This paper found a 0.65% re-infection rate in Denmark:
"Among eligible PCR-positive individuals from the first surge of the epidemic, 72 (0·65% [95% CI 0·51-0·82]) tested positive again during the second surge compared with 16 819 (3·27% [3·22-3·32]) of 514 271 who tested negative during the first surge (adjusted RR 0·195 [95% CI 0·155-0·246]). Protection against repeat infection was 80·5% (95% CI 75·4-84·5). The alternative cohort analysis gave similar estimates (adjusted RR 0·212 [0·179-0·251], estimated protection 78·8% [74·9-82·1])."
This paper indicates 95% efficacy due to natural infection for at least seven months in Qatar:
"Reinfection is rare in the young and international population of Qatar. Natural infection appears to elicit strong protection against reinfection with an efficacy ~95% for at least seven months."
Relative risk is still in favor of being vaccinated: "In addition to not knowing the clinical course of reinfection, we do not know the variants' role in reinfection – primarily because they were not known to be “in play” during the study period. Overall, natural immunity is protective. Perhaps not as protective as vaccination. More importantly, vaccination comes with a far lower risk of morbidity (hospitalization) or death."
"Among eligible PCR-positive individuals from the first surge of the epidemic, 72 (0·65% [95% CI 0·51-0·82]) tested positive again during the second surge compared with 16 819 (3·27% [3·22-3·32]) of 514 271 who tested negative during the first surge (adjusted RR 0·195 [95% CI 0·155-0·246]). Protection against repeat infection was 80·5% (95% CI 75·4-84·5). The alternative cohort analysis gave similar estimates (adjusted RR 0·212 [0·179-0·251], estimated protection 78·8% [74·9-82·1])."
https://pubmed.ncbi.nlm.nih.gov/33743221/
This paper indicates 95% efficacy due to natural infection for at least seven months in Qatar:
"Reinfection is rare in the young and international population of Qatar. Natural infection appears to elicit strong protection against reinfection with an efficacy ~95% for at least seven months."
https://pubmed.ncbi.nlm.nih.gov/33937733/
Relative risk is still in favor of being vaccinated: "In addition to not knowing the clinical course of reinfection, we do not know the variants' role in reinfection – primarily because they were not known to be “in play” during the study period. Overall, natural immunity is protective. Perhaps not as protective as vaccination. More importantly, vaccination comes with a far lower risk of morbidity (hospitalization) or death."
https://www.acsh.org/news/2021/03/24/how-protective-natural-...