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Health and Public Policy

Covid-19: Data-Inspired Observations of Hope

The news media make such hyperbolic statements about the spread of Covid-19 that it is hard to know when things may get back to normal. One “expert” after another appears on CNBC, CNN, ABC, NBC, CBS and MSNBC and makes many valid points about social distancing and prevention (which is good) but they leave the impression that all is lost. These experts mean well in many cases but generally scare people and give no basis of hope that this will end. In the meantime, the economy is stalled and people are frightened. The stock market is punished because the economy is shut down.

To gain some perspective on this, it is important to look at the data and see how fast the cases are spreading and how rapidly the number of deaths is increasing (two different growth rates). This analysis will give an overall picture of the rate of spread of the infection and the death rate. When the rate of spread begins to decrease (this is when the number of overall cases may be growing from one time period to the next but at a slower rate than in a previous period), then we can draw hope that the spread of the disease is slowing and will become manageable.

To look at this I gathered the data from this source and tracked it from March 22, 2020 until today (April 4, 2020). These data show the number of cases and the number of deaths that resulted over that timeframe. The data is as follows:

US Data
DateCasesDeaths
3/22/2035746392
3/23/2042163512
3/24/2049594622
3/25/2060642816
3/26/20749821078
3/27/201042561696
3/28/201057781731
3/29/201314032329
3/30/201568182871
3/31/201807893580
4/1/202002894394
4/2/202385565741
4/3/202597506603
4/4/203006258157

As shown above, the number of cases on March 22, 2020 was 35,746 and that number has expanded to 300,625 in the thirteen “compounding periods” since. This exhibits continuous exponential growth so I used an exponential growth formula to determine the rate of growth during that timeframe. Then I computed some interim growth factor numbers to see if they (the rates of growth) were increasing or decreasing within this time interval (3/22/2020 – 4/4/2020).

Continuous Exponential Growth or Decay
exC
A = ending value (amount after growth or decay)
A0 = 
initial value (amount before measuring growth or decay)
= exponential e = 2.71828183…
= continuous growth rate (also called constant of proportionality)
(k > 0, the amount is increasing (growing); k < 0, the amount is decreasing (decaying)) 
t = time that has passed

Cases

The number of cases on 3/22/2020 was:

35,746 cases

The number grew to a very large number in the 13 intervening days:

300,625 cases


The rate of growth in cases between 3/22/2020 and 4/4/2020 (the overall growth rate) would be:

k(cases overall) = ~.16 or a substantial overall rate of 16%

The time period from 3/22/2020 – 3/29/2020 (7 compounding periods) showed a growth rate higher than this overall rate of:

k(cases 3/22/2020 – 3/29/2020) = .186 (18.6%) or a substantially higher growth rate than the overall rate

The last six days (3/29/2020 – 4/4/2020) has shown another rate of:

k(cases 3/29/2020 – 4/4/2020) = .137 (13.7%) or quite a bit lower than the overall rate of .16 and a lot lower than the previous seven days (18.6%).

So the overall growth rate has been slower in the last six days than in the previous seven days. This is encouraging and shows that the rate of infection may be slowing down and slowing down substantially. This may be due to social distancing or some other factor, but it is happening.

Deaths

The number of deaths on 3/22/2020 was:

392 deaths

The number of deaths on 4/4/2020 was:

8,157 deaths

When we look just at these numbers over a 13 day period we can become frightened. It is a large increase in deaths. This is why we need to look at the rate of increase and see if it is getting higher or going lower.

If we look at the rate of deaths that are occurring in the same time periods we can see a similar phenomenon to the rate of change in the growth of infections:

The rate of growth in deaths between 3/22/2020 and 4/4/2020 (the overall growth rate) would be:

k(deaths overall) = ~.246 or a substantial overall rate of 24.6%

The time period from 3/22/2020 – 3/29/2020 (7 compounding periods) showed a growth rate higher than this overall rate of:

k(deaths 3/22/2020 – 3/29/2020) = .255 (25.5%) or a substantially higher growth rate than the overall rate in the first seven days of the data we are analyzing

The last six days (3/29/2020 – 4/4/2020) has shown another rate of:

k(deaths 3/29/2020 – 4/4/2020) = .208 (20.8%) or quite a bit lower than the overall rate of .246 (24.6%).

More encouragingly this reduction relative to the last seven days is almost 5% (a reduction in rate of twenty percent of the rate of the last seven days. 20.8% is about 20% lower than 25.5%).

So the overall growth rate in deaths has also been slower in the last six days than in the previous seven days. This is encouraging and shows that the rate of deaths due to infection may be slowing down and slowing down substantially. Perhaps people are getting treated more effectively or they are not as sick when they get the disease. It is hard to tell but maybe younger people who are less likely to die from the disease have been infected in the last month.

These data are aggregate data and do not take into account that different regions of the United States suffered infection at different times. Different regions of the country will likely go through a time when there are many people infected and some will survive and recover. A recovery window will not happen over the same timeframe in every municipality.

The encouraging thing is that the growth rates of infections and deaths seems to be slowing down overall. This is good news.

Hopefully the infected (sick) rate and the death rate will peak and start declining soon. On CNBC recently Dr. Scott Gottlieb, former commissioner of the FDA stated that he thought the NYC area could “peak” in the next week to ten days (NYC/greater New York and New Jersey, not the country).

The facts from New York are particularly bleak. Anyone who has ever been on the NYC subway will not be surprised at the high numbers of cases present in NYC. The entire NYC/NJ area probably has the highest per-capita usage of mass transit in the United States. The proximity of people on mass-transit trains and buses and the presence of a virus like this promotes transmission. So NYC as a hot spot is well fortified and probably 6 to 7 weeks into its hot-spot cycle. With about half the known cases in the country, perhaps these declining growth rates and Dr. Gottlieb’s prediction will be good news for the greater NYC/NJ area and portend good things for other regions.

From watching China, South Korea and other countries go through their experience with Covid-19 it is clear that there is about a 8 to 10 week duration of the worst transmission. After this time there is a period where cases diminish at a “decaying” rate. So our experience is likely to be similar across a number of well-known and predictable “hot spots”.

In the United States, these are Seattle/California, New York State and particularly NYC/NJ, New Orleans LA and points south, Florida and the Upper Midwest/Northeast (college towns particularly) areas. In our case the infections may have started at different times and could have predictable “rolling windows” of 8-10 weeks where the virus will rise and then fall in rate of transmission.

Seattle and California seem to have peaked or are close to peaking. Washington state seems to have had the rate of new deaths fall to low levels in the last week. California seems to be behind Washington state but for its size (40 million people) it is not exhibiting huge growth in case load. California has four times the population of Michigan and has fewer cases than Michigan so the aggressive social distancing instituted by the Governor in California a few weeks ago may be working.

Even though the regional rates may vary it does seem like the data are showing that there is a slowing of the rate of infection and death from infection over the last six days. This is some good news in a very dark period for the country.

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