The Problem with “Flattening the Curve”
There are several reasons I hate the term “flattening the curve”. Firstly, it is not an expression that makes sense to mathematicians. You could say, “but it’s a term from epidemiology”, but epidemiologists are trained in biostatistics, so they should know better. In mathematics, when a curve is getting flatter, it means the slope is reducing and tending towards zero. If you want to study exponential growth in an epidemic, the standard (and reliable) plot is total number of deaths as a function of time on a semi-log plot (y axis on log scale). The slope tells you the growth rate. Flat for that plot would mean zero new deaths per day, and so flattening the curve would mean the number of new deaths per day tending towards zero.
Instead, what epidemiologists call “flattening the curve” is really “stretching out the distribution”. What’s worse, instead of that plot showing new deaths per day, it is actually about new infections per day, a concept that is impossible to measure in practice, regardless of how widespread testing gets (and certainly not useful when testing continues to be limited).
Secondly, the meaning of flattening the curve (or “stretching out the distribution”, which is not catchy but accurate) is that in the original curve and the stretched out curve, the total number of infections is the same. This is a setting up a ridiculously low goal for the government to achieve, because the underlying assumption is that the total number of infections is some conserved quantity, which it absolutely is not. Spain and South Korea have roughly equal populations (≈50 million). Yet the number of confirmed cases in Spain is about 150,000 and in South Korea, it is 10,000. This is despite South Korea having five times more dense population and more widespread testing.
Here’s where it gets worse: the so-called “flattening the curve” idea is now being applied to new deaths per day by many countries, and the claim is that if this number plateaus or goes down slightly, “flattening the curve” has been successful. But there is no acknowledgement of what the level of that plateau is (a plateau of 10 deaths a day is obviously not the same as a plateau of 1000 deaths a day). If a government wants to appear effective, all it has to do under the current expectations is to let the number of deaths per day get high enough that maintaining it at that level or slowly bringing it down becomes quite easy. Most will say that Italy and Spain have “flattened the curve”, but they had about 600 and 700 new deaths yesterday, respectively. This is supposed to be considered a success? It’s like someone weighing 500 pounds saying they are maintaining or losing weight… color me unimpressed.
Normally, for any social policy, there is a cost-benefit analysis. This pandemic is the first time I have seen this idea basically ignored. I see many governments saying “social distancing is working because the curve is being flattened”. But we need to acknowledge the cost of the social distancing. For such a large cost, I would have expected better benefits. There is zero doubt that South Korea and Taiwan have had much better outcome than major Western nations, and have paid a much lower cost. But governments of Italy, Spain, UK, France, US and many others are tricking us that they are “winning the war” and the cost is acceptable, because of the low standard set by the monstrous concept that is “flattening the curve”.
Note: Infection and death number are taken from https://ourworldindata.org/coronavirus on April 11.
