Has Covid-19 Become Less Deadly?
Historical Results from the 1918 Pandemic
Recently, the question has arisen about whether the Covid-19
disease (caused by the novel Corona Virus) has become less deadly, though
perhaps more transmissible. This is
actually a distinct possibility, as this pattern has been observed in other
pandemics throughout history. Here is a
quote from a very good book about the 1918 influenza pandemic, that notes how
this phenomenon applied at that time:
“But the 1918 virus, like all
influenza viruses, like all viruses that form mutant swarms, mutated rapidly.
There is a mathematical concept called “reversion to the mean”; this states
simply that an extreme event is likely to be followed by a less extreme event.
This is not a law, only a probability. The 1918 virus stood at an extreme; any
mutations were more likely to make it less lethal than more lethal. In general,
that is what happened. So just as it seemed that the virus would bring
civilization to its knees, would do what the plagues of the Middle Ages had
done, would remake the world, the virus mutated toward its mean, toward the
behavior of most influenza viruses. As time went on, it became less lethal.”
(Barry, John M.. The Great Influenza (p. 371). Penguin Publishing Group. Kindle
Edition.)
It is a matter of natural selection; a virus that is too
deadly kills off its hosts (or generates behaviours such as social distancing
among its hosts), which limits its reproduction. Thus, there is a tendency for less virulent
forms of the virus (created via random mutations) to survive and replicate
themselves, eventually dominating the strains of virus among the host
population. So, the virus can both
become less deadly, but more transmissible over time. Eventually, it can become like the common
cold – a successful nuicance, but not much of a threat.
Data Analysis of the 2020 Pandemic
The scatterplot graphs below show the death rates by
country, expressed as deaths per case, for the early part of the pandemic (Feb-May3,
2020) and the latter part, so far (May4-July6).
The number of confirmed cases of Covid-19 are on the X-axis, while
deaths are along the Y-axis, for about 175 countries. Also included are the linear regression
lines, giving the function relationship between cases and deaths, and the R-square
coefficients, showing how close those relationships are to forming a straight
line.
You will note that the first graph, that uses linear scales,
is not all that compelling, even though the R-square of the lines are high
(0.85 for the Feb-May3 period and 0.90 for the May4-July6 period). That’s because of the huge differences in
country populations and the different stages of the pandemic in various
countries. This has the effect of
clustering the vast majority of points near the origin, thus obscuring the
visual impression of the strength of the relationship.
Once the graph is re-scaled, by taking the (base 10)
logarithms of the numbers of cases and deaths, as in the second chart, the
relationship becomes much more evident.
Taking logarithms “spreads out” the data visually, so that the linear
relationship is evident. Note that the
functional form of the relationship is the same as in the first graph, as is
the R-square.
You might notice that the points don’t seem to be evenly
scatted around the regression line in this graph. That’s a visual effect of taking logarithms,
where distances on the graph are compressed as the numbers grow larger. For example, the distance between the number
2 and 5 is the same as the distance between 5 and 8, in the linear scale
(3). But in the logarithmic scale the
distance between 2 and 5 is .699-.301=.398, while the distance between 5 and 8
is .903-.699=.204. So, that explains why
the points on the logarithmic graph don’t seem to scatter “correctly” for a
linear regression.
The important result is that the slope of the line for the
data of the earlier period (0.065) is much steeper than it is for the later
period (0.036). Stating these results
verbally, we can say that about 6.5% of covid-19 cases died in the earlier
phase of the pandemic, compared to 3.6% in the later phase, based on this
country level regression analysis.
Note that if one does a cumulative world percentage
calculation the figures are 7.2% and 3.7%.
The difference is that the regression figures are essentially an
unweighted average, while the second calculation is a weighted average. But the country-level analysis is useful, as
it shows that the percentage of cases that resulted in death were quite similar
around the world, and that remained true of both the earlier and later periods.
An objection to this finding, is that countries are simply
doing more testing as time goes on, so the cases found will tend to be less
serious than previously, as testing is ramped up. Thus the percentage of cases that result in
deaths will go down, though the disease may actually be just as deadly as it
was in the earlier period.
On way to test this hypothesis, is to look at the data by
sub-sets of countries to see if there is any obvious pattern that arises. It seems unlikely that testing would be
ramped up all over the world at about the same rate, so if that was the cause
of the falling death rates, we would expect variation around the world, in the
rate at which death rates fell. After
all, not all countries have the technical capacity to ramp up testing
substantially in a relatively short time frame.
The table below breaks out the country-level data by
continent, hemisphere and latitude range, to look for such an effect.
|
Geographic Unit
|
Feb-May3 Beta
Coefficient
|
Feb-May3 Rsquare
|
May4-July6 Beta
Coefficient
|
May4-July6
RSquare
|
Early Beta/Later Beta
|
|
World
|
6.5%
|
0.8545
|
3.6%
|
0.9017
|
1.81
|
|
Africa
|
5.1%
|
0.6463
|
1.9%
|
0.8084
|
2.65
|
|
Asia
|
4.2%
|
0.8206
|
2.5%
|
0.9174
|
1.67
|
|
Australasia
|
1.3%
|
0.9998
|
0.8%
|
0.9621
|
1.63
|
|
Europe
|
11.2%
|
0.8162
|
2.3%
|
0.2669
|
4.78
|
|
Europe without Russia
|
11.7%
|
0.8598
|
10.7%
|
0.7457
|
1.09
|
|
North America
|
5.8%
|
0.9999
|
3.7%
|
0.9213
|
1.55
|
|
South America
|
6.0%
|
0.9043
|
3.8%
|
0.9899
|
1.56
|
|
North Hemisphere
|
6.5%
|
0.8533
|
3.5%
|
0.8591
|
1.86
|
|
South Hemisphere
|
5.9%
|
0.9095
|
3.8%
|
0.9854
|
1.57
|
|
High Latitude (40+)
|
11.1%
|
0.8171
|
2.4%
|
0.2633
|
4.66
|
|
High Latitude wo Russia
|
11.8%
|
0.8587
|
10.8%
|
0.7472
|
1.09
|
|
Mid Latitude (20-40)
|
5.7%
|
0.8486
|
4.0%
|
0.8968
|
1.42
|
|
Low Latitude (<20)
|
5.8%
|
0.9954
|
3.5%
|
0.9841
|
1.67
|
As you can see, in all cases the Beta Coeffiient (the pct of
confirmed cases who died) was greater in the Feb-May3 period than it was in the
later May4-July5 period. In most cases
it was about 1.4 to 1.8 times greater in the earlier period, which is what we
would expect if the disease was growing less fatal overall, and if the less
fatal strain was tending to dominate.
There is one major exception to this, which is Europe. The difference in period death rates was much
starker in the European case (4.78 times greater), and somewhat so in the
African case (2.65 times greater) than in the rest of the world. The high-latitude case is also much
different, though that probably reflects the large number of European countries
in that category.
We can uncover what “went wrong” with the regression for
Europe, by looking at the country level data more carefully. To do this, the data is shown on the linear
scale, to see if there are some very influential outlier points, as below. And, we see there are a couple of big
outliers, namely the U.K. and the Russian Federation.
It looks as if the Russian Federation data is badly skewing
the data here, so we will take that out and look at the resulting graph, which
is also shown. The data makes more sense
now, with the resulting regression having an R-Square of 0.75 and the
case-fatality rate now at 10.7%. At this
point in the pandemic, some European countries were undergoing a bad outbreak,
with high fatality rates, while Russia not nearly so badly affected. This also rectifies the anomalous result for the
high latitude category in the latter time period.
So, according to this evidence, though there may be
something to the higher testing hypothesis, it likely does not account for the
entire drop in case-fatality rates.
Another line of evidence can be deduced from the graph
below. This shows the number of tests
versus the number of cases in Europe, during the two time periods. In the first period, the number of tests
compared to cases is approximately 11 to 1, while in the later period, this is
about 44 to 1. The testing rate
increased by a factor of 4, while the case rate actually fell a bit. One would expect a substanial increase in the
number of cases in the later period, if enhanced testing was picking up a much higher
proportion of mild cases in the latter period.
Remarks
Here are some concluding remarks:
- The fatality rate, as measured by deaths per confirmed case fell from about 6.5% to about 3.6% from the Feb-May3 period to the May4-July6 period.
- A drop in fatality rates was seen in most areas of the world, with the pandemic apparently about 1.5 to 2 times as deadly in the earlier period.
- This is a phenomenon that is frequently seen in pandemics, though sometimes a second wave is actually deadlier than the first, as it was in 1918. Eventually however, a virus will become less deadly, due to mutations and natural selection.
- Though the drop in lethality might be partially explained by enhanced testing finding milder cases, this seems to only be able explain a relatively small part of the drop in lethality, at best. Testing rates in Europe expanded by about a factor of 4, but case rates didn’t increase at all, between the two time periods.
There are, of course, cautions about any results of this
sort, especially those that relate to sensitive subjects such as a pandemic. Many people have doubts about the Covid-19
numbers from some countries, whether that be deaths, cases or tests. No doubt there is some reason for concern,
but the fact that the death rate fell in all areas of the world between the Feb-May3
and May4-July6 periods tends to support the idea that the drop in death rates
is real, and not just an artifact of more extensive testing picking up less
lethal cases (though there is likely some truth to that too).
Sources:
KOF Swiss Economic Institute: https://kof.ethz.ch/en/forecasts-and-indicators/indicators/kof-globalisation-index.html
Worldometer Covid-19: https://www.worldometers.info/coronavirus/#countries
Some earlier Covid-19 blogs:
And, here’s a more pleasant travel story than anticipating
the worldwide journey of a virus.
A Drive Across Newfoundland
Germany: https://www.amazon.de/dp/B07NMR9WM8
Australia: https://www.amazon.com.au/dp/B07NMR9WM8
Newfoundland, Canada’s most easterly province, is a region
that is both fascinating in its unique culture and amazing in its vistas of
stark beauty. The weather is often wild, with coastal regions known for steep
cliffs and crashing waves (though tranquil beaches exist too). The inland areas
are primarily Precambrian shield, dominated by forests, rivers, rock
formations, and abundant wildlife. The province also features some of the
Earth’s most remarkable geology, notably The Tablelands, where the mantle rocks
of the Earth’s interior have been exposed at the surface, permitting one to
explore an almost alien landscape, an opportunity available on only a few
scattered regions of the planet.
The city of St. John’s is one of Canada’s most unique urban
areas, with a population that maintains many old traditions and cultural
aspects of the British Isles. That’s true of the rest of the province, as well,
where the people are friendly and inclined to chat amiably with visitors. Plus,
they talk with amusing accents and party hard, so what’s not to like?
This account focusses on a two-week road trip in October 2007, from St. John’s in the southeast, to L’Anse aux Meadows in the far northwest, the only known Viking settlement in North America. It also features a day hike visit to The Tablelands, a remarkable and majestic geological feature. Even those who don’t normally consider themselves very interested in geology will find themselves awe-struck by these other-worldly landscapes.
This account focusses on a two-week road trip in October 2007, from St. John’s in the southeast, to L’Anse aux Meadows in the far northwest, the only known Viking settlement in North America. It also features a day hike visit to The Tablelands, a remarkable and majestic geological feature. Even those who don’t normally consider themselves very interested in geology will find themselves awe-struck by these other-worldly landscapes.
A Ride on the Kettle Valley Rail Trail: A Biking Journal Kindle Edition
The Kettle Valley
Rail Trail is one of the longest and most scenic biking and hiking trails in
Canada. It covers a good stretch of the south-central interior of British
Columbia, about 600 kilometers of scenic countryside. British Columbia is one
of the most beautiful areas of Canada, which is itself a beautiful country,
ideal for those who appreciate natural splendour and achievable adventure in
the great outdoors.
The trail passes through a great variety of geographical and geological regions, from mountains to valleys, along scenic lakes and rivers, to dry near-desert condition grasslands. It often features towering canyons, spanned by a combination of high trestle bridges and long tunnels, as it passes through wild, unpopulated country. At other times, it remains quite low, in populated valleys, alongside spectacular water features such as beautiful Lake Okanagan, an area that is home to hundreds of vineyards, as well as other civilized comforts.
The trail is a nice test of one’s physical fitness, as well as one’s wits and adaptability, as much of it does travel through true wilderness. The views are spectacular, the wildlife is plentiful and the people are friendly. What more could one ask for?
What follows is a journal of two summers of adventure, biking most of the trail in the late 1990s. It is about 33,000 words in length (2 to 3 hours reading), and contains numerous photographs of the trail. There are also sections containing a brief history of the trail, geology, flora and fauna, and associated information.
The trail passes through a great variety of geographical and geological regions, from mountains to valleys, along scenic lakes and rivers, to dry near-desert condition grasslands. It often features towering canyons, spanned by a combination of high trestle bridges and long tunnels, as it passes through wild, unpopulated country. At other times, it remains quite low, in populated valleys, alongside spectacular water features such as beautiful Lake Okanagan, an area that is home to hundreds of vineyards, as well as other civilized comforts.
The trail is a nice test of one’s physical fitness, as well as one’s wits and adaptability, as much of it does travel through true wilderness. The views are spectacular, the wildlife is plentiful and the people are friendly. What more could one ask for?
What follows is a journal of two summers of adventure, biking most of the trail in the late 1990s. It is about 33,000 words in length (2 to 3 hours reading), and contains numerous photographs of the trail. There are also sections containing a brief history of the trail, geology, flora and fauna, and associated information.
After reading this account, you should have a good sense of
whether the trail is right for you. If you do decide to ride the trail, it will
be an experience you will never forget.
Amazon U.S.: https://www.amazon.com/dp/B01GBG8JE0
Amazon U.K.: https://www.amazon.co.uk/dp/B01GBG8JE0
Amazon Germany: https://www.amazon.de/dp/B01GBG8JE0
Amazon Canada: https://www.amazon.ca/dp/B01GBG8JE0
Amazon Australia: https://www.amazon.com.au/dp/B01GBG8JE0
On the Road with Bronco Billy
Spring is on us now, and that brings on thoughts of ROAD TRIP. Sure, it is still a bit early, but you can
still start making plans for your next road trip with help of “On the Road with
Bronco Billy”. Sit back and go on a ten
day trucking trip in a big rig, through western North America, from Alberta to
Texas, and back again. Explore the
countryside, learn some trucking lingo, and observe the shifting cultural norms
across this great continent. Then, come
spring, try it out for yourself.
Amazon U.S.: http://www.amazon.com/gp/product/B00X2IRHSK
Amazon U.K.: http://www.amazon.co.uk/gp/product/B00X2IRHSK
Amazon Germany: http://www.amazon.de/gp/product/B00X2IRHSK
Amazon Canada: http://www.amazon.ca/gp/product/B00X2IRHSK
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