> The effect of infection is stronger wrt to spread for a few weeks or months but that difference isn't a long term thing. That's not how you reach herd immunity, it's how you reach seasonality.

The authors of that study said:

> Community immunity to control the SARS-CoV-2 epidemic can be reached with the acquired immunity due to either previous infection or vaccination.

I haven't seen anything yet that says protection after infection wanes all that much. I see a lot of "we don't know how long it will last", but it seems to last as long as we have data for so far.