Everyone knows people who have become ill with COVID-19 even after vaccination or previous infection, especially with Omicron, which continues to circulate with high transmissibility.
These are called “breakthrough infections”. We do not have a vaccine that will completely eliminate the transmission of the virus, but transmissibility can be reduced by getting vaccinated and boosted.
A study completed in 2022 in California prisons found that among people with COVID-19, those who received at least one dose of vaccine were 24% less likely to spread the virus than unvaccinated individuals were. Those with a previous infection were 21% less likely to spread the infection than those with no previous infection. And those who had been both vaccinated and previously infected were 41% less likely to spread the virus to close contacts compared with individuals who had no previous vaccination or infection. Each dose of vaccine further reduced the risk of passing on the virus by an additional 12%.
How recently a person was vaccinated makes a difference, because the protections provided by vaccine and previous infection begin to fade over time.