Daily update, April 20, 2020....
We begin our 5th week of the COVID-19 shutdown. I have been following the Virginia Statistics since March 12. My goal was to understand how the disease was progressing, and to see if we were "flattening" the curve. (We did). I used Virginia data because 1) it was reasonably uniform in testing criteria, and 2) I live in Virginia. I understand the data, which helps.
Flattening the Curve
My approach was to look at linear trends in the logarithm of the data. Diseases grow exponentially, and logarithmic plots allow is to understand the growth rate of the disease. Early in April, I started to see that the number of new cases were consistently falling below the "the trend". Prior to that, the growth rate day-over-day was about 25%. And gradually it dropped below the trend line.
That I did was looked at the data from the 13th to the 30th of March, defined a line, and looked at 2 and four standard deviations. By about April 5th, it was clear that the multiple days falling below the trend (about 7) was statistically significant, with less than 1% chance (on that day), and essentially zero chance we did not flatten the curve today (April 20).
Policy and results
Another really interesting aspect of the data is that we can really see the impact of policy changes in the growth rate. Roughly 7-10 days after a policy change, the number of cases reflect that. Using the dates of policy changes offset by lag in becoming symptomatic and reporting, we can find each period of time led to a different growth rate.
Initially, we knew something was up, but did not know it was here. In that period, we daw a growth rate of 60%. Fortunately, even though the state of emergency did not go into effect until 3/12, by 3/6, people were aware it was coming. We were increasing sanitary effect, not shaking hands, using Purell, and washing our hands. Plus, we were getting weary of crowds. When the state of emergency was declared, people did not change the actions. The growth rate dropped to 25%. With the first executive order, the growth rate dropped to 18%, and with the stay at home order, it dropped to 11%. This is the cumulative number of cases.
This shows that the Governor's decision to take action slowed the spread, and probably saved lives.
Another way to look at this is a what if. We started to see what was happening elsewhere around 3/4 (Washington State, etc). Up until that time, we were naive. We did not have our first case until 3/8. By then, behavior had changed, but there were other people who had been infected but did not know it. That put us at 26 cases before we can see the change in behavior.
We can use this to ask what if's. In NYC, the first case was about 1-2 weeks earlier. That would mean for the first 14 days, the we would have not known of the problem, and by that time 2800 would have been infected. That would probably mean that today, we would have 100x as many cases, and 100x as many deaths in Virginia: 800,000 cases, and 30,000 deaths (instead of 8000 and 300). Note that we are probably under reporting by a factor of 7 in cases but not deaths. Thankfully, that did not happen (here), but did happen in New York City. (Virginia any NYC have about the same population).
Where we are today and tomorrow
These days, we are seeing growth of about 500 cases per day, which is near the maximum, but have not been growing for the last several days. If we look at the total number of new cases reported in the last 7 days, we see constant values for the last 4 or 5 days. Projecting forward...it seems that we may be at the peak of the first wave. Assuming exponential growth rates of two populations in Virginia, 98.7% followed the rules, 1.3% did not, we find that the latter population is saturating. The 98% of Virginia is still good. This means we are at the peak of the first wave. We will know for sure in th coming days if the number of new cases consistently drops.
On the "going forward", if my forecast is correct, we do have a path to reopening the area. It strongly depends on available testing (both active cases and antibodies), sufficient personal protection equipment, and active contact tracing. There will almost certainly be a second wave once we reopen. Our goal is to not overwhelm the hospitals; if we keep the R number under 1.2, we can succeed. That coupled with better treatments (some -- not those advocated by our so-called leaders are showing promise in the most severe cases), we can survive this (or most of us can).
If we reopen today, with where we are, this shutdown was for nothing.
