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Re:Comparing SARS-CoV-2 natural immunity to vaccine-induced ... by BuGGeH on Wednesday August 25, 2021 @09:03PM (#28309306)
From your same paper.

>These findings suggest that among persons with previous SARS-CoV-2 infection, full vaccination provides additional protection against reinfection

What "2.34 times" is referencing is two groups had COVID-19 but one of them got the vaccine as well. In which case the COVID-19 + Vaccine group has less chance of reinfection compared to those who only had COVID-19.

The original article does mention that COVID-19 + infection does provide more protection as well I believe.

Re:Comparing SARS-CoV-2 natural immunity to vaccine-induced ... by dataflow on Wednesday August 25, 2021 @09:16PM (#28309384)
You're only looking at "protection". It's not just about that individual. That's only half the story. Transmissibility is the other half.

Think about it this way: if we could tell already-vaccinated people to get COVID for extra reduction of transmissions (!), we would do that too. For obvious reasons, we don't do that. But this clearly doesn't apply in the reverse direction!