A doctor-patient role-play is a common role-play.
The roles in this are a sick patient and a doctor (or sometimes another health professional). The patient has to explain what their symptoms are, and the doctor may have to make a diagnosis and should recommend appropriate medical treatment.
The task of explaining one’s medical situation to a doctor is an authentic task, which travellers and immigrants often have to complete. Treating a patient with a medical condition is also an authentic task, but only really for ESP for medical purposes - i.e. for most students it is inauthentic.
At low levels, this can be quite unrealistically modelled, as the students lack necessary medical vocab. At medium levels and above, it’s often the case that the students possess adequate language proficiency but inadequate medical knowledge. This of course may apply to teachers as well, so language analysis for this could be interesting. See the NHS Choices website for clear explanations of common medical issues.