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And once the pandemic is over, how will we assess the impacts and losses? How will we develop a plan of action? The Periscope project brings together the best scientists and experts from 32 European universities, research institutes and think tanks. Gazeta Wyborcza is the only medium cooperating with them. The Periscope project is funded by the European Commission under the Horizon2020 programme.

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Prof. Claudius Gros of the Institute for Theoretical Physics at Goethe University in Frankfurt and Dr Daniel Gros of the Centre for European Political Studies in Brussels are brothers who form an interdisciplinary scientific team.

They have recently derived a mathematical relationship to estimate the rate of vaccination needed to stop the increase in the number of hospitalizations and deaths due to COVID-19.

They have presented the details of their analysis in a publication titled: "How fast do vaccination campaigns need to proceed to outpace the growing number of COVID-19 infections?" They demonstrate that with timely vaccination of the oldest age groups, restrictions can be loosened and lockdowns avoided. Even if the epidemic was still trending upward.

Protect the oldest as soon as possible

The researchers begin with a reminder that COVID-19 primarily threatens the elderly. That's according to hospitalization and death statistics released by the U.S. CDC, among others.

A meta-analysis published by the European Journal of Epidemiology has found that the risk of death from coronavirus infection increases exponentially with age. It doubles for an age difference of about 5.7 years. Namely, for 10-year-olds it is barely 0.002 percent. For 25-year-olds - 0.01 percent, but for 55-year-olds - 0.4 percent, 65-year-olds - 1.4 percent, 75-year-olds - 4.6 percent, and 85-year-olds - as much as 15 percent.

Based on this, the researchers estimate that if the entire German population was infected with the SARS-CoV-2 coronavirus, as many as 1.5 million people over the age of 60 would die, "only" 75,000 of younger people.

Thus, if we want to avoid high mortality and overloading the health care system with severe cases of COVID-19 (i.e., we are trying to "flatten the curve"), the oldest age groups should be vaccinated first. Seniors from the 60+ age group currently represent 26 percent of the European Union population (the lowest percentage in Ireland - about 20 percent, the highest in Italy - 29 percent, in Poland - about 24 percent). As the authors of the paper estimate, vaccinating roughly a quarter of the EU population would prevent up to 95% of deaths!

How to control the epidemic without lockdown?

In their work, the Gros brothers also ask whether it is possible to lift restrictions or at least partially loosen them early in a vaccination campaign. This is an important question for policymakers who must weigh the economic and social costs of lockdowns.

Germany derives a formula to estimate at what vaccination rate the health costs associated with new infections (proportional to hospitalizations and deaths) will not increase exponentially, threatening the collapse of the health care system.

Indeed, a properly conducted vaccination campaign can serve a similar function as a lockdown - to slow and ultimately stop the spread of the SARS-CoV-2 virus.

- We analyze the consequences of a "top-down" vaccination strategy, i.e., from the oldest to the youngest. The key point of our analysis is that vaccination not only reduces the reservoir of those susceptible to infection but also quite fundamentally the risk of death for the population not yet vaccinated. This leads to our model, Professor Daniel Gros told Wyborcza.

The formula determines the minimum speed that a vaccination campaign must have to stop the increase in COVID-19 fatalities. It has the form as below:

With “v” being the fraction of seniors 60+ vaccinated (“v” with a dot denotes the change in this fraction over time, i.e. the rate of vaccination) and “I” being the number of new infections (similarly, “I” with a dot denotes the change over time, i.e. the rate of increase in infections).

It looks complicated, but it can be reduced to a simple practical rule that goes like this:

If the number of new infections increases by X percent from week to week, then to prevent an increase in deaths, X*f/100 percent of the entire 60+ population must be vaccinated during the same period. Here the factor “f” depends on the current fraction of those already fully vaccinated. - For example, if 10 percent of seniors are vaccinated, then “f” equals 8, if 16 percent, then “f” equals 10, Professor Gros explained to us. Let's calculate it with an example: when 16 percent of seniors are vaccinated, and the number of infections increases by 20 percent from week to week, the vaccination campaign should proceed so that the fraction of fully vaccinated seniors increases by 2 percent during the same time. (20*10/100 = 2).

Thus, by controlling the rate of vaccination itself, the number of hospitalizations and deaths can be limited and kept in check. And no more need for other additional physical constraints, i.e. lockdown

What could go wrong?

So much for the theory. In practice, of course, these conditions are not easy to meet, as exemplified by our country. The formula of German scientists is based on the assumption that we vaccinate down the age ladder, that is, starting with the oldest and not leaving too large a fraction unvaccinated in those most at-risk age groups.

Meanwhile, even though in Poland, enrollment for the vaccination of 70-year-olds began in the second half of January, currently still nearly half of them are not yet fully protected by the vaccination. There are even fewer in the 60-year-old group after two doses of the vaccine.

Another issue is the supply of vaccines. After the European Medicines Agency authorized vaccines, companies were quite slow to ramp up production. As a result, during the spring wave of infections, Europe did not have enough doses to "chase down" the pandemic according to the Gros brothers' model.

In another of their papers, the researchers suggest that vaccine contracts should include incentives for accelerated production, such as doses delivered earliest should be more expensive.

- The EU's contracts do not include incentives for companies to increase production as quickly as possible, said Prof Daniel Gros. These are fixed-price contracts - i.e. a dose delivered tomorrow has the same price as one delivered next quarter - which do not encourage producers to speed up delivery.

As the researchers show in their paper, without financial incentives, companies have opted for a slow linear increase in production. From a business point of view, this is optimal because it is expensive to ramp up production quickly. However, the result was that we did not have enough vaccines, the researchers add. Meanwhile, the Gros brothers point out in their analysis, it is fairly easy to design an optimal contract that matches the time-varying price of a dose with the social value of vaccination.

It is comforting to know that if variants of the coronavirus emerge or other bacteria attack us, we already know what to do. Battle-tested technologies offer hope that vaccines can be developed very quickly, and with their help - as German researchers show - epidemics can be kept under control.

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Translated by Chris Borowski

This is a translation of the article from April 26, 2021.

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