A Lesson on Doubling

Exponential growth is characterized by a rate that is increasing with time. One can use a doubling time to describe such growth. For example, now that it is spring time, one can observe how fast weeds grow. If the doubling time in the area that weeds cover is 3 days, one can imagine that starting with a square foot of weed coverage, in the next three days, the weed will cover 2 square feet. In six days, it will be 4, and in nine days, it will be 8 square feet. And in just 3 weeks, that is, 21 days, the weed area would have doubled 7 times. By that time, 128 square feet will be covered by weeds. That will be a lot of work on my weed whacker. The death rate from COVID-19 behaves similarly. And right now, the doubling time for the number of COVID-19 deaths in the US is 3 days.

Above copied from the New York Times

Currently, the number of deaths in the US due to the novel corona virus is just a little under 6,000. If we assume that the doubling time remains constant for the next three weeks, on April 24, the number of the deaths would be 6000 times 2 times 2 times 2 times 2 times 2 times 2 times 2. That is 768,000 deaths. This, however, is really the worse of the worst case scenario. If we look back in the past on what happened in Italy, we see that the doubling time of 3 days does not last that long.

Above copied from the New York Times

A line that roughly describes a doubling time of 3 days is drawn with a thick black line. One can see that the doubling time of 3 days stayed only for about a week in Italy. At the moment, the doubling time for Italy is now much longer, 9 days. So, if we assume that the same "not-so-good" situation will likewise happen in the US then the doubling time of 3 days will probably last another week., which means we will probably get to 24,000 deaths by next week. After that the doubling time, let us assume, will go up to 5 days, so after 16 days, the number of deaths will be 96,000. And copying what happened in Italy, the doubling time should go up to 7 days. So, in three weeks, the number of deaths will be between 100,000 to 200,000. Surprisingly, this is the best-case scenario that the White House provided.

This is a simple doubling exercise and yet, one wonders why the White House paints the worse case scenario as its best case scenario. Is it a simple lowering of expectations so that in the end, someone can declare "victory"?

The following, in my opinion, is a more honest "best case" scenario:

Date        Deaths
April 2        6000
April 7      12000
April 14     24000
April 28     48000
May 20      96000