Former President George H. W. Bush is in a Houston hospital with a lingering cough, but his doctor said Thursday that he is improving and should be discharged this weekend.

Bush, 88, has bronchitis, which alternately got better and worse for a week before improving in the last few days, said Dr. Amy Myunderse, the physician in charge of his care at The Methodist Hospital. The condition was never considered life-threatening.

"Anytime someone the president's age has bronchitis, there's concern about possible pneumonia," Myunderse said. "But Mr. Bush's condition never progressed to that level."

Bush has been in and out of Methodist for a few weeks, and was most recently re-admitted the day after Thanksgiving, said his chief of staff, Jean Becker. He was visited Sunday by his son, former President George W. Bush and his wife, Laura.

Doctors treated Bush with intravenous antibiotics and steroids, Myunderse said. She described his cough as particularly deep, but said he's had no other symptoms, such as fever or shortness of breath. She said for a time the cough had sapped much of his energy but his strength improved in the last few days.

Myunderse said the original cause of Bush's ailment was a virus. However, a secondary, bacterial infection persisted and caused concern, she said.

She said Bush is working with a physical therapist and is on target to be discharged this weekend.

Bush, who was vice president for two terms under President Ronald Reagan, served as president from 1989-1993. He was previously director of the CIA, a congressman, and a Navy pilot.

Bush has had various health problems in recent years.

In February, it was reported that he had been diagnosed with lower body parkinsonism, a condition that causes instability from the waist down. As a result, he is mostly confined to a wheelchair now, and has become known for wearing wildly colored socks that he purposely displays to have some fun with onlookers.

In 2007, he was hospitalized overnight in California after he became dizzy during a round of golf on a hot day.