In another statement on Thursday, the university said it had cleared 43 more students and two faculty members, reducing the number of people under quarantine there to 82.

“We expect the trend to continue as more people provide proof of immunization or are shown by tests to have immunity to measles,” the university said.

Quarantine orders can last up to 21 days from the date of possible exposure. The quarantine period for U.C.L.A. ends on April 30, and the one for California State-Los Angeles, ends on May 2, the Los Angeles County Department of Public Health said Thursday.

The department believes additional measles exposures may have occurred this month at Los Angeles International Airport and at several restaurants near Glendale.

Measles is an extremely contagious virus that can cause serious respiratory symptoms, rash and fever. In some cases, especially in babies and young children, the consequences can be severe. Pneumonia and encephalitis — swelling of the brain — are the most common severe complications.

A single case of the measles can quickly spiral into an outbreak, especially because people might not know they have the illness for several weeks before they begin to show symptoms.

People who do contract measles often seek medical care at hospitals, where they can potentially transmit the illness to other patients, especially those with compromised immune systems. Infants typically do not receive measles vaccinations until they are about 1 year old and therefore are highly vulnerable. Some older people are also at high risk, as are patients who take medication that affects the immune system, like those being treated for arthritis.