Dr. Sharon Alroy-Preis, Israel's director of public health services, had some bad news and good news for CBS' John Dickerson on Sunday's edition of Face the Nation.

Preis told Dickerson that Israel, which has served as one of the best test cases for how COVID-19 vaccinations work in the real world because it vaccinated its population early and often, has found that about 50 percent of the people testing positive for COVID-19 right now are fully immunized, though she clarified that the vaccines are still highly effective at preventing severe disease. 

But even though the data suggest that breakthrough infections may become more common over time (in the U.S., they make up a far lower share of new cases), there's evidence that those individuals are not spreading the virus frequently or widely. Preis explained that, excluding instances of household spread, 80 percent of vaccinated individuals who have been infected have "zero contacts" that have been confirmed to have contracted COVID-19 because of their connection. About 10 percent of those vaccinated, infected individuals have just one contact who likely caught the virus from them, while fewer than 10 percent have more than one contact who later tested positive. "Their ability to infect others is 50 percent lower than those who are not vaccinated," Preis said.