Coronavirus disease (COVID-19) fatality rate: WHO and media vs logic and mathematics

Last update: 2/20/2020 (I’m updating the article just to add additional arguments and to answer reader’s comments)

On January 29th, 2020 Dr. Michael Ryan, Executive Director of World Health Organization  (WHO) on a press conference said that Novel Coronavirus (2019-nCoV) fatality rate is 2%.

During the following days many (if not all) big media corporation published articles with the following statements:

“The mortality rate for the new coronavirus is about 2.1%, currently far lower than the 9.6% of SARS.” BBC

“With a fatality rate of around 2%, which experts agree appears to be the current level for the virus” CNN

“Health experts say they are encouraged by the steady rise in the number of recoveries. They take it as evidence that the treatments meted out have been effective and that the virus does not appear to be as deadly as SARS. SARS had a mortality rate of 9.6 percent, and about 2 percent of those reported to have been infected with the new coronavirus have died.” The New York Times

“The Wuhan coronavirus seems to have a low fatality rate, and most patients make full recoveries.” Business Insider

“The number of confirmed cases and deaths indicate that it is around 2 percent, significantly lower than SARS’ 10 percent.” The Harvard Gazette

What is wrong with all this statements? I believe that they are false and misleading.

Lets determine the terms before we will proceed with any calculations. This is very important to avoid errors and misunderstanding.

How mentioned by WHO and the media 2% figure has been calculated?

Despite different and wrong (e.g. “mortality rate”) terms used by some media  they all were talking about so called

Case fatality rate (ratio) (CFR) – a measure of the severity of a disease and is defined as the proportion of confirmed cases of a specified disease or condition which are fatal. CFR = total number of deaths known by today divided divided by total number of known cases confirmed by today.

Easy to calculate, because number of deaths and number of confirmed cases available in daily reports published by China and other countries.

CFR=10% for SARS 2003 epidemic means that 10% of confirmed cases died. What does CFR=2% means for the COVID-19 epidemic? Almost nothing. It will be explained in the following parts of the article.

Infection fatality rate (ratio) (IFR) – a measure of the severity of a disease and is defined as the proportion of infected people for whom this disease was fatal. IFR = Total number of deaths known by today divided by total number of infected persons.

Without population-based serologic studies (to find out how many people had a virus without symptoms or with mild symptoms), it is not yet possible to know how many people has been infected. If there was infected people who was not positively tested for a virus than IFR will be lower than CFR.

WHO already describes the terms in this document published on Feb 20, 2020.

Mortality rate – a measure of the severity of a disease and is defined as the number of deaths in a particular population, scaled to the size of that population (e.g. mortality rate = 100 deaths per 100,000 population)

Let’s also determine one more term (this one is my own, not used by WHO).

Real (or expected) fatality rate – proportion of confirmed cases that already died or are being expected to die.The difference between CFR and real fatality rate is in the following.

Imagine a disease that kills 100% of infected people (and each infected person is being detected). And let’s say it takes 10 days for a person between first symptoms and death. And we got 100 new cases every 10 days.

day 1: 100 cases, 0 deaths CFR = 0%
day 11: 200 cases, 100 deaths, CFR = 50%
day 21: 300 cases, 200 deaths, CFR = 67%
day 31 (no new cases): 300 cases, 300 deaths, CFR = 100%

Is it correct to say “this disease is not deadly, we have 0 deaths on day 1”? No we have 100 people in a hospital, probably in a critical condition, but they will die in a month.
Is it correct to say “this disease is becoming more deadly, CFR has grown from 0% to 50% on day 11 and to 67% on day 21 and to 100% on day 31”. No, the disease is not killing bigger proportion of infected people. It’s our formula used to calculate CFR is wrong for a growing infection and returns misleading results. While the real fatality rate during all 31 days is 100%.

SARS 2003 epidemic already ended years ago, all patients either died or recovered. So, we can use CFR formula and the result tells us how many of confirmed cases died (a proportion). It was about 10%.

But COVID-19 patients (confirmed cases) are still being (most of them) sick in hospitals, many of them in ICUs. The virus doesn’t kill a person immediately. There is a lag between infection confirmation and death. It means, that by today only those patients died, that have been registered as ‘confirmed cases’ a few days, a week, or even a month ago.

Median time (based on first 41 cases) between symptoms onset and admission into ICU – 10.5 days. And it’s not death yet. They got Coronavirus confirmation probably somewhere between symptoms onset and death. So, there is a lag between case confirmation and death.

Image: The Lancet – Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China

Also we have this information from a doctor from China: “So the second week is what determines whether the illness becomes critical. The third week determines whether critical illness leads to death. ” [The Straits Times

What does the lag between case confirmation and deaths mean for a fast growing epidemic? It means that current death/cases value is useless and real fatality rate may times greater than CFR.

Example. COVID-19, February 2 data:

Most of about 17500 cases are new cases (7 days before there were only about 2800 cases). So, it’s more likely (if we assume that average lag between case confirmation and death is 7 days) that in reality we have 362 deaths not among 17500 cases, but among 2800 cases = 13% case fatality rate. It might be less than 13% if the lag is shorter, but it might be greater than 13% if the lag is longer. In reality the lag is not just one figure, it’s a distribution – for some people it’s shorter, for other people it’s longer and it probably depends on sex, age and other factors. This method is also biased, we don’t have all required data (we don’t know lag distribution) to use this method, but it shows what is wrong with CFR.

Let see what happened in 2003:

“The death rate from severe acute respiratory syndrome has more than doubled, to 5.6 percent, since the epidemic was first detected in mid-March, causing deep concern among health officials.

Although the overall death rate, according to World Health Organization statistics, has hovered around 4 percent in the last three weeks, it has varied widely among the 26 countries, plus Hong Kong, with cases of the disease, known as SARS.

When W.H.O., which is the lead agency investigating SARS, first reported daily statistics, the death rate was about 2 percent. It was 2.4 percent on March 17 and 1.8 percent on March 18. The known number of cases then was fewer than 220.

But as the number of cases has increased — to 3,861 yesterday — the death rate has also steadily risen, leaving health officials worried. Lacking a precise explanation for the rise, health officials have generated a number of theories. In outbreaks of other new infections, the death rate has usually fallen with time.

”It’s worrying, and we hope it is not an indication of a continuing trend,” said Dr. Klaus Stöhr, scientific director of the W.H.O.’s SARS investigation.” The New York Times

Well, scientific director of the WHO was worrying in April 2003 because of CFR=5.6% instead of initial 1.8%. This is what happened by the middle of the summer. CFR raised up to almost 10%.

Does it mean virus mutated or something other changed in ‘real world’? It’s possible, but not necessary at all. Real fatality rate (among confirmed cases) is average (in reality it’s different for different groups of people depends on age, sex and other factors) probability to die for a ‘confirmed case’ person. The real fatality rate during the entire epidemic could be the same, but CFR calculated as deaths/cases will be changing (growing). Just because CFR is based on wrong math that doesn’t take into account the lag between time of case confirmation and death.

So, why journalist are telling us “Coronavirus CFR=2% is less than SARS 10%”? Why they are comparing final CFR for SARS epidemic with current CFR for Coronavirus? Why they forgot about CFR=1.8% for SARS on early stage of SARS 2003 epidemic? Current CFR for a growing epidemic is not a rough estimation, it’s just a value based on wrong math.


Methods for Estimating the Case Fatality Ratio for a Novel, Emerging Infectious Disease (The American Journal of Epidemiology, 2005).


Assessing the severity of the novel influenza A/H1N1 pandemic (BMJ, 2009)


Figure thumbnail gr1

Case fatality rate for Ebola virus disease in west Africa (The Lancet, 2014)

Ebola outbreak 1976. CFR (blue line on the graph) is growing from 20% to almost 100% while in reality almost all patients are dying (green line)…

I created a few models to show that CFR value is not correlated with real fatality rate:

Image: Andrzej Leszkiewicz

Image: Andrzej Leszkiewicz, page ‘Simulation’ of the report

In this mode real fatality rate is 99%! But CFR on early stage of the growing epidemic is slowly growing starting from almost 0%. By the end of epidemic CFR is correct and we see that 99% of ‘confirmed cases’ died. Like Ebola 1976 in the real case mentioned earlier.

So, CFR based on current total number of deaths and confirmed cases is biased and misleading and can’t be used to estimate number of deaths and to compare an epidemic with other epidemics. It doesn’t give us ‘an early estimation’. It gives us just some figure that is not correlated with real fatality rate.

The following graph shows us reported SARS 2003 number of deaths (blue line) and calculated number of deaths (purple line) based on formula: cases confirmed 12 days ago * fatality rate 9.5%:

Image: Andrzej Leszkiewicz, page ‘Simulation / SARS’ of the report

The above model shows how the lag between case confirmation and death works.

Some people suggest to use

Resolved case fatality rate (resolved CFR) = deaths / (deaths + recovered).

This formula won’t give us real fatality rate as well. It takes different time for people to die and to recover.

This is how CFR, resolved CFR and real fatality rate look for SARS 2003 epidemic:

Image: Andrzej Leszkiewicz, page ‘SARS 2003’ of the report.

Both CFR and resolved CFR are correct only for an ended epidemic. Otherwise it’s (significant) either underestimation or overestimation of real fatality rate.

Faster epidemic growth and longer lag between case confirmation and death mean CFR less and less reliable. We get more and more new cases just in a few days, while older cases are still being alive and probably not even developed severe condition yet.

And the COVID-19 epidemic is growing fast (by number of confirmed cases). Much faster than SARS epidemic in 2003:

Image: Andrzej Leszkiewicz, ‘Viruses Comparison’ page of the report

The above charts are screenshots from my Interactive analytical report with a lot of charts and information regarding Novel Coronavirus (not optimized for mobile devices). The report includes: dashboard, time lines (with linear and logarithmical scales), growth rate and forecast charts, daily reports (new cases), World and China maps, Hubei vs Other Provinces comparison, case fatality rate (CFR) calculations using differen methods, clinical data known from published studies (e.g. 99 and 1099 patients data), comparison with other epidemics (including SARS 2003 epidemic), simulations with CFR calculations to visualize that simple CFR=deaths/cases measure is biased and misleading for a fast growing epidemic.

You can see the report right here:

or you can use this link:

So, what we have seen? For a fast growing epidemic CFR is not just bad estimation of the real case fatality rate, but it can’t be used at all. If real ‘case fatality rate’ can be many times greater that CFR then it makes no sense to use such math. At least you should give this figure to the mass media without a proper explanation. It’s misleading.

So, don’t get fooled by current CFR=2% figure. It means fatality rate among confirmed by today cases already can’t be lower (2% already died). But it doesn’t mean that 98% of confirmed by today cases will survive.

And final real rate (when epidemic ended) can be 2% or even less. If there will be many more new cases, but no so many deaths. Because of better treatment or if there will be more mild cases among confirmed cases.

But we can’t use CFR of a growing epidemic to describe how dangerous the epidemic is and we can’t use CFR to compare this epidemic with past ended epidemics like SARS.

By the way, 2,788 people in severe and critical condition has been reported by today. And same issue as with CFR appears with

case severity rate =number of severe cases / number of all cases. Divide current number of severe/critical cases by number of confirmed cases and you’ll  get about 13.5%. But it doesn’t mean that 13.5% of ‘confirmed cases’ eventually require intensive care. Probably much more than 13.5%. Same issue – it’s take time for a virus to do severe/critical harm to an infected person. And real severity rate is very important. It determines how many hospital beds, doctors, medical personnel and equipment we will need to support lives. Lack of the resources will increase the real fatality rate.

2/7/2020 WHO did it again. They voiced that “of 17K patients (4 days ago) 15% – severe cases, 82% – mild cases, 3% – critical cases.” Same wrong math. Number of severe cases divided by total number of cases = 15%. But we had 17.3K cases on Feb 2 and only 4.4K cases 6 days before. So, 12.9K (75%) cases are less than a week old sice confirmation. Not enough time to develop severe condition. “…going from mild to severe symptoms takes about a week…
, “some patients who enter the 2nd week will suddenly get worse” The Straits Time

And, while the media will be spreading the misinformation again, I’m sure they will publish numbers, but they won’t show people the context. This is the context:
Journalist: “how critical are mechanical respirators and what data you have on organ failures?” WHO: “from 17K patients – 15% severe cases, 85% – mild cases”
Journalist: “this is not what I asked about”
WHO: “we don’t have any other details”

Make your own conclusions… The article is about math, not about politic.

2/17/2020 WHO did it once again. WHO press conference
The document China published and WHO mentioned (original source).

Same mistake. It’s not a scientific study. It’s the same data China reports daily, but detailed by age, sex an so on. There were about 45K cases confirmed by February 11. But 20K of them had less than a week since confirmation…

The best way to calculate real fatality rate among confirmed cases is to take into account only cases that already ended by either death or recovery.

This article claims that by Jan 22, 2020 13 (32%) patients were admitted to an ICU and 6 patients died and 7 (17%) were still being in hospital with unknown outcome (of first 41 cases)

This article claims that by Jan 25, 2020 23 (23%) patients have been admitted into intensive care unit and 11 (11%) patients of 99 died while 57 (58%) remained in hospital with unknown outcome (of 99 patients).

CDC of China, in the report mentioned by WHO (a piece of truth reported by China, but ignored by WHO):

14.4% of first 104 cases died.
15.6% of the following 653 cases died.
It means 15.5% of first 757 cases died.

Reporting date – Feb 11. So, for cases with date of onset > 1 month before the reporting date, most people, who had to die, already died – about 15%. And for cases with date of onset < 1 month before the reporting date, people are probably still dying after Feb 11.

5.7%, 1.9%, 0.8% – why CFR is decreasing? Because for each next cohort interval between date of onset and reporting date is shorter. So, less people died by the reporting date.

Does it mean 15.5% of 75K cases will die? No, probably real fatality rate is changing. I don’t want to claim that real fatality rate is 5%, 10%, or 15%, or 20%. I wish it be 0%, but it’s already impossible. But I claim that CFR value calculated as deaths/cases gives us totally useless and unreliable figure on early stage of fast growing epidemic. And we need to know real fatality rate. What WHO and media did by publishing 2% is probably good to delay panic for a bit. But if real fatality is much bigger and this epidemic will turn into a pandemic then this delay will be short and no one will ever believe in what WHO and media share with us. Lie is a wrong method to delay panic. It creates rumors. Rumors create panic. One more negative side of this misinformation is that people (including doctors and authorities) will not be ready to meet real threat. I already see that some epidemiologists believe in this biased figure shared by WHO and by media. And I’m afraid even members of some governments will believe in 2% figure, because WHO all media wouldn’t lie (?). It’s so easy to believe in authority. It’s a bit more complicated to do own math. It will lead to underestimation of the threat, insufficient plans will be written and insufficient measures will be taken while there is a real threat of a deadly pandemic.

Maybe there is a significant age difference between first 757 and the following cases, maybe they are treating new patients better (or worse, due to overwhelmed hospitals). But even if final international CFR will be 2% it won’t justify initial wrong math. If one guessed and won – it’s not a science.

It’s also a mistake to say “COVID-19 fatality rate will be lower than current estimation because of mild cases”. If you’re calculating CFR as deaths / confirmed cases you can’t say CFR is decreasing because of unconfirmed infections. There are no unconfirmed infections in the formula.  You can’t just change denominator without renaming the measure. You either use CFR or IFR. And even if we know number of infected people right now IFR will be as misleading as CFR is. Because number of infected people is also still growing. Same math. Delay between being infected and being dead, which is even bigger confirmation-death lag.

I have to notice that I’m talking only about mathematical point of view. For sure it’s possible that official statistic doesn’t show us real situation. The article is not about politics and it’s not about how many people in China or globally are gonna die. It’s about figures published by WHO and media (without a proper explanation). This article is about wrong math and mathematical fallacies that gives us wrong and misleading figures even when based on valid data.

I’m not an epidemiologist and not a scientist. I’m Excel VBA and Power BI  developer and consultant, data analyst. And this article is just my opinion (with a few links to more reliable sources). But when I see an interested for me subject I strat to study and I’m trying to understand (many journalist do not act like this). I’ve noticed the problem while I was making the report mentioned earlier in the article and I believe that I has to share this information with people. If you don’t agree with the article, then proof that I’m wrong using math and reliable scientific sources. As for me, WHO press conference and media like BBC and CNN are not reliable sources. The American Journal of Epidemiology or The Lancet is more reliable source, isn’t it?

I know, that the main argument against the above will be very simple – the appeal to authority. For one person WHO, BBC and CNN is the authority. No comments. For other person Johns Hopkins is the authority. Well, the appeal to authority is not the best argument if it’s not a reference to science based document published by ‘the authority’. Like this one, already mentioned in the article: Methods for Estimating the Case Fatality Ratio for a Novel, Emerging Infectious Disease (The American Journal of Epidemiology, 2005).

I feel a bit strange. I’m (almost) alone against ‘the authority’. Main subjects of one of the WHO press conferences was misinformation. And I believe that it’s WHO started a campaign of misinformation when they voiced this 2% figure without letting journalists know what it means and what doesn’t. Lately this figure has been shared by media corporations. And so many people believed in “it’s not really deadly! it’s juts 2%”.

I understand that most people don’t read scientific articles in The American Journal of Epidemiology, I understand that probably there are great epidemiologists and medical doctors who know how to save lives, but they probably don’t understand mathematics.

And I understand that many journalist just don’t care about the truth and the math. They are writing “fatality rate is low” now, tomorrow they will be writing “fatality rate is increasing! is virus mutating!”. And it will be a great click-bait to get more readers. But I hope there are journalists that are willing to share truth first of all. I want to see a piece of truth and science, questions and discussion in the media instead of the appeal to authority and parroting.

2/21/2020 Update:

Let’s talk again about a guy from Poland who is neither an expert in epidemiologi nor in mathematical statistics. I have written this article about almost 3 weeks ago, but some experts including epidemiologists are still believe in 2% figure (and often they are mixing up CFR and IFR). And I have to say: It’s not about being right for me. It’s about being ready for the human civilization. Being ready to meet the reality and to fight for every life on the planet.


3/5/2020 Update:

I need to add this.

“Globally, about 3.4% of reported COVID-19 cases have died.” WHO

“Early in the outbreak, scientists had concluded the death rate was around 2.3%.” CNBC

“As COVID-19 spreads scientists are learning more about the disease’s fatality rate. “Globally, about 3.4% of reported COVID-19 cases have died,” Tedros Adhanom Ghebreyesus, the WHO’s director-general, said at a press briefing in Geneva this week. That’s higher than previous estimates of around 2%…” Market Watch

Scientists had concluded? Previous estimates? Does one have to be a scientist to divide number of deaths by number of cases? As for me ‘estimates’ and ‘scientists had concluded’ means there was a scientific study. CFR calculation by dividing one numer by another number is not a study and the result is not an estimated real fatality rate. It’s just senseless misleading figure.

But the media wnet further. Now they are misusing this:

covid 19 mortality rate by age chart

Image: The Business Insider

The graph is based on China CDC February 11 report mentioned earlier in this article.
On Feb 11 there were about 44672 cases cases and 1023 deaths. CFR was 2.3%. Now the media are telling us that ‘death rate’ increased from 2.3% to 3.4%, but no one is telling the truth.

1) the above age distribution is for the same 1023 deaths of 44672 cases. Which means total CFR for all age groups was 2.3%. So, if you’re telling us that ‘death rate’ is greater now (WHO voiced “3.4% globally”, but I have to say that actual CFR for China is 3.7%), then (if we assume that age distribution didn’t change) you already has to multiply each column on the graph by 1.61 to make sure that the graph represents your actual CFR.


Image: Andrzej Leszkiewicz

2) CFR is not real fatality rate. See the above article.

3) If we assume that it takes more time to die for a younger person than same graph for real fatality rate by age groups will be shifted to the left (greater fatality for younger persons).

So, do not misuse total CFR and do not misuse CFR distribution by age.

We know from China CDC Feb 11 report that among first 757 cases fatality rate was at least 15.5%. It looks like it decreased later, not increased later (probably just because later they start testing more people with mild symptoms). But everyone is talking about ‘increasing death rate’ now. How it’s possible? How this stupid world still exists? Are there any scientists and journalists who can meet together and finally make it clear for everyone that CFR is not fatality rate and CFR can’t be used to compare past data with the most recent data,and can’t be used to compare one country with another country, as age distribution of CFR is age distribution of CFR (and make no more sense than total CFR).


By the way: A great sample of information manipulation! Write down that “only about 5% of patients in that study reported sore throat and runny nose” and forget that 11% of those 100 patients died and 58% remained in hospital by Jan 25 (and probably more died later).

The author accepts no responsibility or liability for any losses incurred in connection with any decision made or action or inaction in reliance upon this the article.

Andrzej Leszkiewicz,
Krakow, Poland

P.S. My web site is almost empty. I write my thoughts in social media, not here. The web site is only for big articles on important subjects. So far I have written here only about child militarization in Russia and later the article has been published by InformNapalm.

Take a few minutes and read. The latest update, not included into the article – they already had (by the end of 2019) more than one million of children wearing military uniform and taking military training in schools on daily basis.

Copyright: Andrzej Leszkiewicz.

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