Flattening the curve, (which at this point should be referred to as “curve flatulence”) is one of those phrases which has entered the common lexicon due to the coronavirus epidemic. I am not sure most people understand what it means and as far as I can tell, a lot of people drawing these curves don’t understand them either. One example of such a curve flattening demonstration is below. Now this particular diagram came from that impeccable source the NY Times, but also looks very similar to one from the Mayo Clinic. The important information to be imparted by a typical diagram like this is the area under the curve, which represents some quantity. A lot of these curve drawers aren’t very specific about this. In any event, as we are constantly hectored, we just have to flatten the curve. The reason is to protect health resources from being overtaxed. Now the reason to do that is supposedly to prevent excess deaths from lack of medical attention.

While I don’t have the mathematical formula behind these particular curves, I would point out that the area under the two curves appears relatively equal and maybe we actually have a few more cases in the “with protective measures” curve. Cases is the quantity depicted here. So either way we are going to have the same number of cases, they are just spread out. If you read all the posts, you see me make this point repeatedly. I actually think it would be correct to show more cases in the protective measures case, for the simple reason that you delaying the buildup of the percent of the population with antibodies (“herd immunity”), which ultimately hinders the transmission chain. The reason the “without protective measures” curve ends so abruptly is that herd immunity is developed quickly.

Now, again, what people are really concerned about is deaths. We need another set of curves for that. If you assumed deaths per number of cases remained equal, you would have the same number of deaths under each curve, actually probably a few more under the with protective measures case, because you have more total cases. I don’t think that is what these curve drawers mean to imply. If there is a likelihood of overwhelming health resources, then you could have excess deaths, so that area under the “without protective measures curve” should be larger. Of course, it is very hard to get anyone to actually tell us how many more deaths would occur, and how a reduction in those excess deaths are tied to each mitigation tactic. That is extremely relevant, because I also keep saying that we need to do a benefit/harm analysis for each mitigation measure. If we don’t know how many, if any, excess deaths are being prevented, how can we do that analysis.

One more point, the length of time followed on the x or horizontal axis is important. These curves don’t reflect the reality of coronavirus infection. You are going to see something that looks like a roller coaster–you will have a big bump up in the first year, which then falls at least in part purely because of the seasonality of the virus. But then you will have a series of smaller bumps every year as it re-emerges. The size of those bumps will depend in large part on the percent of the population with antibodies, either obtained through infection or by vaccination. But unless this is a wildly different virus, it will be here and will be back. So extreme mitigation measures on the front end likely make the succeeding bumps higher–meaning more cases and more deaths later.

Flattening the curve also reduces the area under the curve according to most SIR models in epidemiology.

Some references on the subject:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7196894/

https://ms.mcmaster.ca/~bolker/misc/peak_I_simple.html

Interesting blog btw 🙂

Philip