But now the discovery of romantic YouTube videos featuring Patrick apparently addressing an unseen lover may prove to be the best leads so far in unraveling the mystery.
The 30-year-old doctor in residency at Western Michigan University vanished the evening of Dec. 5 after she tried to rent a hotel room at the Radisson in Kalamazoo, which can be verified by the hotel's security footage.
Two hours later, state police found her car abandoned 100 miles away in Indiana, her wallet and credit cards still inside, ABC News reports.
The last person to see the resident in psychiatry was the hotel shuttle driver, who took Patrick to her car at the Borgess Hospital in downtown Kalamazoo, where she worked. The driver said Patrick appeared anxious.
"She seemed as if she was looking around as if someone could be following her," Carl Clatterbuck, a private investigator hired by Patrick's family, tells ABC News.
Investigators have found no evidence of foul play, but they also can't be certain if Patrick's actions on that night were voluntary, CNN reports.
Police used dogs to track Patrick's scent, but the trail went cold some 30 feet away from the ditch where her car rested on Interstate 94.
Investigators have turned to YouTube videos that were posted in early November and feature Patrick talking and singing to someone she calls "baby" and "love." Patrick's family told CNN they didn't know she had any recent romantic relationships.
"Hi, baby," she says in one of the videos. "I am just coming to you to say, 'Hi' and tell you about my day."
In another, Patrick prepares a meal for two of omelets and pancakes and says, "If you were here, this is what would be [on] your plate."
These videos, along with the Radisson hotel footage that has no audio and does not make clear the reason Patrick was unable to book a room, are the evidence investigators have to work with since their physical search has turned up empty.
"We looked everywhere," Sgt. Rick Strong of the Indiana State Police tells CNN.
The Patrick family issued a statement Dec. 14, expressing their grief and hope for Teleka to be found.
"[She is] the sweetest, kindest and most hopeful girl you could ever meet, who was never too shy to show every single last one of her teeth when she smiled. Never too shy to help someone in need and never too shy to laugh out loud at her own sarcastic corny jokes (she thought she was hilarious). And oh, do we need to see her smile again."
"The days since [Teleka's disappearance] have been the most brutal, maddening all-consuming thing we have ever faced," the statement says.
The family's statement also cites a social media campaign, #findTeleka, and a gofundme account which is helping to raise funds for the search effort.