The vaccination strategy for COVID-19 in the Netherlands is to vaccinate the people with the highest risks first. These are our elder and people with underlying health problems. Also see gezondheidsraad, in dutch. With an exception to nurses who are directly in contact with corona patients, the first people to be vaccinated are people with underlying health problems, followed by age 90+, then 80-90, etc. Other countries seem to follow the same approach. In the UK a 91 old woman was the first to receive a COVID-19 vaccine. A 101 year old woman in Germany was among the first to get a vaccine as well.

What would be the vaccination strategy if instead of vaccinating the people with the highest risks first? We would vaccinate to reduce the pressure on the hospitals as fast as possible, but with the probable trade-off that more susceptible people will get COVID-19. In order to find such a strategy we need to compute the following probability: what if you take a person randomly (possibly to be vaccinated) of gender $G$ and in the age group $A$. What is the probability that this person can get COVID-19 and is hospitalized $H$ for corona? According to this alternative strategy, the group $(G, A)$ with the highest probability should be the group to be vaccinated first. Mathematically we have to compute $P(H|G,A)$.

Using Bayesians rule we have
$$
P(H|G,A) = \frac{P(H,G,A)}{P(G,A)} = \frac{P(H)P(G|H)P(A|G,H)}{P(G,A)}.
$$

Because I don’t know the exact distributions of $H$, $G$, and $A$, I have to approximate the probabilities with counting. These calculations are subjective, and there are other, probably better, ways of approximate the true values. Data of all COVID-19 patients is openly available on the site of RIVM. General information on population distribution can be found on the site of CVB. The probability to be hospitalized in the Netherlands $P(H)$ is immediately the most subjective to approximate. First, it’s time dependent. To keep it simple, $P(H)$ represents the probability that an random person gets hospitalized for corona this year. Do we know what the probability is to get corona and be hospitalized this year? I don’t know, because I cannot predict how COVID-19 will spread or mutate. The best I can do is to use the probability that I could have been hospitalized for corona last year:
$$
P(H) = \frac{\mathrm{number\ of\ people\ hospitalized}}{\mathrm{total\ number\ of\ people}}.
$$
Although $P(H)$ is likely to be estimated wrong, it won’t matter for the results. Because $P(H)$ is independent of $G$ and $A$ the results will have no effect on the final conclusion, i.e. absolute the probabilities might be off, but not relatively. If the probability of being hospitalized for corona $P(H)$ will be different from my approximation, the overall burden on healthcare will change, but it won’t effect the relative pressure per gender and age group. Next, if being hospitalized, the probability of you being male or female:
$$
P(G|H) = \frac{\mathrm{hospitalized\ gender\ G\ patients}}{\mathrm{total\ hospitalized\ patients}}.
$$
The age groups we’re considering are 0-9, 10-19, 20-29, 30-39, 40-49, 50-59, 60-69, 70-79, 80-89, and 90+. If being hospitalized and of gender $G$, probability of being in age group $A$.
$$
P(A|G,H) = \frac{\mathrm{number\ of\ hospitalized\ gender\ G\ patients\ of\ age\ group\ A}}{\mathrm{total\ hospitalized\ gender\ G\ patients}}.
$$
Probability $P(A,G)$ of being gender $G$ and of age group $A$ is computed directly from the CVB population distribution.

Filling in the details, with data used on 23th of January 2021, yield the following results

Some interesting remarks:

• There is a large difference between male and females. All males above 40 burden the healthcare more than their female counterpart.
• To release pressure from healthcare the best group to vaccinate first are males between 90+. Next are males between 80 and 90. Then males between 70 and 80. And after that females between 80 and 90.
• Notice that vaccinating males between 70 and 80 releases more pressure from healthcare than vaccinating 90+ females.

Note that I’m not claiming that we should change our strategy. I only want to show that there is a difference, with respect to vaccinating, between protecting the weakest first and releasing pressure on healthcare.