https://www.medrxiv.org/content/10.1101/2022.03.20.22272571v1.full.pdf

For first infections, 19% of cases were associated with hospital admissions.

For second infections, 17% of cases were associated with hospital admissions - not a very significant difference.

For third infections, 25% of cases were associated with hospital admissions.

The authors also found an 8x increase in reinfection during the beginning of Omicron, from November 2021 to January 2022. This was the highest raw increase in reinfections, but the highest rate was just at the beginning of the Delta wave in Spring, 2021.

The authors note that this data is a lower bound.

So not only does reinfection not give you protective immunity, it actually increases your chance of catching it again, and getting a more severe infection. This means that not only is the herd immunity strategy pointless, but it's also actually actively making things worse over time compared to not doing it. Shitty both in the short term and long term.

https://www.medrxiv.org/content/10.1101/2021.07.22.21260972v2.full.pdf

This study, combining 81 different studies in 22 different countries, reported a 3x increased hospital admission rate on reinfections, and a doubling of the number of patients who needed oxygen.