A Few Logical Thoughts About the COVID-19 Coronavirus

February 26th, 2020

(summary at the bottom)

There are lots of takes COVID-19 coronavirus on the news, and they're ripe with misinformation. In a very non-prosaic way, I want to offer a few rational thoughts on the issue.

I want to discuss 3 things:

  1. The "carpenter fallacy", or why you shouldn't listen to medical experts about the epidemic
  2. Why the mortality rate is higher than you think
  3. What if epidemiologists are wrong?

The Carpenter Fallacy

If you want to decide whether you want to gamble on a roulette wheel, who would you rather consult: a statistician/mathematician, or a carpenter who makes roulette wheels?

You would obviously want to consult someone who deals with math and probability. Sure, the carpenter might have some insight into how, for example, the red paint on the wheel has more friction with the ball, so the chance of the ball landing on red is infinitesimally higher than of it landing on black, but the person dealing with probabilities is the person who would help you make a logical decision based on your expected outcome.

Medical staff like doctors and nurses are like the carpenter, and virologists and epidemiologists are like the mathematicians in our story. Medical staff are trained in how to deal with individual cases of illnesses -- they have no expertise on a virus's R-nought (a measure of contagion) or its distribution potential. Thus, any time you read the headline "A doctor says so and so about how scared you should be about the coronavirus", you can safely label it a dangerous and uninformed opinion and discard it.

In the same vein, you shouldn't listen to me too seriously if I say something about the issue's epidemiology -- but I'm not doing that in this essay. I'm just stating some commonsensical facts that are often underreported.

The mortality rate is higher than you think

Say I have AIDS and proceed to have unprotected sex with 1000 people today -- all of whom then catch HIV. If you check in on their mortality status tomorrow, you'll probably see that none of them have died from AIDS in that 1 day. Does that imply that the mortality rate of AIDS is 0% (0 out of a thousand)? No, of course not.

If you check in in a year, N of them will have died from AIDS. Again, N/1000 would not be the mortality rate for AIDS, but it would be closer. Check in in a decade, and M of them have died from the virus -- once again, M/1000 is not the mortality rate, but it's closer to it.

The point is, you can't judge a disease's mortality rate in such a short time after it's started spreading, and you can't judge it by dividing the number of deaths by the number of infections. You have to divide the number of deaths by the sum of the number of deaths and recoveries, and that would still not be completely accurate because you would still not know how the people with the virus who have neither recovered nor died from it will fare.

The oft-repeated 2-4% mortality rate for COVID-19 comes from dividing the reported number of people who have died from the virus (2,771 as of this writing) by its number of reported cases (81,406), which yields a value of 3.4%.

However, if you divide the number of deaths by COVID-19 (2,771) by the sum of the number of recoveries and deaths (2,771 + 30,370 = 33,141), you get a figure of 8.4% -- significantly higher than the oft-repeated 3.4% mortality rate.

The real number, however, is neither 3.4% nor 8.4% -- the only thing we can be sure about is that it's equal to or higher than 3.4%.

Assume the virus stops spreading right now, and after 10 years every person infected has either recovered or is dead. Then, we could divide the number of deaths (which can't logically be fewer than the current 2,771) by the total number of cases (81,406 -- which is equal to the deaths + the recoveries) and we'd have the true mortality rate for the disease. So the mortality is certainly more than or equal to 3.4%.

What if epidemiologists are wrong?

Here are the 4 possible outcomes:

If you were of the school of thought that saving the lives of millions of people is not worth restricting civil liberties, then your desired course of action would be to not do anything. But if you're anything like me and believe that the lives of millions of people are much more important than discomfort for a few months, it would seem obvious to you that heavy action is needed.

Summary

  1. Listen to epidemiologists, not doctors and nurses.
  2. Mortality rate is higher than what is reported, because it should be calculated using (deaths)/(deaths + recoveries), not by (deaths)/(infections). So it's higher than the reported 3.4%.
  3. The consequences of heavy action are minuscule compared to the risks of not taking heavy action.