Facts Interpretations

Sars-CoV-2 preliminary serology test reports from Scotland, Denmark and Finland provide contrasting estimates of Infection Fatality Ratio (IFR)


Randomised Sars-Cov-2 serology surveys were recently conducted in Scotland, Denmark and Finland. Preliminary results were made public. We propose a workflow to interpret results in terms of epidemic dynamics. The Infection Fatality Ratio (IFR) in Denmark is estimated 0.21%. IFR seven times lower are estimated for Finland and Scotland, with low degree of confidence, due to either poor quality of death records, and/or insufficient survey resolution or surveys yet too early in epidemic dynamics. Uncertainties and recommendations to progress on the understanding Sars-Cov-2 IFR worldwide and country after country are discussed. We obviously conclude that “Confirmed Cases” official reports are of little scientific use, systematically underestimating the real number of infected cases and by an inconsistent amount by country and with time within each country.


The concept of Infection Fatality Rate (IFR) vs Case Fatality Rate (CFR) is best explained on Oxford CEBM dedicated page

“The IFR estimates the fatality rate in all those with infection: the detected disease (cases) and those with an undetected disease (asymptomatic and not tested group).”

On, Rich Condit explains the importance of determining the IFR: “This is not just an intellectual exercise.  Understanding the true infection fatality rate has major consequences for planning control measures following our first encounter with SARS-CoV-2.”

In epidemic dynamics modelling, the IFR is an input parameter, the link between the number of simulated infectious (accessible from the numerical model’s output) and the death rate (accessible from experience, and then also simulated). Lourenço et al. have highlighted the importance of serology surveys to help determined the IFR. Ref: “Fundamental principles of epidemic spread highlight the immediate need for large-scale serological surveys to assess the stage of the SARS-CoV-2 epidemic“.

In this study, we analyse recent serology surveys in three northern Europe countries using our numerical model CovModel 1.5 in an inverse problem, since IFR is normally an input of the model. We do a simultaneous match of death records and of the seroprevalence proportion measured in the survey. We back-estimate the reproduction number with time and the IFR.

Recent serology campaigns in Northern Europe countries


The EEID research group published this on 10 April.

We interpreted a seroprevalence of 1.2% at median date 22 March (6 positives over 500) and no detection on the earlier 17 March survey. See Table 1 below.

Table 1: serology results in Scotland


Data were obtained from this source

We interpreted a seroprevalence of 1.8% on 7 April 2020.


Data were obtained from this source:

Three surveys were interpreted, providing seroprevalence of 0.69%, 0% and 3.4% respectively at median dates 26 March, 2 April and 9 April.

Note at time of study (16 April 2020) serology tests were also performed in Germany, but regretfully the date of sampling were not reported which prevented any interpretation.

Surveys summary and comparison

The three countries have comparable population at comparable latitudes, but different epidemic dynamics (Table 1). First death occurred almost simultaneously in Scotland and Denmark, one week later in Finland. The average death incidence on 12 April was comparatively two times higher in Scotland than in Denmark.

Serology surveys are summarised in Table 3. We indicated the time of surveys relative to first death or to first reported case, as to position each survey with respect to the maturity of epidemic. An interesting rule of the thumb is that seroconvertion latence is of the same order as the time-to-death of those infected whom have died (two to three weeks), meaning that a serology survey is most useful when the death signal is present (as to provide information on the infected number that created those deaths).

Table 2: Countries data
Table 3: survey results and comparison

Model – Methodology

One #SIR model CovModel1.5 was built for each country, assuming parameters in Table 1.

In version 1.5, a seroprevalence model was added to the code. How seroprevalence is calculated will be detailed in model description [In progress].

Death rates from Git Hub JHU repository were used as observed data. The three models were matched to observed death rate and observed seroprevalence. Matching parameters were: Ro, R with time (to model social distancing) and rho.

rho is defined as the ratio of severe cases over infected. Since Theta = 0.14, the number of deaths per servere is fixed, any assumption on rho is directly related to the IFR in CovModel 1.5 by IFR = 0.14 x rho

Results: simultaneous death curve and serology tests time-match

Each countries model was easily matched. Ro is uniquely determined from intian slope of cumulative death curve in logarithmic scale; R with time is easily matched from adjusting the curvature of cumulative death curve – thereby proving the efficiency of social distancing measures and the lives they have saved; several values of rho are tried until the simulated proportion of infected is such that the seroprevalence curve matches survey’s number.

Table 4: Model results – estimate of Ro, rho and R during lockdown
Figure 1: death curve match, Scotland
Figure 2: death incidence match, Scotland (simulated infected incidence in red)
Figure 3: serology survey (22 March) match for Scotland. Note that first survey on 17 March did not return any positive, hence can not be plotted on a logarithmic scale.
Figure 4: death curve match, Denmark
Figure 5: death incidence match, Denmark (simulated infected incidence in red)
Figure 6: serology survey (7 April) match for Denmark.
Figure 7: death curve match, Finland
Figure 8: death incidence match, Finland (simulated infected incidence in red)
Figure 9: serology surveys match for Finland. Both surveys #1 and #3 match remarkably well. Not to be forgotten that survey #2, in between dates, on 2 April, did not return any positive.

Discussion: can IFR be determined from advanced interpretation of serology tests ?

This study reveals the conditions necessary to accurately determine IFR from serology test campaigns and epidemiology simulation methods.

Condition 1: serology testing need happen at a time coinciding with peak death incidence, or after. This is because the time lag for seroprevalence (15.4 days) is comparable to the time lag for death to occur (relative to time of infection), and value of information is in the death time series.

Condition 2: serology campaigns need be statistically designed with the right resolution in mind

Condition 3: a sampling campaign representative of a territory , and a model representative of same.

Condition 4: state of the art #SIR or equivalent models need be used for interpretation. Great care must be taken to accurately model the transition from non-susceptible curve to death curve. This is because

Condition 5: accurate understanding of seroconversion time lags in models. What serology tests provide is a flash-back image of what was the disease around two weeks before.

The are other conditions, including good death rate records. Recent change of counts or statistic standards in France and the United Kingdom show the latter is far from being granted.

Scotland did not satisfy Conditions 1, nor Condition 3 because the government did not publish regional death statistics. Denmark was particularly good on 1 and 2. Condition 2 is problematic in Finland, as second week campaign did not return a positive. In all cases, more work is required on 4 and 5 – although simple and powerful, CovModel version 1.5 used in this study remains a screening tool.


We conclude that an ultimate IFR of 0.21% for Denmark is a reasonable estimate.

To put this in perspective, this results in the following numbers on 12 April for Denmark: infected 41,600; infected and recovered 280,700; seroprevalent = 147,200. Actual cumulative death on same day was 273, but note that IFR can not be obtained directly from these numbers due to epidemic dynamics- IFR is an ultimate ratio at end of outbreak.

Despite all limitations inherent to Scotland and Finland results, we observe that IFR estimates appear significantly lower. We strongly recommend more serology campaigns to confirm all early results in these countries and elsewhere. The scientific community and commentators should also keep an open mind on the IFR number. We suggest not pre-assume there should be only one single and universal estimate of the IFR for all countries until all factors affecting this number are understood.

L.S. 17 April 2020