As in Europe, the US is currently experiencing a surge in Covid-19 cases and hospitalizations driven by transmission among the unvaccinated. Two days ago, health officials in Vermont noted that 90% of Covid cases in Intensive Care Units are unvaccinated. Currently 74% of the Vermont population is fully vaccinated. This information allows us to do a simple calculation using only high school algebra to estimate the difference in risk of severe Covid infection among vaccinated compared to unvaccinated.
Let us say the infection rate among the unvaccinated is I and the relative risk of severe infection in vaccinated versus unvaccinated is R. So the infection rate among the vaccinated is R*I.
Let us assume a population of 100 in which 74 are vaccinated and 26 are unvaccinated. Then the number of severe infections requiring admission to ICU is 26*I unvaccinated and 74*R*I vaccinated. So the proportion of ICU cases who are unvaccinated is 26*I /( 26* I + 74 *R*I), and we know that this ratio is 0.9. So we can write:
26*I / ( 26* I + 74 *R*I) = 0.9
Solving this equation for R:
26* I = 0.9 * (26*I + 74 *R*I)
or 26 = 23.4 + 66.6*R
so R = (26-23.4)/66.6 = 0.039
Thus the vaccinated have a risk of severe Covid infection that is 3.9% of that for the unvaccinated. Inverting this, we can say that the unvaccinated have 1/0.039 = 25.6 times the risk of severe infection as the vaccinated. The actual risk will vary somewhat in populations with the mix of Covid variants and the overall time since vaccination, but the figures from Vermont graphically illustrate the huge protection that full vaccination provides. And the evidence is that this protection is definitely enhanced by getting a third booster shot.
A previous post I made on the importance of boosters attracted a couple of anti-vax comments claiming ^ that I was admitting the vaccine did not prevent Covid. I hope the simple analysis above of readily accessible data is adequate to clarify to anyone who thinks like this that the vaccine offers a huge level of risk reduction. And if you were vaccinated more than five or six months ago, get a booster! It improves the level of protection further.