By Lindsay Kimble
Updated October 20, 2015 01:05 PM
Credit: Jason LaVeris/FilmMagic

For the first time since Lamar Odom‘s hospitalization last week, Khlo Kardashian is speaking out about her estranged husband and thanking the Sunrise Hospital team that took care of him.

“This past week has been incredibly difficult. I am so thankful to family, friends and fans, who have sent nothing but prayers and well wishes to Lamar,” she wrote on her website Tuesday. “I also want to take a moment to thank everyone at Sunrise Hospital, including the amazing doctors and nurses for their kindness and diligent work. Under their amazing care, incredible strides have been made. You can never be prepared for an experience like this, but without the outpouring of love and endless prayers that Lamar has received and the strength I was given from my loved ones, it would have been difficult to endure. Thank you for your continued support. God is great!!!”

Kardashian has been by the former NBA player’s side since he was first taken to the Las Vegas hospital after being found unconscious and unresponsive at a Nevada brothel last week.

Odom woke up from a four-day coma on Friday, and, PEOPLE confirmed on Sunday, is now breathing on his own.

On Monday night, Odom and Kardashian were airlifted to Los Angeles, where the athlete was admitted to the intensive care unit at the famed Cedars-Sinai Medical Center.

“Khloé has been praying a lot, both to herself and out loud to Lamar,” a source previously told PEOPLE. “She wants him to know that she’s still on his side, and that everyone is praying for him.”

The entire Kardashian-Jenner family has been supportive of Khloé, who is making medical decisions for Odom since the pair’s divorce has not yet been finalized.