“Nonetheless, fully vaccinated individuals with breakthrough infections have peak viral load similar to unvaccinated cases and can efficiently transmit infection in household settings, including to fully vaccinated contacts.”

 

https://www.theguardian.com/world/2021/oct/28/covid-vaccinated-likely-unjabbed-infect-cohabiters-study-suggests

People who are fully vaccinated against Covid yet catch the virus are just as infectious to others in their household as infected unvaccinated people, research suggests.
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https://www.abc10.com/article/news/health/coronavirus/vaccinated-can-spread-delta-variant-at-home-study/507-54517b00-63b5-437e-a808-b1e61fd67d53

“Nonetheless, fully vaccinated individuals with breakthrough infections have peak viral load similar to unvaccinated cases and can efficiently transmit infection in household settings, including to fully vaccinated contacts.”