Yes, this may be deducted as a Medical Expense as long as the principal reason for being placed in this home is for Medical Purposes. Please keep in mind that only the portion of Medical Expenses that exceed 10% of your AGI will be deductible.
"Payments for in-patient hospital care or residential nursing home care, if the availability of medical care is the principal reason for being in the nursing home, including the cost of meals and lodging charged by the hospital or nursing home. If the availability of medical care isn't the principal reason for residence in the nursing home, the deduction is limited to that part of the cost that's for medical care."
https://www.irs.gov/taxtopics/tc502.html
https://ttlc.intuit.com/replies/4774888
