Here's what you need to know about COVID-19 breakthrough infections

Am I missing something here? From the article "estimated the rate of symptomatic breakthrough infections to be about 35,000 per week among 162 million fully vaccinated people in the U.S " which equates to 1in5000 infections.

Admittedly 16d prior (30 July 2021), but the following link has "97% of hospital admissions, and 99.5% of Covid deaths — are occurring among those who are not vaccinated "

We know that double-vaccines reduce the severity of illness - This is on to of the reduction in infections from the article, but running the maths...

The 7-day average of newly identified cases is 110k/ day or 770k/ week in America according to John Hopkins.
97% of hospital admissions are not double vaccinated, so 3% are double-vaccinated.
3% (assuming all testing positive and deemed themselves ill enough to need treatment)

of the 770k means around 23000 are experiencing serious illness that are double-vaccinated,

Livescience's article (link below) has "Because no vaccine is 100% effective, breakthrough infections have been expected from the start of the vaccine rollout. In the context of clinical trials, about 0.04% of people given the Pfizer vaccine got infected with SARS-CoV-2, versus about 0.07% with Moderna and 0.59% with Johnson & Johnson. "

I do not know the portion of the population that has each vaccine and do not have the time to, but lets use 0.1%.

770000*0.1%= 770/ week but I assume I do not understand efficacy and the impact on people.

What I am taking from this is, 35k are estimated to have breakthrough infections BUT 23k double-vaccinated are admitted to hospital every week.
We know the serious illness is significantly reduced, so how many on top of the 23k are having breakthrough infections?

The following link has a lot of writing, but included "In addition, English data found that the Oxford-AstraZeneca vaccine was 92% effective in preventing hospitalization after two doses. "

That would mean the 23k in hospital account for 8% of those that are infected... or 288750 infections amongst double vaccinated.

There are countless reasons to a potential discrepancy, but I do wonder how effective the first vaccines adminstered are now and it would explain the push for booster shots...

Take care people, the Winter will be very rough going if you rest on your laurels!