Pope Francis is not “in danger of death,” but he’s also not fully “out of danger,” members of his medical team said Friday.

At a press conference in Rome’s Gemelli Hospital, Dr. Sergio Alfieri, the head of the team caring for the Pope, and Dr. Luigi Carbone, the vice-director of the Vatican’s health-care service, spoke for about 40 minutes to a roomful of journalists. The pair said they believed the Pope would be hospitalized for “at least” the entirety of the next week.

Alfieri emphasized that the Pope is not attached to a ventilator, although he is still struggling with his breathing and consequently keeping his physical movements limited.

Nevertheless, the physician said, the Pope is sitting upright in a chair, working, and joking as usual.

Alfieri said that when one of the doctors greeted the Pope by saying, “Hello, Holy Father,” he replied with, “Hello, Holy Son.”

Asked by a journalist what doctors’ greatest concern is, they noted that there is a risk that germs in the Pope’s respiratory tract might enter his bloodstream, causing sepsis.

Alfieri did say, however, that he was confident Pope Francis would leave the hospital at some point and return to Casa Santa Marta in the Vatican—with the proviso that when he does so, his chronic respiratory issues will remain.

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