The growth rate calculations that I published in my last post showed that the infection and death rates due to Covid-19 are both declining. Again, these are the growth rates and not the absolute numbers of cases. The decline in rate of growth is encouraging however. The last few days I performed the calculations on the last seven days of data (rolling seven-day window) and the growth rate has gone down 1-2% per day so this trend seems to be continuing.
The data I use are United States aggregate (all regions) data and as I also pointed out in the last post, different regions will peak at different times.
As for the predictions of when certain regions will peak this article explains that some of our current “hot-spots” may be seeing their peak now (New York/New Jersey either today or tomorrow). Boston may reach the peak soon (Boston April 18th). So there appears to be hope (which we all need) as to when this thing will begin to decline so that we can start planning on going back to work. A combination of testing and appropriate workplace and social behavior can give us confidence over time that we can be with others we know are safe.
This will require staying socially distant in the near term and not going back to socializing in packed bars and restaurants immediately but with some testing and reconfiguration of social norms we can at least start seeing people in person in certain circumstances again. Restaurant tables farther away than they used to be and testing to ensure that we are safe to be with others will probably be some of the “new normal”.
Going back to work will require a plan of testing and verification of health status but if we can see the case numbers peak and then if we have four to six weeks to plan on how to go back to work it would let us all help revive the economy again. If New York could start re-opening its economy by mid-May to late May with Boston and other Northeast cities a week or two after that, then the economy has a chance to be starting to operate again by late June or July.
Having tests available to identify those who may have been exposed and developed immunities (anti-bodies in their system) to Covid-19 will be a key component to help us plan a way forward. When testing is in place and we can identify those who may be safe to work in a certain environment then we can move on to the second phase of economic re-entry: therapeutic treatment of the population.
Having therapeutic drugs to help give people who are infected some kind of treatment (instead of a ventilator) and those who are not infected some limited scope immunity would allow us to function as a society again. I think that it will be some time before we are all packing bars and restaurants again, but at least having some ability to be in public and not feel that we are going to get deathly ill and be confined to an ICU bed would be progress.
Many companies are in clinical trials with therapeutic drugs to help give individuals some limited scope immunity or to allow the infected to get better sooner. The therapeutics should allow those who get sick to avoid severe lung disease and the need for ventilators and ICU care. For others, therapeutics can allow them to fight the disease off without getting sick or becoming severely ill.
Next year a vaccine would allow us to know that we are generally safe from this disease but in the interim it would be nice to be able to feel relatively comfortable having dinner with friends (in our homes or at an appropriately reconfigured restaurant where staff have been tested, etc.). If we had therapeutics that would allow us to even have passive temporary immunities to the virus until a vaccine is available we could get to the next step in this fight.
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:
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
A = ending value (amount after growth or decay) A0 = initial value (amount before measuring growth or decay) e = exponential e = 2.71828183… k = 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
The number of cases on 3/22/2020 was:
The number grew to a very large number in the 13 intervening days:
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.
The number of deaths on 3/22/2020 was:
The number of deaths on 4/4/2020 was:
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.
This dread virus causes one to really stop and think about what is happening to our world and society. To make sense of this I wanted to look at the numbers as much as I can from my socially distant location. I am truly fortunate to be out of the way of a lot of human contact as there are not that many people around my location this time of year.
For those who are not as fortunate and who have to live in a major city, I thought it might help to think about this from a mathematical perspective to give people hope that social distancing is necessary and helpful at this time. Being trained as an engineer it helps me make sense of how things are unfolding in the spread of the disease by looking at the reported cases and the death and recovery rates of the United States as a whole and some of the more hard-hit regions of the country like New York, New Jersey and Washington state.
These data (below) seem to indicate that one contracting Coronavirus here (U.S.) so far has a 1.1% chance of death versus the world at large (4.25% – 4.3%). We should not look at this percentage difference and assume that we are 4 times “better off” in terms of being safe from death in terms of encountering this infectious disease.
One theory of a lower death rate here is that fewer people in the United States smoke tobacco products than they do in other parts of the world. Despite that fact, we should not assume that we are safer than anyone else in the world in relation to death from coronavirus. It is too early on in our measurement of the spread of the disease to draw such conclusions.
Most importantly, we should not get comfortable with this premature set of statistics and ignore government health procedure warnings. Some people may look at the small number of deaths and feel that they can ignore government health warnings (like students have been doing on spring break). This group of people (those not heeding health guidelines) need to understand that we might not have seen an advanced stage of the disease and therefore have not seen the worst of its effects.
To accentuate the point, these data could mean that we just have not seen enough cases or detected as many serious cases and that hospitalization may spike in the next two weeks causing us to “catch up” with the rest of the world in terms of mortality rate. This would be truly a disaster, so I believe that we all need to take this seriously and “shelter in place” avoid public contact and social gatherings (even in private homes).
Staying distant from one another is very difficult for human beings to do but we have to do it to avoid the chance that we accelerate our rate of infection and the percentage “death rate” to that of the rest of the world.
Ray of Hope
As a “ray of hope” however, we may be fortunate enough to have learned from the experience of those in other parts of the world despite our slow response to the virus in general. An example may be our initiative to seriously consider treatments that have worked on patients elsewhere. For example, we may have a “head start” on the use of therapeutics that can ease suffering in the United States.
These therapeutic approaches could ease the suffering of individuals and relieve the pressure on hospitals by allowing fewer people to require ventilators. Despite this hopeful approach we should not count on that to keep the “death rate” down. Our scientists and the FDA are also racing (literally) to approve new treatments and possible vaccines but these are a few months (new therapeutics) and at least a year (vaccines) away from general adoption.
Being well aware that the United States is slow to implement testing of its citizens we cannot know the current true infection rate. It is encouraging to see on the local news that drive-through testing facilities are being established in Massachusetts. These facilities require a person to have a doctor’s note verifying that they have coronavirus symptoms to be tested (otherwise they are turned away according to local news reporters) but at least we have a means to test those who are likely to be infected and to start getting some good data on actual versus false infection rates.
According to this website: https://www.worldometers.info/coronavirus (selected because it seems to stay updated regularly; and it is in agreement with the Johns Hopkins University data https://coronavirus.jhu.edu/map.html that is quoted on CNN and other news outlets), the death rate percentage across the world and the United States (percentage of deaths in relation to all infected persons) is relatively constant (percentages below).
The number of World-wide Coronavirus cases is 324,064 with 13,782 deaths, 96,006 cases showing recovered, 214,276 active cases with 109,788 closed cases (recovered plus deaths).
World-wide Cases (as of March 22, 2020 1:15 P.M. EDT United States)
324,064 total confirmed cases
96,006 recovered cases
214,276 Currently infected patients (as we know and estimate due to lack of U.S. testing)
204,121 – Mild cases (95%)
10,155 – Serious or critical cases (5%)
109,788 closed cases (96,006 recovered plus 13,782 deaths)
This leads to the following percentage calculations based on a given outcome:
Percentage (World-wide) of deaths per infected person – 4.25%
(13,782/324064 = .0425)
Percentage recovered – 29.6%
(96,006/324,064 = .296)
United States case data(as of 1:15 P.M. EDT United States)
35,746 coronavius cases (it increased while I was writing this) by about three thousand known cases)
178 Recovered cases
35,176 currently known infected cases
35,176 Mild cases (98%)
708 Serious or critical cases (2%)
570 Closed cases
178 Recovered/discharged (31%)
392 Deaths (69%)
Percentage (U.S.) of deaths/infected person – 1.09%
392/35,746 = .0109
Percentage recovered/discharged – .5% (one half of one percent)
178/35,746 = .00498
These percentages do not reflect any inference about a person’s age when they contracted the coronavirus or their general health condition. It is just raw data to see how this virus is impacting the US versus the world NOW. These percentages could change drastically as the virus spreads in the population and has more longevity in the general population. As more cases are confirmed through expanded testing and as the disease manifests over time, the picture of how many people die from this dread virus and recover from it could change radically.
Again, at risk of repeating myself, these data seem to indicate that one contracting Coronavirus here (U.S.) so far has a 1.1% chance of death versus the world at large (4.25% – 4.3%). This could mean that we just have not seen enough cases or detected as many serious cases and that hospitalization may spike in the next two weeks causing us to “catch up” with the rest of the world in terms of mortality rate. Hopefully that will not happen, and our use of therapeutics can reduce the suffering (and death rate) that is being experienced by many people across the world.
Catching up with the death rate elsewhere would truly be a disaster, so I believe that we all need to take this seriously and “shelter in place” avoid public contact and social gatherings (even in private homes). Staying distant from one another is very difficult for human beings to do but we have to do it to avoid the chance that we accelerate our rate of infection and the percentage “death rate” to that of the rest of the world.
We should have faith in the scientists to find a therapeutic course of treatment that gives hope this year, and a vaccine that keeps this dread disease from re-appearing next year. In the meantime we should all be prudent and remain away from others and exhibit responsible social behavior, despite our fundamental urges to be with other people.