First, the bad news.
The death toll from Coronavirus in the U.S.A. stands at 4,059, and more alarming is the fact that yesterday brought nearly a thousand deaths in a single day. The numbers keep rising.
America has confirmed 188,639 cases (many more unconfirmed), more than any other country in the world (although Italy leads in fatalities with 12,428). The total number of cases in the U.S. shows a very unfortunate and frankly, scary trend: exponential growth.
Exponential growth definitely does not follow a straight line — not even close. But if we plot it on a logarithmic scale, it does — at least approximately. That is the nature of exponential growth.
Now some good news.
The earlier numbers are quite small, which makes their random fluctuations relatively large, and they are plagued by uncertainty of detection and reporting, even more so than recent data are. So, I’m going to focus at what has happened since March 5th, 2020. I’m also going to look at the number of new cases each day, rather than the total number of cases. If I graph that data, I get this:
If I graph it on a logarithmic scale, it looks like this:
The good news is that the number of coronavirus cases doesn’t follow a straight line exactly, not even on a logarithmic plot. What that means is, that it’s not showing “exponential growth” exactly — at least, not at a constant growth rate.
That departure from straight-line behavior isn’t just random fluctuation. It can be statistically verified, and even quantified. Here is one good statistical model, consisting of two straight-line segments representing two different growth rates:
The growth rate of new cases seems to have slowed around Mar. 23rd (give or take a day or two), with the result that it has reduced the number of cases we would have had lately. By a lot. The red arrow above shows where we would have been yesterday if growth had continued at the same rate; clearly there are fewer cases with the newer, slower growth rate.
The difference may not seem so impressive on the above plot, because it’s on a logarithmic scale. Let me show you what it looks like on the usual kind of plot (just the numbers, please)
At the previous rate of increase, we were on track to have more than 100,000 new confirmed cases yesterday. Thanks to the reduced growth rate, we only confirmed 24,742. Our health care system is already burdened by the cases we have now. Imagine how bad it would have been if, insteading of dealing with 24,742 cases, we had to handle over 100,000.
Why did the growth rate decrease? There are many possible reasons, and many factors, but my hypothesis is that the primary driver has bee social distancing and protective measures (handwashing etc.). [Caveat: I am not an epidemiologist.] People may feel their efforts are in vain, contributing little if anything to help. But by slowing the spread of the disease, we give our already-overworked health care system more time to cope. Previously, new cases were increasing at 29%/day; now they’re going up at a much slower rate, only 11%/day.
And that means more lives saved.
So — congratulate yourselves. You are the ones who made this possible, who made it work. Social distancing and protective measures are NOT in vain.
These things work. They save lives. They already have. Don’t stop now.
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