I\u2019m going to lead with numbers today and follow with some thoughts on what they might mean.<\/p>\n\n\n\n
Growth rates for reported cases and deaths continue to decline, though that decline seems to be slowing. For example, here are the growth and death rates for the past week. This is the percentage increase from the previous day. So, 4\/9 had 7.92% more cases and 12.87% more deaths than 4\/8 did.<\/p>\n\n\n\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Cases\u00a0 \u00a0 \u00a0 Deaths
4\/9 \u00a0 7.92% 12.87%
4\/8 \u00a0 8.18% 14.76%
4\/7 \u00a0 8.70% 17.55%
4\/6 \u00a0 9.16% 13.76%
4\/5 \u00a0 8.22% 13.61%
4\/4 \u00a0 12.20% 18.34%
4\/3 \u00a0 13.18% 21.26%<\/p>\n\n\n\n
You can see that both growth rates are down from a week ago. However, over the last 5 days the case growth rate has stayed in the neighborhood of 8%. The death growth rate has bounced around more in that period, so it\u2019s harder to read a trend in this small snapshot. It does seem to be decreasing overall, but more unevenly than the death rate.<\/p>\n\n\n\n
Taking the average of the last 5 days\u2019 growth rates gives us a rate of 8.44% for cases and 14.51% for deaths. Because both of these rates are falling, I\u2019m going to round down to 8% and 14% for today\u2019s projection. This should compensate a bit for the decrease. There are fancier ways to do that, but they aren\u2019t really worth doing given that we\u2019re only interested in getting a rough idea where these numbers are headed and that there are so many outside variables that could impact them. With that said, here\u2019s the projection:<\/p>\n\n\n\n
Cases Deaths
4\/10 508,216 19,124
4\/11 548,873 20,653
4\/12 592,783 22,306
4\/13 640,205 24,090
4\/14 691,422 26,017
4\/15 746,735 28,099
4\/16 806,474 30,347
4\/17 870,992 32,774
4\/18 940,672 35,396
4\/19 1,015,925 38,228<\/p>\n\n\n\n
The first thing to notice is that these numbers require over 40,000 new cases each day. Compare that to the new case numbers over the last week.<\/p>\n\n\n\n
4\/9 34,514
4\/8 32,985
4\/7 32,258
4\/6 31,120
4\/5 25,796
4\/4 34,128
4\/3 32,577<\/p>\n\n\n\n
For the last week we have seen numbers mostly in the low 31,000 to 35,000. Do we really think those numbers are going to be over 40k tomorrow, or are we now in a situation where we\u2019re just adding about the same number of cases each day? In essence, this is the question of whether our cases are continuing to grow exponentially or whether we have switched to linear growth – is each day\u2019s case count a percentage of the previous day\u2019s. (There are other types of growth, e.g. logarithmic, but I\u2019m aiming for simplicity here and the essential question is whether the growth is no longer exponential.) This is a question that can\u2019t be answered by simple math. Given the underlying problems with this data (e.g. that it\u2019s only reported cases, testing isn\u2019t widespread, etc.) and our purpose of just having a general idea, it probably isn\u2019t worth doing the fancier math to decide the issue. The past week\u2019s new case numbers do seem all within a narrow range. That and the consistent small decrease in percentage growth we saw at the top of the post are reasons to suspect that we\u2019ve entered a linear growth period, at least for cases of about 32,0000 cases per day. Personally, I\u2019m not ready to make that call, but if these numbers stay in the same range for a few more days I probably will be. Just for the record, here\u2019s what the numbers look like if we are just adding 32,000 cases per day.<\/p>\n\n\n\n
4\/10 502,570
4\/11 534,570
4\/12 566,570
4\/13 598,570
4\/14 630,570
4\/15 662,570
4\/16 694,570
4\/17 726,570
4\/18 758,570
4\/19 790,570<\/p>\n\n\n\n
We\u2019ll see which projection works best over the next few days.<\/p>\n\n\n\n
There\u2019s an optimistic and a pessimistic way of viewing all this. I\u2019ll go through both<\/p>\n\n\n\n
Optimistically, the move toward slower and possibly linear growth rates is great news. It means the curve is flattening. This is just the sort of effect we would expect from social distancing effort and mirrors the flattening we\u2019ve seen in Washington. It shows that by taking precautions we\u2019ve slowed the virus spread enough that we may not overwhelm the medical system to the degree we might have. So long as we continue this same level of precautions, we\u2019ll be saving lives while we wait for a vaccine to be developed.<\/p>\n\n\n\n