Numbers, continued

The last time I posted I worked up a rough estimate of the doubling time for corona virus cases in the US. The CDC reported 4226 cases on 3/16 and 85356 cases on 3/26 and that represented a doubling time of 2.31 days.

Again, my numbers should not be taken seriously. Like I said, this is just an old blackboard exercise on the natural logarithm and not a proper analysis of the data on COVID-19 infections.

The new number of US infections, according to the CDC, is 140904. This represents, now, 13 days of growth. So, like before, I take the natural logarithm of 140904 and that’s approximately 11.86. I subtract the natural log of our beginning number, 4226 (8.35), and get 3.51 for the 13-day period. Divide 3.51 by 13 and you get 0.27 per day. That’s 27% growth, and that’s a bit lower than the 30% we got last time.

Sure enough, if I divide the natural logarithm of two (ln 2 = 0.693) by 0.27, just like last time, I will get an estimate of the doubling time. This calculation results in 2.56 days.

So, the doubling time has increased from 2.31 to 2.56 days. That’s good. You want to see the rate of growth slow down. The number of infections is still growing rapidly, but not as fast as before. You’ve experienced this driving your car. You hit the freeway on-ramp at 35 mph and power up to 65 mph in a few seconds so you can merge with traffic. That’s acceleration—an increase in your rate of speed. Later you make a gradual increase from 65 mph to 75 mph in order to pass someone. That increase of 10 mph happens in about the same amount of time as your increase from 35 mph to 65 mph, which was a 30 mph increase. So you are still accelerating, but the change in your speed, over the same time period, is slower.

I reported four days the last time, so my rough math reflects the same thing!

Of course, the number of infections may not be a particularly useful or even a robust number. You need widespread testing to get a handle on the true infection rate and we don’t have widespread testing in this country so we are still a bit in the dark. Compare Iceland, for example, which has tested 3.5% of their population. We’ve tested less than 0.2% of our people! That reflects very poorly on our political leadership, of course. But more than that it means we are making public policy decisions based on incomplete information. Perhaps after we get through this mess we will be better prepared for future disease outbreaks.

If we stick to the plan—social distancing, sheltering in place, etc.—we can get out of the dangerous growth phase and get a handle on this pandemic. We can see the doubling time continue to increase (which means the infection rate will be decreasing) and give our health care system a chance to cope.

So, do your part.

3 thoughts on “Numbers, continued”

1. Dan Belik says:

You’re not far off. As per my previous comment, I think death rate is probably a better proxy for infection rate than cases, although their are problems with that as well. Here are some charts that give some country by country and state by state death rates: https://www.nytimes.com/interactive/2020/03/21/upshot/coronavirus-deaths-by-country.html. It would appear that the US death rate and therefore, IMO, infection rate, has a doubling time between 3 and, say, 5 days. Which shows your work to be not too bad, and, if high, logically so due to the increase in testing.

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2. […] do some math. On 3/16 there were 4226 cases. That’s 23 days of growth and we see a ten-fold increase. When something grows by a factor of […]

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