Corona confession: Why aren't I worried? (I should be).
Quantifying coronavirus uncertainty and how we feel about it
In recent conversations about COVID-19, the coronavirus originating in Wuhan, I wonder if my friends seem to lack an appropriate level of concern.
If I am honest, I wonder if I lack an appropriate level of concern.
The issue is, my friends and I are all good at math. Here are some points that a mathematically literate person has no trouble grasping.
Overdispersion of R0
The basic reproduction number (R0) is the expected number of people that an infected individual infects. The reported number for COVID-19 is 1.4–6.6. But that number is a distribution, as pictured in the following figure.
Moreover, R0 itself is a mean of a much broader distribution with a particular long right tail. In a public letter, University of Toronto epidemiologist David Fisman writes
While average estimates of R0 are helpful, it is also important to note that other betacoronaviruses of public health importance (SARS, MERS) have been notable for the "overdispersion" of their reproductive numbers. Without getting too technical, this means that the average R0 is quite different from the variability in the R0. We actually have a distribution of R0 with a long "tail", which is a mathematical shorthand for superspreader events, where a case infects a large number of individuals. For example, there was at least one SARS superspreader who generated 76 downstream cases.
Chinese numbers are junk
In practical terms, Chinese hospitals have lacked sufficient supplies even to diagnose all their new potential cases, much less care for their diagnosed sick.
Some are suggesting the growth numbers are being doctored. A user on Reddit published this graphic made the rounds on Reddit a few weeks back, leading to speculation that the numbers China is reporting are fake numbers simulated from a mathematical model.
I agree that there is way too little variance and that R2 statistic is laughably high (though it seems like an odd choice of parameters for a quadratic model, perhaps they used some sigmoidal model so they can eventually claim the virus is leveling off).
Further, there is certainly some selection bias at play. Many people in China may be suffering from the virus and avoid the hospital. There’s no cure, and China’s containment measures are frighteningly draconian. Having your whole family quarantined just to have your sick uncle receive inadequate treatment at an overburdened hospital might seem like a bad trade. Why not just keep your sick family member’s illness a secret and hope for the best? WSJ reporting suggests even deaths are underreported.
But beyond this, the political system in China is such that the provincial governments have a long history of misreporting statistics to Beijing, and Beijing is known for fudging its domestic numbers to the rest of the world. There is no reason to believe the situation with COVID-19 is any different.
This is to say that the numbers to watch are the numbers from outside China. But these numbers are still too low to get a clear picture.
Thinking of someone who might have some insight into COVID-19 or how we react (or ought to react) to related news? Share this post.
“But more people have been killed by the flu…”
The retort to this sentiment is that there is more uncertainty around COVID-19. An financial quant might characterize much of that uncertainty as Knightian uncertainty. Knightian uncertainty is a lack of any quantifiable knowledge about some possible occurrence, such as a global pandemic. This type of uncertainty can’t be quantified and properly insured against. Put simply, COVID-19 is still an unknown unknown while the flu is not.
Numbers will never be enough
These issues are pretty concerning. So why aren’t we more freaked out?
I have ideas, but if I had to give it a single reason, I’d say its because it’s unclear what to do. Worry is useful emotion only if it motivates action. But what is actionable about a maybe-pandemic, aside from maybe adjusting your investment portfolio and stocking up on medical face masks?
I got started on a post about decision theory for pandemics and other black swan catastrophes but got stuck on this point. It is tough to define an action set that’s more nuanced than cultish survivalism.
I welcome your thoughts. @osazuwa.