Coronavirus - Statistics Update

We have been warned that as America reopens, the virus will spread more rapidly. But this didn't show up in the data until very recently. About a week ago, I did a quick check and didn't see any evidence. It's different now.

My data comes from Bing's COVID tracker. I prefer to focus on active cases, since you can't be infected by people who have recovered. However, I noted earlier that the recovery data is not very reliable. First, not every county's recovery data is reflected in Bing's tracker. The data that is reported appears to be cumulative recoveries rather than daily recoveries. That's fine, but on some days, the cumulative total of recoveries goes down - which should be impossible. It can't be daily recoveries because the sum of them all eclipses the total number of cases - also impossible.

Instead, I focus on total confirmed cases. Since the virus spreads exponentially, it's best to take logs (see my explanation in an earlier post). In the graph below, "logC" is the log of confirmed cases and "t" is time. The rapid growth slowed around late March and early April. It continued to slow for a while until the very end of the graph. It's hard to see, but that's why we rely upon statistical tests rather than just eyeballing pictures.

The tests found that there were 6 different periods. In each period, the slope is significantly different from the previous period. For the first 5 periods, the slopes were getting closer and closer to 0. That's a good thing. It means that the disease's spread is slowing down. Unfortunately, Period 6 (June 21 - present) is different. The slopes for Periods 5 and 6 are circled in the picture below.

The slope is about the same as it was in Period 4, which was mid May. It's true that testing has expanded. This means that we are detecting more cases than before. However, it does not entirely explain the increase. The expansion in testing started well before June 21. I don't know if new lockdowns are justified. The benefits of flattening the curve have to be weighed against the economic costs. I'm working on a research project to address this, but progress has stalled. In the meantime, I hope you're staying safe and healthy.

America is Reopening, but the Curve is Still Flattening

As the shutdowns gradually end, the big fear is that there will be a surge of new cases. I find that the number of active cases has continued to rise. However, the growth rate has not increased. The curve is still flattening.

My data comes from Bing's Covid-19 tracker. I focus on active cases (active = confirmed - recovered - deaths). Neither the dead nor the recovered can spread the virus - that's why active cases are the relevant factor. My earlier blog post was about total confirmed cases, but when I turn my attention to active cases, I still get the same result: the curve started to flatten in early April.

Here is the graph of active cases in the US.

You can see the exponential growth. As I explained earlier, when you have exponential growth, it's better to look at the log graph:

It's still spreading, but not as rapidly as before.

When examining the data, I asked, "When did the curve's slope change?" I found that it changed several times.

Time1 is before March 20. Time2 is from March 20 - April 7. Though this was during the lockdown, the disease was actually spreading more rapidly than before. However, it can take up to 2 weeks before symptoms appear, so this increase reflected cases that had started earlier. Time3 is April 8 - April 29. Here we see the curve flattening: the coefficients (circled in red) started shrinking. However, they were still positive. Overall, that means that the virus was spreading but the growth rate was slowing down. Time4 is April 30 - May 9. Some states had started reopening by then. Nevertheless, the growth rate kept slowing down. Right now, we are in Time5: May 10 - present. The growth rate is even slower.

This analysis does *not* prove that the reopenings were a success or that shutdowns were unnecessary. A longer shutdown would have driven down the growth rates more quickly, but we don't know if that benefit outweighs the economic costs. That question is too complicated for a single blog post. I have one piece of the puzzle: the curve is still flattening in spite of the reopenings. Other researchers will have to fill in the rest.