I’m going to lead with numbers today and follow with some thoughts on what they might mean.
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.
Cases Deaths
4/9 7.92% 12.87%
4/8 8.18% 14.76%
4/7 8.70% 17.55%
4/6 9.16% 13.76%
4/5 8.22% 13.61%
4/4 12.20% 18.34%
4/3 13.18% 21.26%
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’s harder to read a trend in this small snapshot. It does seem to be decreasing overall, but more unevenly than the death rate.
Taking the average of the last 5 days’ growth rates gives us a rate of 8.44% for cases and 14.51% for deaths. Because both of these rates are falling, I’m going to round down to 8% and 14% for today’s projection. This should compensate a bit for the decrease. There are fancier ways to do that, but they aren’t really worth doing given that we’re 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’s the projection:
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
How plausible are these numbers?
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.
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
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’re 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’s case count a percentage of the previous day’s. (There are other types of growth, e.g. logarithmic, but I’m aiming for simplicity here and the essential question is whether the growth is no longer exponential.) This is a question that can’t be answered by simple math. Given the underlying problems with this data (e.g. that it’s only reported cases, testing isn’t widespread, etc.) and our purpose of just having a general idea, it probably isn’t worth doing the fancier math to decide the issue. The past week’s 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’ve entered a linear growth period, at least for cases of about 32,0000 cases per day. Personally, I’m 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’s what the numbers look like if we are just adding 32,000 cases per day.
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
We’ll see which projection works best over the next few days.
What does all this mean?
There’s an optimistic and a pessimistic way of viewing all this. I’ll go through both
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’ve seen in Washington. It shows that by taking precautions we’ve 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’ll be saving lives while we wait for a vaccine to be developed.
Pessimistically, we have to remember that our data has fundamental flaws and may not correlate to the actual spread of the virus. We do not have widespread testing yet, and reported cases depend on testing to a fair degree. Here is what testing numbers have looked like over the past week. (This data is from https://covidtracking.com/data )
# tests % positive
4/9 162,258 19.40%
4/8 140,194 19.29%
4/7 147,750 19.11%
4/6 146,658 18.96%
4/5 138,133 18.89%
4/4 225,890 18.88%
4/3 129,717 19.51%
There are a couple of things to notice here. First, we’re not seeing consistent growth in testing over the period. In fact, the average daily growth in number of tests over this period is about 9% per day, very close to the average daily growth in number of cases over the same period. Second, the percentage of tests that come back positive has been pretty stable at about 19%. Together, these two facts suggest that the flattening curve in reported cases may just be the result of inadequate testing. If we mostly report cases based on positive tests, and we aren’t growing our testing much, then we wouldn’t expect to see a lot of growth in reported cases.
It’s difficult to know which of these views is most correct, though there is likely some truth to each. For now, I’m going to try to stay open to both possibilities while looking for data that can test between them.
In the meantime, keep up the social distancing and precautions. There’s every reason to think they are helping, even if we can’t say by exactly how much.
Thanks for reading.