Check people coming into the hospital. An “light” check, probably just a visual presence.
Check people coming onto the floor. A much harder check. At elevators and stairs. ID, reason, etc.
A sterile area around his room. No other patients for 6 or 8 room in each direction down the halls. No one gets in without very proper vetting. For example, a hospital ID is not sufficient. Why are you here? Someone from the medical staff to personally vouch for them.
Then, as quickly as possible, move him to a jail medical ward.
Too much work just kill the bastard