Parents who were formerly on the state’s HUSKY A insurance will run out of time this week to transition to another insurance plan.

Out of the 13,800 parents receiving temporary insurance, nearly 4,400 had enrolled in new healthcare plans as of July 21. Another 9,400 still need to sign up.

Access Health CT said it’s holding enrollment fairs on Saturday, July 30, in Hartford, Bridgeport, New Haven, and Willimantic. Parents have until July 31 to sign up for a new plan, but after Saturday they will only be able to sign up online. The call center isn’t open on Sundays.

As part of the 2015 budget cuts, the HUSKY A plan ended for parents who fall into certain income levels.

The income threshold dropped from 201 percent to 155 percent of the federal poverty level — that’s an income range of $37,665 to $48,843 for a family of four.

Access Health CT has already sent letters and postcards to those impacted. It is also calling individuals reminding them to sign up for new insurance.

“We don’t want anyone to experience a gap in coverage,” Access Health CEO James Wadleigh said. “We know our outreach strategy is working, because we continue to see TMA [Transitional Medical Assistance] individuals enroll every day and every person who signs up for a new plan is considered a success.”