Rising percentages of fully vaccinated Covid-19 patients in hospitals are actually pretty good news
Lately, Covid-sceptics have begun gloating about the rising percentages of fully vaccinated people in the hospital wards. On closer inspection, however, one would almost wish they were higher yet.
When on Wednesday 14 October the European network RTL broadcasted that data from Dutch hospitals indicated that the large majority of covid-patients in them were unvaccinated, politician Fleur Agema replied on Twitter: “The real news is, of course, that a quarter of hospitalized Covid-19 patients is fully vaccinated” (my italics). This, in turn, provoked one “Aquarius” to suggest yet another satanic conspiracy to cover up the ineffectiveness of vaccines with “lies”. To prove his point he added the list below of Covid-19 hospitalizations at CWZ, a leading hospital in and around the Dutch city of Nijmegen, published by the immunologist prof. Theo Schetters of the University of Pretoria, S.A.:
Alas for the elusive Aquarius, there wasn’t a conspiracy to be seen — unless it was too well cloaked for anyone to find it. Agema, on the other hand, was absolutely right about that 25% being the real news. She just forgot to mention that it is actually damn good news, for it proves that the vaccines are effective and offer real protection. Here’s why.
Next to the rising percentages, Schetters’s little list comprised a second set of data: the absolute numbers of patients admitted to the hospital, in the column marked n, for number. And the two sets are essentially related.
To see this, we must first construct a model, a severely simplified representation of the real world. First, to dispense with decimals in our arithmetic, we suppose that the chance of anyone contracting Covid-19 is 10% per month — this is horrendously high, way worse than the actual infectiousness of any variant of the virus. We also accept that this percentage does not change over time, eliminating cumbersome complications like seasonal variability. Thirdly, we posit that every infection automatically entails hospitalization, so that the number of infections equals the number of hospitalized patients — once more, reality is thankfully not as bad. Finally, we’ll just ignore the immunizing effects of prior infections.
Now that we have constructed the stage, let the drama of the influence of vaccines and the degree of vaccination in the population begin! We’ll open with the rather widely believed Covid-sceptic scenario: the vaccines are ineffectual rubbish, offering no protection at all.
In this scenario, among every 1000 individuals we would expect to see about 100 new Covid-19 patients being admitted to hospital every month. Among them, the percentage of vaccinated people should closely mirror the actual level of vaccination among the population. However, this does not conform at all to the reality reflected in Schetters’s table. Admittedly the percentage of vaccinated patients is on the rise, but it does not anywhere near follow the general degree of vaccination. Meanwhile the number of patients treated at the Nijmegen hospital plummeted from 36 in August to just 9 in October, a staggering 75% decrease where no change at all is expected, since the vaccines change nothing. And no, herd immunity can’t explain these discrepancies, simply because far too few people have in reality been infected yet for it to become significant.
So let’s put on a radically different scenario, one in which vaccination is indeed effective, offering no less than 90% protection. Under these assumptions we begin to see meaningful effects even at modest levels of vaccination. Among every batch of 1000 people, once a mere 30% of the population has been jabbed, the unvaccinated, now numbering 700, will produce their usual 10% of infected individuals, resulting in 70 new patients. Of the rest, the 300 that have been vaccinated, only 3 will fall ill — 27 infections will have been successfully headed off by the body’s vaccine induced defences. So there will be only 73 new patients in all, and just over 4% of them will have been vaccinated.
As the level of vaccination approaches 60%, the effects increase from meaningful to outright impressive. Among 1000 people, the 400 remaining unvaccinated produce just 40 hospital cases, and the vaccinated 600 no more than 6. The total monthly toll is now down from 100 to a mere 46, but look at the percentage of hospital beds accommodating someone vaccinated: 13%, up from 4. The share of fully vaccinated people has more than tripled! And it gets worse. When the vaccination level reaches 90%, only 10 unvaccinated victims remain, as opposed to 9 vaccinated ones. Nine out of nineteen, that’s almost 50%! Once the vaccination level passes the 95% mark, there will be only 5 unvaccinated cases, far outnumbered by almost 10 vaccinated ones.
Finally, when everyone has been vaccinated, we shall find 100% vaccinated people in the hospitals, but there will be only 10 of them, down from 100.
This is very close to what Schetters’s table shows. In short, taking vaccines to actually work pretty good conforms far better to reality than supposing that they do not. That said, the percentage of vaccinated patient Schetters found in the CWZ hospital beds in October remains astonishingly high, but that can readily be explained by the fact that there were only 9 patients in all. With numbers that small, one accidental extra patient, or one lacking, has enormous arithmetic consequences. At the end of the day, reliable statistics remains a game of large numbers.
All ideological and conspiratorial blah-blah aside, the true heart of the matter lies with n, the number of actually suffering individuals. The lower it gets, the better, and vaccines turn out to be an effective means to that end. This is not a debatable opinion, but simple arithmetic. It’s the way things work. So Agema, Aquarius and all their sceptic sympathizers do well to go and get themselves inoculated.
