The (un)fair allocation of scarce vaccines and how maths can provide a solution

By Prof Carlos Alós-Ferrer

Prof Carlos Alós-Ferrer. Image: Nomis Foundation

The Covid-19 global vaccine roll-out is considered one of the greatest achievements in modern medical history, saving hundreds of thousands of lives. However, it was marred by decisions that saw those most in need of a vaccine in some countries wait too long, while those perceived to be least at risk getting them first. Now, Prof Carlos Alós-Ferrer of the University of Zurich writes about how he and his colleagues' latest research in Frontiers in Public Health shows that one maths procedure can ensure a fair distribution of scarce vaccines across the globe.

Remember when Covid-19 vaccines first became available? After many months of lockdowns and  increasing casualty rates, people across the planet were allowed to exhale a collective sigh of relief.  However, as is always the case when new vaccines are developed, there were not enough doses for all who wanted them. Rationing had to be imposed. Unfortunately, the rationing procedures violated elementary ethical principles, which might have led to some elderly and at-risk patients being neglected while younger, healthier citizens were already vaccinated.

How did it go wrong? Vaccine acquisition and allocation across the world was as centralized as possible, to avoid a free-for-all race where individual countries and regions tried to secure vaccines for its citizens to the detriment of others. The World Health Organization and other organizations supported a multi-country initiative called COVAX, the EU acted on behalf of all its member states, and large countries like the US took charge of distribution among their constituent states.

What these organizations apparently forgot was that, first, there is a large debate in medical ethics on what constitutes a fair and ethical allocation of vaccines, and, second, that there are scientists (mathematicians and economists) who study the allocation of scarce resources.

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Priority and equality

In the case of vaccines, two ethical principles are most important. First, there should be priorities. To avoid collapse, medical personnel should be immunized first. The elderly and those at higher risk should be inoculated before others. And so on. This principle, called ‘prioritizing according to needs’, requires that the priority classes (as decided by the competent medical authorities) should be respected, and immunization of a priority class should not start until those in previous priority classes have been inoculated.

Second, everybody within a given priority class should be treated equally. This principle, called ‘treating equal people equally’, requires that people with the same priority have the same chance of receiving the vaccine, irrespective of irrelevant factors as, say, in which country or state within the alliance they might reside.

My new article in Frontiers in Public Health, joint with J García-Segarra and M Ginés-Vilar, shows that the allocation of Covid-19 vaccines violated those principles. And not only in theory. For instance, the differences in vaccination rates for given priority classes in EU countries was astonishing. By the 12th week of 2021, the percentage of vaccinated healthcare workers (the highest priority class) was as high as 71.5% in Romania or 66.9% in Estonia and as low as 36.8% in Denmark or 21.5% in Iceland.

And that is ignoring special cases as Bulgaria, where vaccine hesitancy kept the rate even lower, or Hungary, which secured additional vaccines on its own. 10 weeks later, some EU-countries such as Spain and Belgium had received enough vaccines for all healthcare workers and all those aged 70 or older, while Denmark, France, and Greece only had received enough to immunize those older than 80. Such differences did not go unnoticed by the population either, as shown by a number of anecdotal cases of individuals crossing national boundaries to receive their vaccines earlier.

Why did this happen? The allocation protocols used by COVAX or the EU followed political criteria, but ignored scientific and ethical ones. Essentially, they divided the stock of available doses in lots proportional to the population of the member territories, and shipped lots to them with instructions to immunize people according to priorities. The problem is that the proportion of the priority classes is different in different territories.

Suppose two territories have the same population, so they will receive the same number of vaccines, say 500,000. The first territory has a relatively young population, with just 300,000 healthcare workers and elderly citizens, and hence will immunize all of them and start immunizing those with lower priority. The second territory has a relatively old population, with 700,000 healthcare workers and elderly people.

Hence it will not even have enough vaccines to immunize all the elder citizens. Even though both territories receive vaccine doses from the same alliance, 200,000 elder citizens in the second might be dying from lack of vaccines while 200,000 younger, healthier citizens are already vaccinated in the first territory.


How to allocate scarce vaccines

Did this need to happen? No. The problem can be solved using techniques from the mathematical social sciences. In our article, we have shown mathematically that there is one, and only one, way to allocate vaccines ensuring that, in multi-territory vaccine alliances, priority classes are respected and people within given priority classes are treated equally. The procedure, the ‘Priority-Equality Protocol’, is a bit more complex than the ones that were used for the case of Covid-19, but not exceedingly so.

First, one adds up the size of the priority classes across territories, eg how many healthcare workers, elderly, etc, are there in the entire EU. Second, the stock of vaccines is allocated to the priority classes (not to the countries) proportionally to their size. Last, vaccinations are shipped to countries earmarked for the priority classes, proportionally to the size of those classes relative to the corresponding ones in other countries. For instance, the two territories in the example above would have received 300,000 and 700,000 vaccines, respectively, corresponding to the number of healthcare workers and elder citizens.

Of course, administrative and logistical problems remain. However, what the maths says is that there is no other method respecting both ethical principles mentioned above. We all hope there will not be a next time, but, if there is, we now know better: the Priority-Equality Protocol is ready to use and any other protocol would (now knowingly) be a violation of elementary ethical principles.

Carlos Alós-Ferrer is a professor of decision theory and neuroeconomic theory at the university of Zurich (Switzerland), endowed by the Nomis foundation, and co-editor in chief of the Journal of Economic Psychology. A mathematician by training, he uses psychology, economics, and neuroscience to investigate how humans make economic decisions, and how those decisions could be improved. Born in Spain, he has been a professor at the Universities of Salamanca (Spain), Vienna (Austria), Konstanz (Germany), Cologne (Germany), and now Zurich. He maintains a blog at Psychology Today.

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