The media has reported that the director of the World Health Organization estimated the mortality rate of the novel coronavirus (Covid-19) to be approximately 3.4% [1]. But let’s take a look at what he actually said. On March 3, 2020, Director-General Tedros Adhanom Ghebreyesus stated that “Globally, about 3.4% of reported COVID-19 cases have died.”

Note that he did not say that he was reporting a mortality rate of the virus; he was reporting a statistic of how many patients had died. What the media reported and what people heard was that the probability of death given you contracted the disease was 3.4%. That is, they heard . However, this is incorrect.

What we actually have is a probability chain: . The quantity that director Ghebreyesus reported was .

We don’t know , but we have a high estimate. A recent study from China analyzing approximately 72,000 hospital patients found that approximately of hospital records were for confirmed Covid-19 cases and approximately of confirmed cases experienced mild symptoms [3]. Assuming independence, and since we would not expect people with mild symptoms to be tested, a high estimate of . However, this is an extremely biased sample: hospital patients. Therefore, as long as everyone who requires it receives proper medical care, I expect this to be an extreme upper bound.

Assuming a perfect test with , an upper bound on the estimate of is . Note that this is close to the lower range of the WHO’s estimate: 0.7% – 4%. Note, also, that is is very similar to the mortality rate of the flu [3.1].

It is difficult to know how extreme this upper bound is, but we have a hint. On 2/28/2020, a man went to a rock concert with a packed audience in New Zealand (an island country) and was later diagnosed with Covid-19 [4]. “He was in the general admission standing area in the front left-hand quadrant.” states Ministry of Health director-general of health Dr. Ashley Bloomfield. This is almost as infectious a situation as possible. And yet, New Zealand currently has 5 confirmed cases of the virus, one of them being a woman who got the disease on a cruise ship [5]. There have been 0 deaths due to the virus in New Zealand.

Summary: My estimate of the mortality rate of the Coronavirus: less than .

Note that I have not considered the effectiveness of healthcare in this analysis. Additionally, note that if one conditions on previous patient susceptibility, then the probability of death differs dramatically. In the study of [2], there were no children killed by the virus (this includes two infants who contracted the virus from their mothers). The elderly and those who are immunocompromised have a much higher probability of dying, while the young and healthy have a much lower probability.

In conclusion, wash your hands.

[1] https://www.cnbc.com/2020/03/03/who-says-coronavirus-death-rate-is-3point4percent-globally-higher-than-previously-thought.html

[2] http://weekly.chinacdc.cn/en/article/id/e53946e2-c6c4-41e9-9a9b-fea8db1a8f51

[3] https://www.sciencealert.com/large-chinese-study-finds-most-coronavirus-infections-are-mild

[3.1] https://www.sciencealert.com/covid-19-s-death-rate-is-higher-than-thought-but-it-should-drop

[4] https://www.theguardian.com/world/2020/mar/06/man-with-coronavirus-went-to-packed-rock-concert-at-new-zealand-arena

[5] https://www.nzherald.co.nz/nz/news/article.cfm?c_id=1&objectid=12314739