A recent study demonstrated that following breakthrough infections in individuals receiving two mRNA COVID vaccines, qualitative recovery of virus from the nasopharynx was reduced to 21 percent compared to 40 percent for non-vaccinated or partly vaccinated individuals. There was no significant difference in the quantum of viral recovery between the 72 vaccinated and 53 unvaccinated subjects.
The study also determined that protection waned approximately five months after completing a two-dose regimen of mRNA vaccine confirming the need for a booster dose that has shown to be effective in Israel and the U.K. A third dose effectively represents a "fully vaccinated" status. 
This will clearly reduce the probability of breakthrough infections and dissemination of virus among those who received their second mRNA vaccine more than six months previously. Currently about 70 percent of the U.S. population has received two mRNA priming doses but only 32 percent have received an additional booster contributing to enhanced and durable immunity
*Pena-Hernandez, M.A. et al comparison of infectious SARS-CoV-2 from the nasopharynx are vaccinated and unvaccinated individuals. MedRxiv (2021) doi.org/10.1101/2021.12.28.21268460