Covid19 Vaccines Effect on Case Fatality Rates – Suddenly, then Gradually
Since I live in Alberta, Canada, I am particularly interested in the Covid19 situation in that province. Nonetheless, there are a lot of Covid commonalities around the world, so I tend to think that understanding the dynamics of the pandemic and the ensuing vaccination roll-outs in one place can be of more general interest (i.e. what works in one place will generally work in others). There are some caveats to that, of course. The level of economic development of an area will affect the pandemic’s development, as will other factors such as governmental form, weather and latitude.
Hemingway had one of his characters explain the process of going bankrupt as “gradually, then suddenly”. Flipping that expression on its head, we can say that the reduction in Covid deaths in Alberta due to the vaccination rollout could be described as “suddenly, then gradually”. That effect can be seen in the accompanying graph, which shows a rapid reductions in deaths as the percentage of the population that had been vaccinated went from 0 to about 8%, then reduced in a much more gradual maner. Applying a logarithmic function to the data yields a very good fit, with an R-square of about 0.81. That’s the percentage of variance in the data that can be explained by the fitted function. Another way of expressing that is by noting that the data points tend to be pretty close to the fitted line.
An alternative way of looking at the data is to break it up into two distinct phases. In statistics this is known as a “piecewise smooth” fit. In that case we have two linear functions, as in the second graph, with the first line having a very good fit (R-square = 0.73) and the second line having a much looser fit (R-square = 0.19). The logarithmic fit is also shown on the graph (in red) for comparison.
The reason for the two distinct phases of the vaccine roll-out’s effect on Covid Case Fatality Rates is that the most vulnerable groups were vaccinated earliest, and thus the effect on deaths was quite dramatic during that phase. The Case Fatality Rate by Age is shown in the third graph. As you can see, it is dominated by the older groups, especially the 70-79 and 80+ age groups. Conversely, there were very few deaths among those under 50, with 0 deaths in the under 20’s.
In Alberta, as was common in most countries, the older groups were vaccinated first. The rollout looked something like the table below (note that due to supply constraints and other factors, there was some deviation, but this was the general idea):
· January: Ages 75+. Special arrangements were made for those in nursing homes.
· March 15: Ages 65-74.
· April 30: Ages 50-64
· April 6: Ages 40+
· May 6: Ages 30+
· May 10: Ages 12+
And from the next graph, you can see that the 8% vaccination level (i.e. the inflection point on the Vaccination Rate vs Case Fatality Rate) does occur at about the 15th of March.
The Alberta government doesn’t make the vaccination rates by age public, but you can use this data to get a pretty good guess of what they are probably like. In fact, if you constrain the problem with an overall vaccination rate of about 25% and a case fatality rate of about 0.25% (the numbers in mid-April 2021), a likely solution is given by a vaccination by age rate something like this:
Under 1 year: 0%
1-4 years: 0%
5-9 years: 0%
10-19 years: 0%
20-29 years: 5%
30-39 years: 10%
40-49 years: 25%
50-59 years: 45%
60-69 years: 55%
70-79 years: 80%
80+ years: 90%
Of course, a lot of other possible vaccination by age distributions will also work, but this one is pretty likely, based on the actual age-based vaccine rollout.
One other interesting, if highly speculative, exercise is to project these trends forward and see where the near-zero Case Fatality Rate is likely to be. While this isn’t herd immunity, it might be called Case Fatality Rate herd immunity. And it is a pretty important measure – once a society has cut its Covid deaths to near zero and also brought the case count way down, it should be able to go back to normal, for the most part.
The graph shows that the Case Fatality Rate should be very close to zero once the vaccination rate goes to somewhere between 50% and 60%, depending on whether you prefer the logarithmic function or the piecewise linear function. This assumes that the oldest groups continue to get at least some priority in vaccinations. It also assumes that the vaccines continue to protect against fatal results, with no extra-lethal variants evolving.
If current vaccination trends continue, that should happen at about mid-June 2021.
Sources:
https://www.alberta.ca/stats/covid-19-alberta-statistics.htm
https://www.worldometers.info/coronavirus/#countries
https://github.com/owid/covid-19-data/tree/master/public/data/vaccinations
Some earlier Covid-19 blogs:
https://dodecahedronbooks.blogspot.com/2021/03/covid-19-vaccines-positive-results-from.html
https://dodecahedronbooks.blogspot.com/2021/03/covid-19-vaccines-how-successfully-are.html
https://dodecahedronbooks.blogspot.com/2020/12/covid-19-vaccines-comparison-of.html
https://dodecahedronbooks.blogspot.com/2020/09/covid-19-continues-to-travel-around.html
https://dodecahedronbooks.blogspot.com/2020/07/has-covid-19-become-less-deadly.html
https://dodecahedronbooks.blogspot.com/2020/07/july-2020-update-covid-19-death-rates.html
https://dodecahedronbooks.blogspot.com/2020/05/covid-19-death-rates-correlate-highly.html
https://dodecahedronbooks.blogspot.com/2020/06/covid-19-impact-on-employment-no-impact.html
https://dodecahedronbooks.blogspot.com/2020/04/is-there-model-that-can-predict-when-to.html
https://dodecahedronbooks.blogspot.com/2020/03/estimating-fatality-rate-of-coronavirus.html
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And, here’s a more pleasant travel story than anticipating the worldwide journey of a virus.
A Drive Across Newfoundland
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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.
A Ride on the Kettle Valley Rail Trail: A Biking Journal Kindle Edition
by Dale Olausen(Author), Helena Puumala(Editor)
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.
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
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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
