Kanye West and Kim Kardashian are living separately following West's hospitalization

Kim Kardashian and Kanye West are living separately following West's release from the hospital, sources tell PEOPLE magazine.

The 39-year-old rapper is reportedly not living at home with Kardashian and their two children, Saint and North, as he continues treatment for "undisclosed mental health issues."

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Earlier tihs week, West was released from UCLA's Resnick Neuropsychiatric Hospital, but earlier reports indicating that he would be home for son Saint's first birthday on Monday appear to be inaccurate.

"He is receiving outpatient care elsewhere with a medical team," the source told PEOPLE. "Kim still seems concerned but is supportive. They don't know for how long Kanye will need outpatient care."

See photos of Kim and Kanye together:

Additionally, another source says that Kardashian is "overwhelmed" by the entire situation and that "she is very worried about the kids being around Kanye."

That being said, there's nothing that indicates that Kardashian has any intention of leaving West's side -- whether she's physically next to him or just there in spirit. "There are frustrations and problems, like any relationship, but they love each other deeply," the source continued.

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