Why COVID is Freaking Out Epidemiologists
Mar. 23rd, 2020 06:21 pmLook, I get it. Exponential math isn’t easy for most people. Most people barely remember what the “2” in x2 means. So let me do my best to remind you.
Instead of x2, where the “2” means “multiply x * x,” and a “3” would mean “multiply x * x * x” and so on, the math of an epidemic is about 10x, where “x” is some number times the number of days that have gone by.
How do we calculate that number? Well, we count the dead by days. We make a series: from the first death, on March 1st, through March 22nd, that series reads: 1, 6, 9, 11, 12, 15, 19, 22, 26, 30, 38, 41, 49, 57, 68, 86, 109, 150, 207, 256, 302, 419. That’s total, by the way, not “per day.”
That… doesn’t look so bad. Until you plot it on a graph.
That’s kinda scary. But it doesn’t scare epidemiologists nearly as much as this graph:
This graph takes those numbers above and shows what it would take, what the ‘x’ would be, to make 10x equal that number. That’s called the logarithm-base-10 of the death numbers. Oddly enough, it’s possible to do exponents with fractions. Everyone who made it through middle school math knows 22 is 4, but 22.5 is 5.65… something. It goes on for a while.
So on March 1st, we hit 100, that is, 1 death. (If you recall your exponents, anything to the zero is 1, except zero.)
On March 5th or thereabouts, we hit 101, that is, a total of 10 dead.
On March 17th, we hit 102, that is, a total of 100 dead.
See that second graph, and the line through it? That’s called the trend, and right now, the trend is going up. Without comprehensive testing and the isolation of infected people, that number will go up as the virus seeks out new people to infect. This is the relentless logic of epidemiology.
Eventually, the infection burns itself out. A lot of people will manage to shrug off the infection. A lot more will get sick but not require hospitalization. And many who get hospitalized, provided there are resources, will survive. But not everyone– right now it looks like somewhere between 1% and 3% of those who catch it die, mostly the elderly and those with underlying conditions which weaken their ability to respond to the infection. Eventually, we’ll develop a species-wide immunity.
But before that happens, the virus has to roar through the system. That will either happen quickly, or slowly. If it’s slow enough, there’ll be enough doctors and ventilators to keep those who need them alive. The elderly and immunocompromised still die.
The math as of today is this: if ‘x’ is the number of days since March 1st, when we had our 1st recorded death on US soil, then the estimated number of dead, given 21 days of data, is currently
So what does that math show? That math shows that on March 26th, we’ll have a thousand people dead. Still not bad; 38,000 people die of automobile crashes every year, and last year’s influenza ended 78,000 lives that didn’t have to end quite so soon.
But then April 6th rolls around and 10,000 people will have died.
Somewhere between April 15th and April 17th, 100,000 people will have died. Now things are getting scary. It's worse than the flu.
And then, somewhere between April 26th and April 28th, a million people will have died of COVID-19. If we’re very lucky, this number will come later, after mid-May; if that happens, we’ll have engaged in social distancing enough as a country, not just one city here or there, to keep everyone who could survive with medical attention alive.
This is the relentless mathematics of epidemiology.
As I said, eventually every pandemic burns itself out. There 327 million people in the United States, the disease appears to be more infectious than influenza and is asymptomatic for much longer, so reservoirs of it could persist for many months. The kids on Spring Break who are now going home and hugging their parents and grandparents could be harbingers of a massive wave two weeks from now. The CDC believes eventually everyone in the United States will have come into contact with it.
Which, look, you can’t sugar-coat this at all. All the best models are telling us that if the United States continues without a lockdown, 2.2 million people will die.. (Reuters link, if you don’t want to deal with the NYT paywall.) Right now, the US is on track for 1.6 million, and even if we implemented everything that wasn’t a full-on Chinese police-based lockdown, we’re still looking at over a million. The full report is available, and it makes for some sobering reading about the availability of critical care facilities.
I dunno. I hope I’m wrong. But Iran and Italy are early signs that this disease can get very, very bad very, very quickly. And so far, there have been exactly zero indicators that we’re on the downward slope.
Instead of x2, where the “2” means “multiply x * x,” and a “3” would mean “multiply x * x * x” and so on, the math of an epidemic is about 10x, where “x” is some number times the number of days that have gone by.
How do we calculate that number? Well, we count the dead by days. We make a series: from the first death, on March 1st, through March 22nd, that series reads: 1, 6, 9, 11, 12, 15, 19, 22, 26, 30, 38, 41, 49, 57, 68, 86, 109, 150, 207, 256, 302, 419. That’s total, by the way, not “per day.”
That… doesn’t look so bad. Until you plot it on a graph.
That’s kinda scary. But it doesn’t scare epidemiologists nearly as much as this graph:
This graph takes those numbers above and shows what it would take, what the ‘x’ would be, to make 10x equal that number. That’s called the logarithm-base-10 of the death numbers. Oddly enough, it’s possible to do exponents with fractions. Everyone who made it through middle school math knows 22 is 4, but 22.5 is 5.65… something. It goes on for a while.
So on March 1st, we hit 100, that is, 1 death. (If you recall your exponents, anything to the zero is 1, except zero.)
On March 5th or thereabouts, we hit 101, that is, a total of 10 dead.
On March 17th, we hit 102, that is, a total of 100 dead.
See that second graph, and the line through it? That’s called the trend, and right now, the trend is going up. Without comprehensive testing and the isolation of infected people, that number will go up as the virus seeks out new people to infect. This is the relentless logic of epidemiology.
Eventually, the infection burns itself out. A lot of people will manage to shrug off the infection. A lot more will get sick but not require hospitalization. And many who get hospitalized, provided there are resources, will survive. But not everyone– right now it looks like somewhere between 1% and 3% of those who catch it die, mostly the elderly and those with underlying conditions which weaken their ability to respond to the infection. Eventually, we’ll develop a species-wide immunity.
But before that happens, the virus has to roar through the system. That will either happen quickly, or slowly. If it’s slow enough, there’ll be enough doctors and ventilators to keep those who need them alive. The elderly and immunocompromised still die.
The math as of today is this: if ‘x’ is the number of days since March 1st, when we had our 1st recorded death on US soil, then the estimated number of dead, given 21 days of data, is currently
10(x * 0.0943) + 0.5031.So what does that math show? That math shows that on March 26th, we’ll have a thousand people dead. Still not bad; 38,000 people die of automobile crashes every year, and last year’s influenza ended 78,000 lives that didn’t have to end quite so soon.
But then April 6th rolls around and 10,000 people will have died.
Somewhere between April 15th and April 17th, 100,000 people will have died. Now things are getting scary. It's worse than the flu.
And then, somewhere between April 26th and April 28th, a million people will have died of COVID-19. If we’re very lucky, this number will come later, after mid-May; if that happens, we’ll have engaged in social distancing enough as a country, not just one city here or there, to keep everyone who could survive with medical attention alive.
This is the relentless mathematics of epidemiology.
As I said, eventually every pandemic burns itself out. There 327 million people in the United States, the disease appears to be more infectious than influenza and is asymptomatic for much longer, so reservoirs of it could persist for many months. The kids on Spring Break who are now going home and hugging their parents and grandparents could be harbingers of a massive wave two weeks from now. The CDC believes eventually everyone in the United States will have come into contact with it.
Which, look, you can’t sugar-coat this at all. All the best models are telling us that if the United States continues without a lockdown, 2.2 million people will die.. (Reuters link, if you don’t want to deal with the NYT paywall.) Right now, the US is on track for 1.6 million, and even if we implemented everything that wasn’t a full-on Chinese police-based lockdown, we’re still looking at over a million. The full report is available, and it makes for some sobering reading about the availability of critical care facilities.
I dunno. I hope I’m wrong. But Iran and Italy are early signs that this disease can get very, very bad very, very quickly. And so far, there have been exactly zero indicators that we’re on the downward slope.
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