Second Corona Wave? A Swiss Study Under Scrutiny

In this article:

  • The current extrapolation study by Lemaitre, Fellay et al. predicts a catastrophic scenario for Switzerland in case the lockdown measures are completely stopped.
  • Fellay deduces from the extrapolation that a far-reaching lockdown of social life is inevitable and that a vaccine is the only permanent solution.
  • The projection has three major flaws: (1) the obvious clustering of COVID-19-associated deaths among elderly people with pre-existing conditions is not fed into the calculation; (2) the baseline reproduction rate is probably wrong, since its calculation does not take into account the massive increase in the number of tests since the beginning of March; (3) the presumably significant number of asymptomatic SARS-CoV-2 carriers is disregarded.
  • Fellay’s statements regarding necessary future measures can therefore not be regarded as scientifically valid.

„Researchers warn of millions of infected people in Switzerland“ captioned the SRF (Swiss Radio and Television) an article from 29 April 2020. There is talk of a second wave of coronavirus, the extent of which has been projected by an international team of researchers led by Joseph Lemaitre and Jacques Fellay of the EPFL in Lausanne.

Fellay, on whom the present article focusses because of his public statements, does research at the EPFL in Lausanne on „Human genomic studies in infectious diseases„. In other words, his work centers on the connection between genetic characteristics of individual people and their susceptibility to viral infections. In particular, he and his research group have investigated the viruses HIV, hepatitis C, cytomegalovirus, and the Epstein-Barr virus. The coronavirus is not (yet) on this list.

Such an approach would actually be desirable in connection with SARS-CoV-2. Not much is actually known about the relationship between the course of the disease and individual dispositions, except that old age and previous illnesses increase mortality. In the present study, however, Lemaitre, Fellay et al. do not carry out this urgently needed causal analysis but work purely statistically.

What makes the study so explosive?

What is so controversial about this study that it should enjoy special attention among the flood of scientific publications on coronavirus? I see four reasons for this.

Fellay’s political role

For one, there is Jacques Fellay’s political role. He is a member of the Swiss Federal Council’s scientific committee on coronavirus. His opinion will presumably influence the Council’s decisions. An analogous example from abroad makes this plausible: Neil Ferguson’s model calculation a few weeks ago had a decisive influence on the corona policy of Great Britain and the USA, and prompted their governments to significantly tighten the measures.

Fellay’s remarks

Secondly, there are Fellay’s statements regarding future anti-corona measures. The aforementioned SRF quotes them in such a way as to connote their following from the study results (which, as we will see in a moment, is not the case). Below are the quotes and a short commentary on each of them:

Once the pressure has eased a little, as it has since the beginning of this week, the epidemic can circulate more evenly among the population. It is therefore essential to accompany this gradual easing of the lockdown with all possible other measures to prevent the virus from regaining the upper hand. And it is this game of hide and seek that we must learn to master.

Jacques Fellay

Fellay makes an almost trivial observation here, namely that once the measures are relaxed, the virus, in so far as present, can circulate more evenly in the population. This is straightforward, because traffic movements are rising again. However, Fellay uses the term „epidemic“ instead of the more neutral and undisputed „virus“, suggesting that Switzerland still has a COVID-19 epidemic – which is highly questionable, given the figures (see below). Finally, his „hide-and-seek“ metaphor is more suggestive than scientific: it gives the impression that we are in a kind of „guerrilla war“ against a phantom enemy and should therefore do everything possible to keep him in check.

The ban on some festivals in the summer will not allow us to keep the reproduction rate below 1.2.

Jacques Fellay

It is completely unclear how Fellay arrives at this assessment. His study, as we shall see, does not warrant such a conclusion. It only calculates possible scenarios based on different reproduction rates, but does not make any statement about which measures could help achieve a given reproduction rate. His words imply, however, that much more than „a few festivals“ ought to be canceled – in other words, an even greater eradication of social and cultural life than has already occurred?

If we return to our accustomed way of life, the epidemic will very quickly overwhelm us. We must continue to maintain a certain distance, whether by keeping more than two meters away from other people or by wearing masks.

Jacques Fellay

Again, it is unclear how Fellay can be so certain that the epidemic would quickly overwhelm „us“ (i.e. probably Switzerland) if we returned to our accustomed way of life. Again, his study provides no justification for this, as it does not even attempt to show how people’s lifestyles correlate with different reproduction rates.

We must be aware that we can all be very happy if a vaccine is made to work within 12 or 18 months

Jacques Fellay

That’s a big gun Fellay is bringing in. His statement implies that a vaccine is the only way out of the corona situation. But that would require a number of things: (1) that we are dealing with a highly dangerous virus, (2) that a „second wave“ is very likely, and (3) that even if (1) and (2) are correct, there are no alternatives to vaccination. (1) and (3) are not treated by the study at all (actually, (1) is simply presupposed in an unwarranted way, without argument), and (2) follows from the study only on the basis of questionable assumptions, as I will show.

Defective media coverage

The third reason for an analysis of the study is the quality of media coverage. Influential Swiss leading media apparently don’t do their work properly. For example, the quoted SRF article does not even attempt to explain, let alone analyze, the methodology of the study, but largely contents itself with quoting Fellay. The “Aargauer Zeitung” at least explicates the approach of the study but reproduces its results without critical examination. What sticks with the reader is the impression that without further measures, millions of Swiss will be infected and that a high toll of lives will have to be paid. Such conclusions urgently need to be checked for plausibility due to the seriousness of their consequences.

International exemplarity

The present study only deals with Switzerland. However, it is to be expected that methodologically very similar projections will be made in other countries (or have already been, see the Ferguson study). Thus, the Fellay study could serve as an example of a science politicians use to justify serious decisions. An analysis of the study’s methodology therefore facilitates evaluating similar work in other countries.

The study’s methodology critiqued

Lemaitre et al.’s projection is a stochastic model. The basic question is how hospitalization and death numbers could develop depending on the basic reproduction rate R0 of the virus, which in turn depends on the measures taken.

The assumptions of the study are as follows. Since the main errors lie here, I will analyze them in more detail.

Uniform susceptibility

A uniform (equal) susceptibility for infection with SARS-CoV-2 is assumed for all people in the Swiss population („The entire population is assumed to be susceptible at the beginning of the model.“) Apparently, this assumption refers to the future development from „today“ (approx. beginning of May); for the period up to the end of April concrete data were already available, and no model needs to be created for this.

This is astonishing, since the situation by the beginning of May is clearly a different one than in early or mid-March. The uniformity assumption ignores the fact that in the meantime a certain (albeit unknown) number of people have undergone the infection and thus presumably possess natural immunity. The study by Ioannidis et al. in Santa Clara County, California, suggests that there may have been a good 50 times more people infected with SARS-CoV-2 than thought (and that those people now have immunity because of antibodies, which is in fact what the scientists tested). Other studies such as those by Streeck et al. or a meta-study by Ioannidis as well as various other expert estimates (see below) make plausible the assumption that the number of undetected infection cases is many times higher than the number of registered infected persons, and that this is an international phenomenon.

Baseline reproduction rate too high

Lemaitre et al. assume a very high R0 reproduction rate („baseline transmissibility“) of 2.76, which follows from the epidemiological data collected in March and April. More precisely, R0 is being calculated (among others) from the occurrence of new infection cases during a given time period. The crux is now that these numbers are not statistically reliable, since no standardization of the test positives to the number of tests performed (which increased sharply over time) was made. Prof. Christof Kuhbandner from the University of Regensburg has clearly shown, using the examples of Italy and Germany, how dramatically the increase in infection cases was overestimated, because the greatly increased number of tests per day was not taken into account. In Switzerland, too, the number of tests has risen steeply, particularly in the first few weeks, as can be seen from the Swiss BAG data (see Figure 1a). The baseline reproduction rate Lemaitre et al. assume will thus be much lower if the massively increased number of tests is taken into account. The authors themselves address this point: „Uncertain parameters include…R0″.


Fig. 1a: Test numbers in Switzerland since the beginning of the corona situation. (Source: BAG, as of 17.05.2020)

How much should the assumed R0 differ from the actual one? If the necessary statistical checks are made, i.e. if the number of positive test results on a given day is divided by the number of tests performed on that day (as requested by Prof. Kuhbandner), the following picture emerges for Switzerland (Fig. 1b):


The daily case numbers were divided by the number of tests performed on that day. The corresponding ratio of 1 March 2020 was set as the reference standard (growth factor 1). Data source: BAG

It should be noted that the starting date chosen here is 1 March, immediately after the first federal measure (of 28 February, prohibition of large events > 1000 people). The very first (registered) corona case in Switzerland is dated 25.02.2020.

The ordinate (vertical axis) now shows a growth factor of corona positives compared to their number on 1 March. (If the 25.2. is taken as the reference point, an even more dramatic divergence between artificially increased and statistically corrected growth factor results). While the positive test results suggest an increase of up to 140-fold, the statistically corrected increase is only up to 10-fold. Moreover, it can be seen that the number of cases has been declining since the end of March, although the time lag between infection and notification/test is not even taken into account here (usually 5-12 days incubation period, plus a few days before the infected person set off for the test). Incorporating this latter factor suggests that the spread of SARS-CoV-2 was already declining at the time of the „big lockdown“ on March 16th or shortly after.

Too high probabilities of hospitalization and death

Other parameters included in the extrapolation are incubation time, probability of hospitalization and probability of death.

The incubation period has been investigated by studies (some quoted by Lemaitre et al.) and should be robust. However, the other two parameters suffer from the fact that the number of asymptomatic courses is unknown. The authors themselves admit this: „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. (my emphasis). This „substantial asymptomatic burden“ is very likely given. According to Chinese data, the number of asymptomatic SARS-CoV-2 carriers could be up to 80% of those infected, other sources report 50% (Iceland), or again 80% (India). The director of the US National Institute of Allergy and Infections Diseases, Dr. Anthony Fauci, estimates the incidence at 25 to 50 percent. Plausibly, therefore, there is an enormous error potential here.

Studies by Streeck et al. in Gangelt (Germany) and a review of Ioannidis that directly address the IFR (Infection Fatality Rate, the percentage of infected people who die) point in the same direction. According to Streeck et al. and Ioannidis, the IFR lies between 0.03% and 0.5% (lower and upper limit of the Ioannidis study; Streeck et al. lie in between with 0.37%). In any case, this number is much lower than the assumption of up to over 3%, which was used at the beginning of the coronavirus spread by politicians such as Austria’s Chancellor Kurz as a reason for the drastic measures. It also is in the same ballpark as annual influenza (IFR approx. 0.2%).

Equal mortality risk for all

A very problematic assumption is that of a uniform risk of infection, hospitalization and death: „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.” According to the BAG (situation report retrieved on May 16, 2020) of „the 1528 deceased persons for whom complete data are available … 97% suffered from at least one previous illness.“ Moreover, when looking at the age distribution, it becomes clear that the deaths are almost exclusively restricted to the age group 60+, and in particular to the group 80+.

It is incomprehensible why Lemaitre et al., against their better judgment, have not included this important factor in their calculations. There seems to be no good reason for this omission.

Model simulation for March and April totally off the mark

To make the extrapolation more realistic, the authors applied a statistical filter to take into account the range of values for the model calculation parameters. A total of 30,000 random simulations were selected, which in turn were weighted according to the degree of fit with actually observed clinical courses. This allows a comparison between actual data and the model calculations, at least for the time elapsed until the end of April (Fig. 2). There is a striking discrepancy in the case numbers (far left diagram; actual numbers in black, shaded color = 95th percentile and light color = 50th percentile of the model calculations ):


Fig. 2: Simulation with the initial conditions used by Lemaitre et al. vs. actual data (according to OpenZH) up to and including April 8. See text for explanation.

Obviously, the model (based on the assumed R0) calculates much higher case numbers than actually obtained. Perhaps the difference is due to the lockdown measures. In any case, the discrepancy would be fully consistent with the assumption that the R0 was simply chosen much too high.

Results of the projections

Die Ergebnisse der Hochrechnungen sind in den Abbildungen 3 und 4 grafisch dargestellt.

The results of the extrapolations are displayed in Figures 3 and 4.

Fig. 3 shows the calculated developments of hospitalization figures (left) and intensive care cases (right). The three colors of the curve represent the courses of „measures completely cancelled on 1 May“ (R0 = 2.76, orange), „relatively strict measures“ (R0 = 1.2, green) and „relatively lax measures“ (R0 = 1.5, blue). There are several curves for each scenario because the initial parameters fed into the model have a certain bandwidth.


Fig. 3: Hospitalizations according to the model as a function of the baseline reproduction rate (return to original R0 is assumed if the measures are completely terminated).

Fig. 4: Proportion of simulations, as a function of the reproduction rate, which result in an overload of the intensive care units.

Fig. 4 shows the proportion of simulations, as a function of reproduction rate, which result in overloading of intensive care units. If the measures are removed, the model predicts an overload of capacity with a high probability even for 3,000 available intensive care beds, for R0 = 1.5 only in the case that only 1,000 beds are available, and at 1.2 practically no overload at all.

Expressed in figures, the following picture emerges:

  • All measures stopped on 1 May (R0 = 2.76): Model predicts median 27,000 simultaneous hospitalizations at the peak on 15 June, including median 4,000 simultaneous intensive care cases (and almost certain hospital congestion), 6 million infected persons, and 13,000 cumulative deaths on 15 June and 26,000 on 15 September.
  • With R0 = 1.5: 6,000 simultaneous hospitalizations on June 15 – 900 simultaneous intensive care cases (with only 1000 intensive care beds already a high risk of overload) – 2.1 million infected persons – 5,000 and 19,000 deaths
  • With R0 = 1.2: 4’000 – 600 – 1.2 million – 3’000

Analysis and evaluation of the results

If the projections are correct, then stopping the measures would be downright disastrous. An R0 of 1.2, or even 1.5, does not seem to push the Swiss health system (with an assumed 2,000 intensive care beds) to its limits, but it does claim many lives (although a sound assessment is only possible by thoroughly examining excess mortality and death causality). It is unclear which types of measures are suitable to keep R0 from rising above 1.5. Fellay has cast his vote. It can be assumed that in case of doubt, politicians also prefer to „play it safe“. In other words: measures would rather be too strict than too „lax“, and rather maintained too long than too short.

Furthermore, the question arises as to how COVID-19 can be got rid of at all, so that normality returns. The problem is that the supposedly life-protecting scenarios (especially R0 = 1.2) result in a longer persistence of the virus in the population (see green curves in Fig. 3). This creates a dilemma: Either continue with a lockdown and keep the death rates low but keep the virus in the population, or achieve rapid herd immunity and/or eradication of the virus but possibly risk many deaths. Fellay’s solution, as already mentioned: A vaccine must be found.

This dilemma is eliminated if the extrapolation is incorrect. The arguments put forward suggest this. The study therefore has two massive flaws, which the authors admit, but whose significance they massively understate; in fact, these flaws call into question the validity of the entire study:

  • The clearly existing causal relationships between COVID-19-associated deaths and old age as well as previous diseases are completely ignored. If they were taken into account, the death and ICU figures would be significantly lower.
  • Similarly, the base R0, to which a return is assumed if all measures are discontinued, is probably much too high. This then results in far too many cases, and together with the overestimated susceptibility and mortality and the clearly underestimated number of asymptomatic cases, one gets far too many ICU and death cases.

In view of these problems, it is highly alarming how dogmatically Fellay advocates a vaccine as the only solution and the fight against the virus as a highly delicate „guerrilla war“. His study does not justify such conclusions; an all-round view of the data now available to us rather suggest that „lockdown“ policy and the obsession with a vaccine should be abandoned as soon as possible.

Policymakers ought to finally make a thorough analysis of the available data, rather than relying on extrapolations based on messed up raw data.

Photo by Fusion Medical Animation on Unsplash

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