Are you familiar with the term "almost mutually exclusive"?
So how does getting a vaccine once a year for 5 straight years mean the vaccine works?
And we're told it's spread to vaccinated children by sneezing adults.
Then we're told a booster shot is likely necessary.
Shouldn't the sneezing adults be spreading it to unvaccinated adults at work?
Isn't that how the flu is spread among adults?
I think you missed the main point because some of the ideas were not made explicit in the original quotes. Let me try: Older children caught the disease disproportionally because their immunity wore off; younger children, who had been vaccinated more recently, were protected. Thus another booster would help extend protection to older children. Adults, even less protected because their immunity wore off long ago, spread the disease to other adults (yes, exactly as you suggest), to older children whose immunity has lapsed, and to unvaccinated babies and younger children. A late booster would help everyone by enhancing the herd immunity. And even if you caught the disease, having been vaccinated reduced the symptoms.
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! See above.