Table 1.
Estimations assuming a uniform attack rate.
We show our estimation for the uniform infection fatality rate (UIFR) before and after quantifying the effects of the systematic under-counting of deaths. We also estimate the percentage of the population infected in each country by the end of May of 2020. Errors include the statistical error (±sigma, the standard deviation obtained through error propagation of the results in Table 1, and the uncertainty of the prevalence survey in Spain) and a systematic error of 35% of possible under-counting of deaths, see Section 4.2).
Fig 1.
Normalized number of deaths occurred in French hospitals as a function of age.
A We show the evolution with time of the cumulative number of deaths normalized by the number density of individuals in age group α (i.e. in Eq (2)). In B, we show
as function of the age group, for all the times in A (the darker the color, the more recent the measurement, and we give some dates in the legend). This quotient is essentially time-independent as discussed in Eq (7), and it lets us estimate the quotient between the UIFR (the IFR under the assumption of uniform attack rate, see Eq (6)) of the two age groups, that is,
.
Fig 2.
Under-counting of deaths per age groups.
We show the fraction of under-counted deaths, per age groups, observed when comparing the number of deaths certificates where COVID-19 was mentioned either confirmed or suspected, and the official deaths attributed to COVID-19, relatively to this second number, see Eq (1) for the definition, for England and Wales in A, and for the Community of Madrid B. The horizontal lines mark the mean rate of ‘under-counting’ below 80 years old.
Fig 3.
Normalized number of deaths in different countries as a function of age.
A We show the normalized number of deaths per age group (defined in Eq (2)) for a selection of countries affected by the COVID-19 epidemic at very different scales. In B, we show the same data (excluding the Netherlands) but where each country has been multiplied by a constant so that it collapses with the Spanish curve in the age region in between 30 and 70 years old. The values of each country’s constants are given in S2 Table. In black, we show the country average for each age segment (errors calculated with the boostrap method up to a 95% of confidence), and in C the fit of this average to a pure exponential function, see Eq (8).
Fig 4.
Probabilities assuming a uniform attack rate.
A We use the measurements of the number of infections in Spain to estimate the UIFR using Eq (3) in both regions. We fix the constant in S2 Table using the estimation of the UIFR in Spain for the age group 50-59 to infer the values of the country average UIFR (from the collapse of Fig 3B). We show this first estimation in red, and in green, we show the UIFR after correcting the under-counting of deaths over 70 years old. We compare these results with the estimation by Verity et al. [25] and the CFR (i.e. the probability of dying for confirmed COVID-19 cases, not the IFR) by age in South Korea. In B, we use the IFR estimations from A̠ and Table 1, to predict the seroprevalence of anti-SARS-CoV-2 antibodies in the population of Geneva, Switzerland, from the official distribution of deaths per age of a total of 277 deceases. The predicted fraction of infections is given in dots (in green, if we used the bare estimation of Eq (9), in violet, if we include the corrections linked to under-counting). In horizontal lines (and the 95% of confidence interval in gray shadow), we show the actual values measured from the antibody survey of Ref. [47] in patients of different age-groups.
Fig 5.
Other probabilities as function of age assuming uniform attack rate.
In A we show the probability of being classified as official case, , being hospitalized,
, admitted in intensive care,
, and dying,
, in Spain in Spring 2020, as function of the age using age segments of 10 years. B, we show the same data but were the kid’s information has been grouped by smaller age-segments, evidencing the severity of the cases in patients under 2 years old. A is generated using the data by the Spanish Health Ministry up to the 22nd of May and B with the data published by the RENAVE, see Materials and S1 Table.
Fig 6.
Uniform versus non uniform IFR.
A We show the relative risk of infection for an age segment rα (see Eq (4) and definition below) taken from the sero-epidemiological study of the Spanish population [46]. While the youngest segments of the population seem to be less hit by the virus, the distribution of the infections is rather similar to that of a uniform attack rate, indicated by the dashed line rα = 1 here. The 95% confidence interval for rα is indicated by the red shadow. B We show the estimated uniform and nonuniform IFR for Spain and compare it with the CFR as a function of age. The error for the non-uniform IFR is shown by a red shadow.
Table 2.
We estimate the percentage of unreported number of deaths for each country together with the expected fatality ratio once included these estimated missing deaths. In the parenthesis we include the expected values if the current death counting was perfect (no missing deaths, left side of the parenthesis) and if heavy under-counting was present, such as the one observed when comparing with number of deaths with COVID-19 in the death certificate (right side of the parenthesis).