 1.5, which assumes that current measures are replaced from May 1st on by a combination of measures that keeps the \(R_0\) around 1.5.

Scenario outcomes

Hospitalization

**Fig. 1**: Daily hospital occupancy for 15 simulation realizations for three scenarios with current measures until May 1st followed by 1) a return to baseline transmissiblity, 2) measures that keeps R0 around 1.2 and 3) measures that keeps R0 around 1.5.

Fig. 1: Daily hospital occupancy for 15 simulation realizations for three scenarios with current measures until May 1st followed by 1) a return to baseline transmissiblity, 2) measures that keeps R0 around 1.2 and 3) measures that keeps R0 around 1.5.

Table 1. Median and 95%PI of several modeled variable on three timeframes.
May 15
June 15
September 15
median 95% PI median 95% PI median 95% PI
Peak current hospitalizations
Stopped 4,000 (1,100-9,000) 27,000 (15,000-30,000) 27,000 (20,000-30,000)
R0 around 1.2 4,000 (1,000-9,000) 4,000 (1,100-9,000) 5,000 (2,800-9,000)
R0 around 1.5 4,000 (1,000-10,000) 6,000 (2,300-12,000) 11,000 (8,000-15,000)
Peak current ICUs
Stopped 600 (180-1,500) 4,000 (2,300-5,000) 4,000 (3,100-5,000)
R0 around 1.2 500 (160-1,400) 600 (180-1,400) 800 (400-1,400)
R0 around 1.5 700 (150-1,600) 900 (310-1,800) 1,600 (1,200-2,200)
Cumulative infections
Stopped 1,000,000 (400,000-2,200,000) 6,000,000 (4,000,000-7,000,000) 8,000,000 (6,000,000-8,000,000)
R0 around 1.2 800,000 (280,000-1,800,000) 1,200,000 (500,000-2,400,000) 4,000,000 (2,100,000-5,000,000)
R0 around 1.5 1,000,000 (280,000-2,000,000) 2,100,000 (800,000-4,000,000) 6,000,000 (5,000,000-6,000,000)
Cumulative ICUs
Stopped 2,600 (900-5,000) 15,000 (6,000-22,000) 24,000 (20,000-25,000)
R0 around 1.2 2,400 (800-5,000) 3,000 (1,200-7,000) 11,000 (6,000-14,000)
R0 around 1.5 2,900 (800-6,000) 5,000 (1,600-10,000) 18,000 (14,000-19,000)
Cumulative hospitalizations
Stopped 14,000 (5,000-28,000) 80,000 (31,000-110,000) 120,000 (100,000-120,000)
R0 around 1.2 12,000 (4,000-27,000) 16,000 (6,000-40,000) 60,000 (31,000-70,000)
R0 around 1.5 15,000 (4,000-30,000) 28,000 (9,000-50,000) 90,000 (70,000-90,000)
Cumulative deaths
Stopped 2,300 (800-6,000) 13,000 (2,200-23,000) 26,000 (22,000-27,000)
R0 around 1.2 2,400 (600-6,000) 3,000 (1,000-7,000) 12,000 (5,000-15,000)
R0 around 1.5 2,900 (800-7,000) 5,000 (1,300-10,000) 19,000 (15,000-21,000)

ICU capacity

**Fig. 2**: Probability of exceedence of ICU capacity thresholds for three scenarios with current measures until May 1st followed by 1) a return to baseline transmissiblity, 2) measures that keeps R0 around 1.2 and 3) measures that keeps R0 around 1.5.

Fig. 2: Probability of exceedence of ICU capacity thresholds for three scenarios with current measures until May 1st followed by 1) a return to baseline transmissiblity, 2) measures that keeps R0 around 1.2 and 3) measures that keeps R0 around 1.5.

Software

Using the Pipeline from Johns Hopkins ID Dynamics Working Group:

  • EPFL: Joseph Lemaitre

  • JHU: Kyra H. Grantz, Joshua Kaminsky, Steve Lauer, Elizabeth C. Lee, Justin Lessler, Hannah R. Meredith, Shaun A. Truelove.

  • University of Utah: Lindsay T. Keegan

  • Developper without affiliations: Sam Shah, Josh Wills

  • Open-Source Software

Methods

Model assumptions

We built a spatial, stochastic, Susceptible-Exposed-Infected-Recovered (SEIR) model of SARS-CoV-2 transmission in Switzerland.

Population. The total population was collected from the website of the Swiss Federal Statistical Office. The entire population is assumed to be susceptible at the beginning of the model. We assume equal risk of infection for all individuals at a given time.

Mobility Data from Office Fédéral du développement territorial: VM-UVEK (2019): Verkehrsmodellierung im UVEK; Daten Zustand 2017. Zenodo: http://doi.org/10.5281/zenodo.3716134.

Initial conditions. We fit our initial conditions for each canton using our inference model. Our likelyhood uses cases, death and hospitalization, and output the number of infected at the start of the model. Baseline transmissibility in the model was estimated with the available epidemiological data (see Section “Inference”).

Reproductive Number. The reproductive number \(R_0\), or the average number of secondary cases caused by a single infected individual in a susceptible population, varies by scenario. Note that the reproductive number is highly-context specific. There is still uncertainty in the range of possible \(R_0\) values for SARS-CoV-2, and varying effectiveness of non-pharmaceutical interventions, including social distancing, improved hand hygiene, and case detection and isolation, may further reduce \(R_0\). We here produce time-varying estimates of \(R_0\) based on our analysis of COVID-19-related deaths, hospitalizations and cases across cantons in Switzerland (for details see the “Inference” tab). These estimates capture the decrease in time of \(R_0\) linked to the implementation of NPIs starting March 14th in the country. Our preliminary estimates are of a baseline \(R_0\) of 2.76 (1.98-3.14 95% CI) prior to interventions. The median estimated value of \(R_0\) after NPI implementation is of 0.52 (0.38-0.7 95% QR, 0.47-0.58 IQR) in the period of March 28 - April 2nd, resulting in a median change of 83% (77%-88% 95% QR, 81%-85% IQR). For specific scenarios we assume that \(R_0\) returns linearly to either the baseline value (Current Measures Stopped) or a fraction of it (both Trace and Isolate scenarios) in 1 week.

COVID-19 Natural History. From analysis of 181 confirmed SARS-CoV-2 cases among travelers and other publicly reported cases, Lauer et al. estimate the incubation period, or the time from exposure to symptom onset, to follow an exponential distribution with mean 5.2 days (IQR 1.5, 7.21 days). The average duration of infectiousness following symptom onset is between 1.3 days and 3, following an Erlang distribution with 3 compartments. We thus sample across a range of possible mean serial intervals (time from symptom onset of an index case to symptom onset of a secondary case infected by the index) from 6.5 to 8.2 days.

Rates of Death and Hospitalization. From our analysis of 391 confirmed SARS-CoV-2 infections in Shenzhen, China, Bi et al. estimate the average time to hospitalization from symptom onset follows a log-normal distribution with median 3.42 days (IQR 2.01, 5.83) (Fig. 3). Other rates where derived from Vaud cantonal hospitalization data. We fitted a log normal distribution to the observed distribution of time hopsitalized, time in ICU, time from hospitalization to ICU and time to death. We estimate from current data that, among those hospitalized, 20% will be admitted to the ICU.

Filtering. Simulated time series of incidence and hospitalizations are based on 30’000 random draws from reasonable bounds of the parameter values. Among these draws, we resample to narrow the set to a simulation that matches the observed reality in hospitalization. Namely, we assign to each simulation a weight that is proportional to the likelihood of incident hospitalizations.

We use simple statistical models using the cumulative distribution of times to hospitalization, ICU admission, and death, as well as the durations of hospitalization and ICU stay to calculate the number of incident and cumulative hospitalizations and ICU admissions and deaths per day, accounting for appropriate delays since infection and symptom onset.

Uncertain parameters include the length of the serial interval, \(R_0\) and the probability of hospitalization. Simulated time series of incidence and hospitalizations are based on 30’000 random draws from reasonable bounds of the parameter values (Table 1). Simulated trajectories are then resampled based on the degree to which they match the observed time series of cumulative hospitalizations, which gives a set of simulations which represent well the observed data.

**Fig. 4**: Simulation envelopes of the Current Measures scenario up to April 8th. Black dots is the data as made available by [OpenZH](https://github.com/openZH/covid_19). The shaded area show the 95 percentile and the bright area the 50 percentile. On the left, we present modelled infections against reported cases.

Fig. 4: Simulation envelopes of the Current Measures scenario up to April 8th. Black dots is the data as made available by OpenZH. The shaded area show the 95 percentile and the bright area the 50 percentile. On the left, we present modelled infections against reported cases.

Limitations

We note several limitations to our work, among which:

There remains considerable uncertainty around some of the key epidemiologic features of COVID-19, including the average duration of infectiousness and time to recovery or death. We have used commonly accepted and well supported estimates as well as hospitalization data from the canton of Vaud up till April 8th, and believe that they are appropriate for planning purposes.

We assume equal risk of infection and progression to hospitalization or death among all individuals in the country at a given time point. There is evidence of age-specific differences in clinical burden and perhaps in susceptibility to infection that are not (yet) considered here.

We do not explicitly model the role of asymptomatic infection when calculating the number of expected hospitalizations. All infectious individuals are considered at risk of hospitalization, though some may recover or die prior to hospitalization. A substantial asymptomatic burden may reduce the number of hospitalized cases.

We do not consider changes in intercantonal mobility from the NPI in place, but we plan to do so in the near future.

Key Sources

  • School closure impacts based on data from (Jackson et al. 2020), (Cauchemez et al. 2008) and (Litvinova et al. 2019)

  • Approximate generation time is based on data from (Bi et al. 2020)

  • Serial interval and incubation period from (Lauer et al. 2020)

  • All the hospitalisation parameters: time in ICU, time to discharge, time to death, percent that die in hospital, … comes from our study of Canton de Vaud data.

Inference

We support our planning scenarios model with a modelling analysis of the epidemiological data available up to April 8th. We aim at inferring time-varying estimates \(R_0\) at the national level following the progressive introduction of NPIs from March 2nd to March 20th.

Inference methods

Infection dynamics and hospitalization model We implement for inference a stochastic dynamical model of the epidemic and hospitalization processes based on the SEIR template used for our scenario generation. The infection dynamics part of the model is the same as the one used for scenario building. Hospitalization dynamics are here modelled explicitely, as opposed to the statistical approach used in scenario buidling. This is done so as to allow the formulation of data likelihood functions which incorporate them. The model assumes that infected people have a certain probability of developing severe symptoms, which then either are hospitalized or not. Infected can dye either outside of the hospital system or within it, either in an ICU or not. The number of compartments in each stage of the disease is determined by fitting an Erlang distribution to the observed times of each transition between classes. These were determing based on hospital data from VD up to April 8th.

Inference We fit the model to curated data from OpenZH, available here These include the current number of hospitalized COVID patients, and the cumulative numbers of deaths, cases and hospital discharges. The latter was not available in all cantons. Time-varying transmission \(R_0(t)\) was estimated following a similar approach than that in (Cazelles 2018), with assumptions on the natural history of SARS-CoV-2 detailed in the Methods section.

We choose to only use deaths and hospitalizations for model estimation due to the challenges linked to COVID-19 case identification and heterogenous testing strategies adopted across cantons. The observation model is formulated as follows:

\[ \begin{aligned} deaths(t) &\sim Poisson(\Delta D(t)) \\ \Delta hosp(t) &\sim Skellam(\Delta H(t), \Delta D_H(t) + \Delta R_H(t)) \\ \end{aligned} \] where, \(\Delta I(t)\), \(\Delta D(t)\), \(\Delta H(t)\), \(\Delta D_H(t)\), \(\Delta R_H(t)\) are respectively the number of new infected, deaths, hospitalized, and deaths and discharged from hospitals at time \(t\), and \(\Delta hosp(t)\) is the difference between the number of current hospitalizations at times \(t\) and \(t-1\), for which we choose a Skellam distribution. The full log-likelihood of the observation model was taken as the sum of the individual log-likelihoods of the two data types. The model was fit using multiple-iterated filtering as implemented by (Ionides et al. 2015) in the POMP R package.

Estimates of time-varying \(R_0\)

**Fig. 5**: Time-varying estimates of $R_0$ in Switzerland. Light gray and dark gray envelops give the 50% and 95% quantile ranges of the smoothing distribution of $R_0$ given the data.

Fig. 5: Time-varying estimates of \(R_0\) in Switzerland. Light gray and dark gray envelops give the 50% and 95% quantile ranges of the smoothing distribution of \(R_0\) given the data.

Fit to data

**Fig. 6**: Fit of model to data. Data (points) are plotted agains Light gray the 50% (dark gray) and 95% (light gray) quantile ranges of the smoothing distribution of the epidemiological variables given the data. The units of all y-axis are daily numbers. Note that model estimates provide the assumed true number of infections, which can larger than reported cases due to underreporting.

Fig. 6: Fit of model to data. Data (points) are plotted agains Light gray the 50% (dark gray) and 95% (light gray) quantile ranges of the smoothing distribution of the epidemiological variables given the data. The units of all y-axis are daily numbers. Note that model estimates provide the assumed true number of infections, which can larger than reported cases due to underreporting.

References

Bi, Qifang, Yongsheng Wu, Shujiang Mei, Chenfei Ye, Xuan Zou, Zhen Zhang, Xiaojian Liu, et al. 2020. “Epidemiology and Transmission of COVID-19 in Shenzhen China: Analysis of 391 Cases and 1,286 of Their Close Contacts,” March. https://doi.org/10.1101/2020.03.03.20028423.

Cauchemez, Simon, Alain-Jacques Valleron, Pierre-Yves Boëlle, Antoine Flahault, and Neil M. Ferguson. 2008. “Estimating the Impact of School Closure on Influenza Transmission from Sentinel Data.” Nature 452 (7188): 750–54. https://doi.org/10.1038/nature06732.

Cazelles, Clara AND Dureau, Bernard AND Champagne. 2018. “Accounting for Non-Stationarity in Epidemiology by Embedding Time-Varying Parameters in Stochastic Models.” PLOS Computational Biology 14 (8): 1–26. https://doi.org/10.1371/journal.pcbi.1006211.

Ionides, Edward L., Dao Nguyen, Yves Atchadé, Stilian Stoev, and Aaron A. King. 2015. “Inference for Dynamic and Latent Variable Models via Iterated, Perturbed Bayes Maps.” Proceedings of the National Academy of Sciences 112 (3): 719–24. https://doi.org/10.1073/pnas.1410597112.

Jackson, Michael L, Gregory R Hart, Denise J McCulloch, Amanda Adler, Elisabeth Brandstetter, Kairsten Fay, Peter Han, et al. 2020. “Effects of Weather-Related Social Distancing on City-Scale Transmission of Respiratory Viruses,” March. https://doi.org/10.1101/2020.03.02.20027599.

Lauer, Stephen A, Kyra H Grantz, Qifang Bi, Forrest K Jones, Qulu Zheng, Hannah Meredith, Andrew S Azman, Nicholas G Reich, and Justin Lessler. 2020. “The Incubation Period of 2019-nCoV from Publicly Reported Confirmed Cases: Estimation and Application.” medRxiv. https://doi.org/10.1101/2020.02.02.20020016.

Litvinova, Maria, Quan-Hui Liu, Evgeny S. Kulikov, and Marco Ajelli. 2019. “Reactive School Closure Weakens the Network of Social Interactions and Reduces the Spread of Influenza.” Proceedings of the National Academy of Sciences 116 (27): 13174–81. https://doi.org/10.1073/pnas.1821298116.