Investigators believe “Today” show co-host Savannah Guthrie‘s mom, Nancy Guthrie, is “still out there” as the high-profile search in Arizona continues without a suspect identified in the case, Pima County Sheriff Chris Nanos said Thursday. The FBI also announced a $50,000 reward for information.

A ransom note that investigators said they’re taking seriously included a deadline of 5 p.m. Thursday, Heith Janke, the special agent in charge of the FBI’s field office in Phoenix, told reporters during a news conference.

“If a transfer wasn’t made, then I think a second demand was for next Monday,” Janke said. He said he wouldn’t provide details about what the note said would happen if the demands weren’t met.

Separately, an alleged imposter was arrested for making a phony ransom demand in the case, Janke said.

Nanos provided new details about what investigators have uncovered since Nancy Guthrie, 84, was last seen when she was dropped off at her Tucson, Arizona, home Saturday night after dining with family. Investigators believe Guthrie was taken from her home over the weekend and have been investigating her disappearance as a crime.

A doorbell camera at Guthrie’s home was disconnected at approximately 1:47 a.m. Sunday, Nanos said. At around 2:12 a.m., one of her home’s cameras detected what the system classified as a person, but Nanos said investigators and analysts haven’t been able to recover footage of that from the system, and it’s possible what was detected could have been an animal. At about 2:28 a.m., Guthrie’s pacemaker disconnected from an app on her cellphone.

Detectives returned to Guthrie’s neighborhood Wednesday to conduct some follow-up work at her home and in the area, the Pima County Sheriff’s Department said. Guthrie was last seen at her home Saturday night after having dinner at the home of her other daughter, Annie Guthrie, and being driven home by her husband, Tommaso Cioni, Nanos told CBS News.

The sheriff’s department has said neither a suspect nor person of interest has been identified in the case.

Nancy Guthrie needs daily medication, adding more urgency to the search. Nanos dismissed the possibility that she may have wandered off, saying she doesn’t have cognitive issues and her mobility is limited.

In an emotional social media video posted Wednesday, Savannah Guthrie said her mother’s heart is fragile and that she lives in constant pain and needs her medicine to survive.

Savannah Guthrie also spoke directly to her mother’s possible abductors.

“We are ready to talk, however, we live in a world where voices and images are easily manipulated,” she said. “We need to know, without a doubt, that she is alive and that you have her. We want to hear from you, and we are ready to listen. Please, reach out to us.”

She also addressed the ransom note, saying the family was doing everything they can to bring her home.

Savannah Guthrie appeared with her brother and sister in the video, and they all spoke to their mother.

“You are a strong woman, you are God’s precious daughter, Nancy,” Savannah Guthrie said. “Mama, if you’re listening, we need you to come home, we miss you,” Annie Guthrie said. “We love you, Mom, stay strong, come home,” her brother Charles Camron Guthrie said.

The FBI, which has been helping the sheriff’s department, was sending additional personnel to assist in the investigation, CBS News learned Wednesday.

President Trump said on social media that he spoke with Savannah Guthrie. “We are deploying all resources to get her mother home safely,” Mr. Trump wrote on his Truth Social platform. “The prayers of our Nation are with her and her family.”