COVID-19 Crude Fatality Rates, Media Freakouts, and Capacity Analyses
The best way to understand this is to look at the rain.
The crude fatality rate for COVID-19 is almost assuredly being overstated by the media, but the mathematics for it go deeper than that, and a failure by our media to either understand or convey this properly is hindering the overall dialogue. The fact that the media’s business model in 2020 is to peddle anxiety for clicks, and that the general population has awoken to that fact, has made every article or media piece about basically everything into one great “crying wolf” exercise. But this COVID-19 outbreak may in fact be the wolf, and the best way to explain why, I think, is by looking at similar other processes in nature with which we’re more familiar. Like rain.
Stormwater Hydrology of Thneed Factories
Rain falls on your twenty-acre piece of forestland. Some of the raindrops hit the trees, some hit the ground. Some of the ones that hit the ground leak into the ground. The ones that don’t leak into the ground run off along it, into tiny creeks, which slowly join, and flow off of your twenty acres past your neighbor Big Joe, who has a little shack down by the creek. This is a routine event. You see it happen, you know what it looks like, and you have an intuition about it because this is something you experience your entire life. If you were to stand, boots on, heels planted in the creek at your property line in a storm, you know what would happen around you. The flow rate in the creek would increase, the water level would rise to fill the banks, and then it would subside. You made a graph of this, showing the flow rate in the creek over time, and your graph looks like this:
This is called a “hydrograph” by hydrologists. It shows the rate of raindrops conveyed downstream by the creek, past Big Joe’s shack. The units on this graph are (cubic feet per second) of water, a volumetric flow rate, on the Y axis, and (seconds) of time on the X axis. Which lends us an interesting mathematical trick you learn in early calculus. You can tally up the area under that curve, and multiply cubic feet per second by seconds and get cubic feet. The total volume of water that travels past Joe during the storm is represented by the area under that curve. Fear not, oh Muggle of Math, this is as complicated as we’re going to get in this article.
Now you decide to build a Thneed Factory on your land, because Thneeds are a fine something that all people need. You cut down the trees, flatten the land, build a building with a roof, and pave the parking lot. The rain now behaves very differently. None of it drops on the leaves of the trees, nor leaks into the ground. It all runs off, through inlets, into pipes which flow faster than the old creeks did, and it flows right past Big Joe’s shack. The total volume of runoff goes up, because less leaks into the ground, and the rate it leaves your twenty acres goes up as well, because it’s running off faster. You stand in the creek at the property line, boots in the mud, watch, and make your graph. Now the hydrograph looks like this:
The area under the curve, which is the volume of raindrops which make it downstream, is larger. The peak rate of runoff is larger too. And Big Joe’s shack floods, so he sues you, and you discover in court that you should have built a “detention pond” for your Thneed factory.
Detention ponds are simple things conceptually. You dig a big hole at the low end of your Thneed factory, route all your runoff into it, and only let it out through a few carefully designed holes or slots in a big concrete riser. The flow out of the detention pond never exceeds a limit, ideally set by how much water the creek can convey without flooding out Big Joe. The results look like this:
The purple hydrograph leaving the detention pond still has the same higher volume as the red hydrograph did, but it never exceeds the capacity of the creek. It takes longer to drain out, so the creek is flowing longer than before, but Big Joe never gets flooded. There’s a very interesting version of this floating around in certain media spaces right now that doesn’t measure raindrops, it measures people infected with COVID-19. Let’s talk about that.
But first let’s talk about dead people.
Crude Fatality Rate
The World Health Organization’s final report on their joint mission to China had some interesting things to say about the crude fatality rate of COVID-19.
As of 20 February, 2114 of the 55,924 laboratory confirmed cases have died (crude fatality ratio [CFR2] 3.8%) (note: at least some of whom were identified using a case definition that included pulmonary disease). The overall CFR varies by location and intensity of transmission (i.e. 5.8% in Wuhan vs. 0.7% in other areas in China). In China, the overall CFR was higher in the early stages of the outbreak (17.3% for cases with symptom onset from 1- 10 January) and has reduced over time to 0.7% for patients with symptom onset after 1 February (Figure 4). The Joint Mission noted that the standard of care has evolved over the course of the outbreak.
To understand what’s going on here, we need to understand Crude Fatality Rate.
This is a fraction. If more people die, the fraction goes up. If more people are confirmed to have it, the fraction goes down. This means that sampling bias can tremendously affect your results. In the early days of the outbreak in Wuhan, there may have been a great many people who had it and got better, and did not get tested, and therefore didn’t find themselves in the denominator of that fraction. As testing became more prevalent, the denominator goes up, and the CFR goes down.
Put simply, aggressively testing for the disease makes it look like more people have it, but also makes it look like it’s less deadly. Less testing makes it look like less people have it, but makes it look more deadly. But that’s only part of what’s going on.
Part of the high early fatality rate in Wuhan probably has to do with lack of preparedness, and lack of understanding what needed to be done to treat this disease. Treatment, for what it’s worth, isn’t much. Basically you just help people breathe while they’re infected, and wait for their bodies to fight it off, and treat other symptoms as best as you can. Like influenza, it mostly kills the old, the sick, and the infirm.
Part of the high Wuhan fatality rate probably has to do with poor initial testing — that denominator thing I mentioned above. But part if it may be that the hospitals didn’t have the room to treat the old and infirm that needed treatment, because they were beyond capacity. This is where our stormwater hydrology graphs start to reappear, with each raindrop being a virus infected old person.
Epidemic Policy Calculus
Much of the national media and social media banter I see today, on March 10th 2020 as the virus takes hold in the United States, has to do with what measures should be done to control it. Japan closed public schools, do we? China quarantined whole regions of their country, throwing a monkey wrench into the world economy. Should we? The answers all go back to that graph. Let’s look at it again with different labels.
People are going to get sick from this thing. It seems inevitable. It cannot be contained. This correlates to the “more rain turns into runoff” scenario in our hydrology example, where the area under these curves is “sick people.” The short-term policy question is what to do about that. Diseases travel by “vectors,” basically human to human contact. If you reduce human to human contact then the rate of spread will be flatter. Even though all the same people will probably be infected at some point, they won’t be infected all at the same time, which means hospitals won’t be over their treatment capacity. That’s the theory, just like stormwater detention to abate flooding, to make sure a stream doesn’t exceed its capacity.
Alternately, we could raise the dashed line (hospital capacity) somehow. Convert every medical office in the country from their weird specialty into temporary ICU wards. Train the orthopedic surgeons to be temporary flu nurses. Widen the stream to carry the flow.
Or we could let it ride, on the presumption that our dashed line is already high enough, or on the presumption that hospitalizing most people doesn’t actually help that much anyway, or on the presumption that the very old and infirm were likely to die in a few years from something else regardless. That’s a horrible thing to say, that nobody’s saying out loud, but has some basis in mathematical truth.
It’s hard to say. The problem is we need numbers to fit on this graph. How big is the red curve going to get? Where is the dashed line actually? Are we sure that closing grade school will get us from the red curve to the purple curve? What is the opportunity cost of forcing every single parent in the United States to quit their job, or to put their kids in daycare where they’re just as likely to transmit the disease? Could we even do something as rash as closing public schools, when our country is a world leader in single parents and dual income households?
If we were to institute mass quarantine measures, including the closing of public schools, would that also reduce transmission of the “normal flu?” By how much? Around 60,000 people a year die from influenza, generally in the same overall age group as are dying from COVID-19. If cancelling public schools were to save 6,000 lives from the normal flu, does this mean that we as a country have chosen, in an ordinary year, to sacrifice 6,000 lives per year on the altar of institutionalized education?
Do our very institutions themselves need to change to adapt to a globalized world with increases in disease vectors? Is school worth it, or can we get most of that with iPads in smaller, less crowded environments? Maybe living in rural areas isn’t so bad after all? Maybe the homeschool folks aren’t crazy?
These are all the hard questions, and to answer the hard questions we need someone to put numbers on that graph.
But then how many people get infected while we try to generate those numbers?
post publication edit — one stab at those exact numbers can be found here:
