It’s a small change to the state’s policy on who must quarantine, but it saves Connecticut from an embarrassment that comes from a rising number of COVID cases.

Until now, anyone traveling from states with at least 10 new cases per day per 100,000 residents or a 5 percent positivity rate had to quarantine on entering Connecticut, or prove they were safe.

Lamont changed that “or” to an “and” on Monday — just as Connecticut passed the threshold of 10 cases per day per 100,000 people for the last seven days.

Lamont said the change is meant to narrow the list of states affected by the quarantine requirements, while also allowing officials to enforce mandates more effectively.

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“We brought the number of states that fall in that category from over 40 down to about 33, which is more manageable and we can be strict about enforcing that and make sure (travelers) test and quarantine and we hold them accountable,” Lamont said.

But if he hadn’t made the change, Connecticut would have had to quarantine itself — a conundrum many people have wondered about since the quarantine policy took effect.

As it stands now, the state is well below the 5 percent threshold, with a positive test rate of 1.9 over seven days, compared with an average of 5.3 percent across the nation— still one of the lowest rates of any state.

Connecticut has averaged 10.6 new cases per day per 100,000 residents for the last seven days. That is largely because this state reported 142,527 tests over the last week — one of the highest testing rates in the nation. Like Connecticut, the United States as a whole has seen rising numbers in the last month, with an average of 17 new cases per 100,000 in the latest figures.

On Monday, Connecticut’s positivity rate over the past seven days rose to 1.9 percent, up from the 1.7 percent reported on Friday.

There were also 12 new deaths reported, bringing Connecticut’s death toll to 4,554.

Connecticut surpassed 2 million cases over the weekend, logging a total of 2,037,017 tests in total, with 62,830 positive and confirmed cases. That’s a positivity rate of 3.1 percent, reflecting the huge spike in the spring.

Hospitalizations have also risen sharply to 195, from 110 two weeks ago.

Southeastern Connecticut has been the nexus of the spike in cases and briefly saw an increase in inpatients two weeks ago. But the vast majority of hospitalization increases has come in Fairfield, Hartford and New Haven counties.

Dan Haar contributed to this story