This article out of Michigan is nicely done:
In the last 30 days, vaccinated individuals in Michigan have represented 28.1% of hospitalizations, and nearly 15.4% of COVID-19 deaths, according to data from the Michigan Department of Health and Human Services. That’s 6,151 out of 26,272 total cases, 198 out of 704 total hospitalizations, and 10 out of 65 deaths.
But it’s important to look at those numbers in context: Age remains the biggest risk factor for COVID hospitalization and death, and 82.5% of Michigan residents age 65 and older are fully vaccinated. That means the people at biggest risk of death and hospitalization are also people most likely to be inoculated.
Here’s how that can impact the numbers, assuming a variant that can hospitalize 750 of 1,000,000 unvaccinated persons in a week (the current COVID hospitalization rate in Florida), and a vaccine that is 95% effective against hospitalization.
In a population of a million people where half are vaccinated, that means 375 of the 500,000 unvaccinated people are hospitalized with COVID and 19 of the 500,000 who are vaccinated. That’s a total of 394 hospitalizations -- with 356 hospitalizations prevented by vaccination -- and the vaccinated persons comprise 5% of the hospitalizations.
If 90% of the population is vaccinated, than 75 of the 100,000 unvaccinated people are hospitalized and 34 of the 900,000 who are vaccinated. That’s a total of 109 hospitalizations with 641 hospitalizations prevented by vaccines. Yet now almost half of the total hospitalizations are fully vaccinated persons.
The math shows the vaccines undeniably worked: Hospitalizations are way down, even as the number of fully vaccinated persons who are hospitalized increases, both in raw numbers and in percentage of total cases.
Bottom line: As vaccination rates rise, expect an increase in breakthrough cases, hospitalizations and deaths.