Do you have any studies which you can point to that actually that demonstrate that "natural immunity provides a fraction of the immune response that being vaccinated does"?

From what I can tell even the CDCs latest online review, as of Oct 2021, doesn't have any evidence that one is better than the other in terms of antibodi titers [1] In fact the most recent CDC published studies, from this year, have shown naturally induced immunity to be superior to vaccine induced immunity in terms of both illness and death [2]

[1]https://www.cdc.gov/coronavirus/2019-ncov/science/science-br...

[2]https://www.cdc.gov/mmwr/volumes/71/wr/mm7104e1.htm?s_cid=mm...