Blair Fix

As 2021 comes to a close, I'm having a distinct sense of déjà vu. A year
ago, I [wrote a
post](https://economicsfromthetopdown.com/2020/12/28/as-2020-ends-lets-celebrate-science/){target="_blank"
rel="noopener"} celebrating COVID vaccines as a triumph of science. And
I noted that vaccine discovery is a *collective* endeavour. The
cumulative number of major vaccines tracks closely with the cumulative
number of scientific papers, a bellwether for humanity's collective
knowledge. Here's the trend:

[]{#fig-vax-papers}

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2021/12/vax_papers.png?w=723&amp;ssl=1"
decoding="async" data-recalc-dims="1" />
<figcaption>Figure 1: The cumulative number of major vaccines
tracks with the cumulative number of scientific papers. [<a
href="#sources-and-methods" target="_blank" rel="noopener">Sources and
methods</a>]</figcaption>
</figure>

This trend is a beautiful reminder that science is a social endeavour.
No matter how novel, every discovery builds on the work of others.
Science, in other words, is the quintessential public good. And so are
vaccines.

Looking at the roll out of previous vaccines, however, I noted a
perverse (but unsurprising) trend. Instead of chasing people, *vaccines
chase dollars*. Pick any vaccine you want, and you'll find that the
corresponding vaccination rate tracks with GDP per capita. Sadly, the
roll out of COVID vaccines is no exception. Here's the latest data:

[]{#fig-vax-gdp}

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2021/12/vax_gdp.png?w=723&amp;ssl=1"
decoding="async" data-recalc-dims="1" />
<figcaption>Figure 2: Total COVID vaccines administered vs. GDP
per capita. [<a href="#sources-and-methods" target="_blank"
rel="noopener">Sources and methods</a>]</figcaption>
</figure>

What I did not anticipate, back in December 2020, was that a significant
portion of rich-country citizens would choose to remain unvaccinated.
Although anti-vaxers are a source of frustration for those of us who
want to get on with a post-pandemic life, there is an upshot. It seems
plausible that by avoiding vaccines, rich anti-vaxers are freeing up
some supply for poor countries. In a year like 2021, you have to take
whatever solace you can get.

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You can use/share it anyway you want, provided you attribute it to me
(Blair Fix) and link to [Economics from the Top
Down](https://economicsfromthetopdown.com/).

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### Sources and methods {#sources-and-methods target="_blank"}

Data for the number of scientific papers comes from Sci-Hub, via
[Library Genesis](http://gen.lib.rus.ec/dbdumps/){target="_blank"
rel="noopener"}. The raw data comes as an SQL database dump. If you're
interested, I built an R function that can parse this data. Check it out
at [Github](https://github.com/blairfix/read_sql){target="_blank"
rel="noopener"}.

Data for new vaccine dates is from
[Wikipedia](https://en.wikipedia.org/wiki/Timeline_of_human_vaccines){target="_blank"
rel="noopener"}.

Data for COVID vaccination rates is from [Our World in
Data](https://ourworldindata.org/coronavirus){target="_blank"
rel="noopener"}. GDP per capita data is from the [World
Bank](https://data.worldbank.org/indicator/NY.GDP.PCAP.CD){target="_blank"
rel="noopener"}. For both sources, I've used the most recent data (in
each country) that is available.

As 2021 comes to a close, I’m having a distinct sense of déjà vu. A year ago, I wrote a post celebrating COVID vaccines as a triumph of science. And I noted that vaccine discovery is a

 collective

endeavour. The cumulative number of major vaccines tracks closely with the cumulative number of scientific papers, a bellwether for humanity’s collective knowledge.

COVID Déjà Vu

A hellish year is over and a vaccine is rolling out. Let’s be thankful for science.

We've finally reached the end of 2020, a year that many people are happy
to forget. In the history books, 2020 will be known for little besides
the Covid pandemic. Fortunately, the end of this disaster is in sight.
With multiple vaccines starting to roll out, it looks like 2021 will be
a better year.

Speaking of vaccines, I've been racking my brain to find things to be
thankful for this holiday season. It's not easy. My wife, daughter and I
are in lockdown in Toronto. The rest of our extended families are in
lockdown in Alberta and BC. So no family Christmas this year. I suspect
it's the same for many people. Fortunately, the Covid vaccine provides
some light at the end of the tunnel. This is something to celebrate. But
more than that, we should celebrate the whole enterprise that made the
vaccine possible --- *science*.

In the grand scheme of our species, it was not long ago that we believed
infectious diseases were caused by ['bad
air'](https://en.wikipedia.org/wiki/Miasma_theory){target="_blank"
rel="noopener"}. The idea that [germs cause
disease](https://en.wikipedia.org/wiki/Germ_theory_of_disease){target="_blank"
rel="noopener"} became widely accepted only in the late 19th century,
thanks largely to the work of [Louis
Pasteur](https://en.wikipedia.org/wiki/Louis_Pasteur){target="_blank"
rel="noopener"}. Vaccines are a [similarly
recent](https://en.wikipedia.org/wiki/Timeline_of_human_vaccines){target="_blank"
rel="noopener"} invention.

Our knowledge of infectious diseases is certainly something to
celebrate. But as a political economist, I can't help note how
vaccination is stubbornly related to social inequalities. Vaccines are
the ultimate public good --- a life-saving device that is the product of
our collective scientific effort. Predictably, though, this public good
is not shared equally. In the last mile, vaccines are paywalled by
private companies. So while in principle vaccines could be free for
every human, in practice they are not. The result is that vaccination
rates grow with income. The richer the country, the higher the
vaccination rate. Here's the relation in 1988.

[]{#fig-vac-1988}

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2020/12/vac_rate_1988-1.png?w=723&amp;ssl=1"
decoding="async" data-recalc-dims="1" />
<figcaption>Figure 1: Vaccination rates vs. GDP per capita in
1988. The vaccination rate is the share of one-year-olds
vaccinated against diphtheria, pertussis, and tetanus. (I’ve plotted the
vaccination rate on a reverse log scale, meaning it zooms in as
vaccination rates approach 100%.) [<a href="#sources-and-methods"
target="_blank" rel="noopener">Sources and methods</a>]</figcaption>
</figure>

Over the last 30 years, we've made progress in vaccinating the world's
population. Figure [2](#fig-vac-2017) shows the data in 2017. Relative
to 1988, the vaccination rate has increased across all countries. Still,
vaccination is a function of income. The richer the country, the more
people get immunized.

[]{#fig-vac-2017}

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2020/12/vac_rate_2017-1.png?w=723&amp;ssl=1"
decoding="async" data-recalc-dims="1" />
<figcaption>Figure 2: Vaccination rates vs. GDP per capita in
2017. The vaccination rate is the share of one-year-olds
vaccinated against diphtheria, pertussis, and tetanus. (I’ve plotted the
vaccination rate on a reverse log scale, meaning it zooms in as
vaccination rates approach 100%.) [<a href="#sources-and-methods"
target="_blank" rel="noopener">Sources and methods</a>]</figcaption>
</figure>

### Vaccines and cumulative scientific knowledge {#vaccines-and-cumulative-scientific-knowledge target="_blank"}

When a pharmaceutical company patents a new vaccine, the logic is that
they did the work ... so they should reap the reward. True, the company
probably did R&D and clinical trials. But this alone did not create the
vaccine. At every step, the company built on existing scientific
knowledge.

Take the Pfizer Covid vaccine. It's the first vaccine to [use RNA to
produce an immune
response](https://en.wikipedia.org/wiki/RNA_vaccine){target="_blank"
rel="noopener"}. That's a major achievement, but not one produced by
Pfizer scientists alone. Just understanding the [RNA
molecule](https://en.wikipedia.org/wiki/History_of_RNA_biology){target="_blank"
rel="noopener"} itself has been a century-long project that started in
the 1930s. Every aspect of the Pfizer vaccine probably has similarly
deep roots.

Vaccines are the product not of one company, but of our cumulative
scientific knowledge. Figure [3](#fig-article) shows a way to visualize
this fact. I've plotted here the growth of the cumulative number of
scientific papers published over the last three centuries. Think of this
corpus as humanity's accumulated knowledge. Along the curve, I've
labelled the dates of new vaccines. Unsurprisingly, new vaccines have
come as our scientific knowledge exploded.

[]{#fig-article}

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2020/12/article_cumsum-1.png?w=723&amp;ssl=1"
decoding="async" data-recalc-dims="1" />
<figcaption>Figure 3: Vaccines and the growth of cumulative
knowledge. I’ve plotted here the growth of the cumulative
number of scientific papers over the last three centuries. Along the
curve, I’ve labelled the timing of major new vaccines. (Note: the y-axis
uses a square-root scale.) [<a href="#sources-and-methods"
target="_blank" rel="noopener">Sources and methods</a>]</figcaption>
</figure>

True, only a tiny fraction of scientific papers are directly related to
immunology. But knowledge is like the tree of life. As you trace it
backwards, it becomes clear that there is only one tree. Here's a way to
think about it. Suppose that an article about a vaccine trial references
45 other papers. Each of these papers in turn cites 45 papers ... and so
on. At this rate, after 6 generations of articles the web of citation
reaches 83 million papers (45^6^). That's roughly the whole of the
scientific corpus.

Because vaccines are a product of our cumulative knowledge, the number
of major vaccines scales with the cumulative number of scientific
papers. Figure [4](#fig-vac-count) shows the trend.

[]{#fig-vac-count}

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2020/12/article_vaccine_count-1.png?w=723&amp;ssl=1"
decoding="async" data-recalc-dims="1" />
<figcaption>Figure 4: Cumulative number of major vaccines
vs. the cumulative number of scientific papers. (Note that I’ve
used a log scale on both axis.) [<a href="#sources-and-methods"
target="_blank" rel="noopener">Sources and methods</a>]</figcaption>
</figure>

What's interesting is that the trend is non-linear. The cumulative
number of vaccines grows roughly with the square root of the cumulative
number of papers:

::: {style="text-align:center"}
[ \displaystyle \text{number of vaccines} \propto \sqrt{\text{number of
papers}}]{.katex-eq katex-display="false"}
:::

What this means is that over time, producing new vaccines becomes more
knowledge intensive. That's not surprising. The first vaccine was
discovered by accident. In 1796, the British doctor Edward Jenner found
that getting infected with cowpox (a mild disease) conferred immunity to
smallpox. The [smallpox vaccine was
born](https://en.wikipedia.org/wiki/Smallpox_vaccine){target="_blank"
rel="noopener"}. (Side note: vaccines owe their name to this cowpox
discovery. The word 'vaccine' comes from *vacca*, the Latin word for
cow.)

As time went by, the development of new vaccines became less
serendipitous. The [polio
vaccine](https://en.wikipedia.org/wiki/Polio_vaccine){target="_blank"
rel="noopener"}, for instance, was a massive public health effort. In
1954, the Salk vaccine was tested on 1.8 million US children. That's
hardly a small-scale operation.

We see this kind of trend throughout science. Three centuries ago, Isaac
Newton did basic science using inclined planes. Today, physicists do
basic science using billion-dollar particle accelerators. As science
advances, new discoveries become more intensive, both in terms of
resources and prior knowledge.

And that brings me back to paywalls. It's a crime when vaccines get
paywalled in the last mile. But it's also a crime when *scientific
knowledge* gets paywalled. Here, however, we have something to
celebrate. In principle, the vast majority of scientific papers are
paywalled. But in practice, almost all scientific knowledge is freely
available on the internet. That's thanks largely to one renegade
scientist --- [Alexandra
Elbakyan](https://en.wikipedia.org/wiki/Alexandra_Elbakyan){target="_blank"
rel="noopener"}. She created the [Sci-Hub
database](https://sci-hub.st/){target="_blank" rel="noopener"} that now
houses more than 80 million scientific articles, all available for free.
It's these Sci-Hub papers that I've plotted in Figure [3](#fig-article).

As we head into 2021, let's be thankful for the Covid vaccine. But let's
also be thankful that for the first time in history, virtually all
scientific knowledge is available for free. That's something to
celebrate.

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[![](https://economicsfromthetopdown.files.wordpress.com/2021/03/by.png?w=150){.aligncenter
decoding="async"
recalc-dims="1"}](http://creativecommons.org/licenses/by/4.0/){rel="license"} 
This work is licensed under a [Creative Commons Attribution 4.0
License](http://creativecommons.org/licenses/by/4.0/){rel="license"}.
You can use/share it anyway you want, provided you attribute it to me
(Blair Fix) and link to [Economics from the Top
Down](https://economicsfromthetopdown.com/).

------------------------------------------------------------------------

### Sources and methods {#sources-and-methods target="_blank"}

Data for vaccination rates vs. GDP per capita is from [Our World in
Data](https://ourworldindata.org/vaccination){target="_blank"
rel="noopener"}.

Data for new vaccine dates is from
[Wikipedia](https://en.wikipedia.org/wiki/Timeline_of_human_vaccines){target="_blank"
rel="noopener"}.

Data for Sci-Hub papers by year is from [Library
Genesis](http://gen.lib.rus.ec/dbdumps/){target="_blank"
rel="noopener"}. The raw data comes as an SQL database dump. If you're
interested, I built an R function that can parse this data. Check it out
at [Github](https://github.com/blairfix/read_sql){target="_blank"
rel="noopener"}.

We’ve finally reached the end of 2020, a year that many people are happy to forget. In the history books, 2020 will be known for little besides the Covid pandemic. Fortunately, the end of this disaster is in sight. With multiple vaccines starting to roll out, it looks like 2021 will be a better year. Speaking of vaccines, I’ve been racking my brain to find things to be thankful for this holiday season. It’s not easy.

Messaggi di Rogue Scholar

COVID Déjà Vu

As 2020 Ends, Let’s Celebrate Science