Police searching for a woman and four children abducted from their home over the weekend said they believed all five were still alive Monday but shed no light on their possible whereabouts.

An Amber Alert continued Monday for the children, ages 16 months to 9 years old, and their mother, 31-year-old Kimberly N. Walker, whom police believed were in extreme danger.

An arrest warrant with charges of attempted murder and several counts of confinement has been issued for Walker's ex-boyfriend, Jerry D. White, 30.

Police Detective Sgt. Bill Wargo said White has a criminal history that includes weapon charges and has spent time in prison.

"We believe he is armed and he is holding Miss Walker and her children against their will," Wargo said at a news conference Monday afternoon.

Police said White had been harassing Walker for several days and that her sister and her sister's boyfriend had decided to stay with her and the children. Walker called police Friday and said White had confined her in her car before stealing the vehicle, authorities said.

Police believe White broke into Walker's house about 2 a.m. Saturday and shot her sister's boyfriend, Lathie Turnage, 30, of Chicago, once in the face and once in the chest. White then held everyone captive until fleeing with Walker and their four children about 11:30 a.m., police said.

Wargo said police had received reports of possible sightings of Walker and her children from other Midwest law officers. He declined to elaborate.

"At this time we don't know where he's at," police Detective Sgt. Bill Wargo said of White. "We have several possibilities that we are looking into right now."

Police were especially concerned about the oldest child, 9-year-old Jaylan Walker, who has severe asthma and requires use of a ventilator every few hours, Wargo said. Jaylan's ventilator and inhalers for his asthma were left behind when the family disappeared.

"We're concerned about all four children, but Jaylan ups the ante a little bit with his medical condition," Wargo said. "We know he's not received that medical attention that he needs."

Wargo said Elkhart police, who are being helped in the investigation by the FBI, were checking drug stores in hopes of finding a clue to the family's whereabouts. They also are checking reports of stolen vehicles.

Walker's sister's car, in which the family was last seen, was found in a parking lot on the north side of the city on Sunday. Walker's vehicle also was found in the city.

Wargo said police were looking at all means of escape.

"We've looked at every possibility for somebody to get out of this area," he said.

Though police believe White might have fled to Chicago, where he has friends and family, Wargo said he is just as likely to still be in the Elkhart area.

A cousin of Jerry White told the Chicago Tribune that White had not contacted family members.

"We are all trying to locate him and let him know that he is welcome to contact us in some kind of way," said Brenda White, 45, of Chicago. "... We want to take him to the police to get this over with.

"We want to find Jerry safe and sound. We are afraid the worst will happen to him on the street."

Brenda White said her cousin is not violent.

"They are saying that Jerry is armed and dangerous. Not Jerry," she said. "He would not harm anyone."

A two-member rapid response team from the National Center for Missing & Exploited Children is helping police answer phones to free manpower for the investigation.

The other missing children are Justin Walker, 8; Kyara Walker, 6; and 16-month-old Kayla Walker.