Do you believe illness is caused by "demons?" Do you believe medicine belongs in demonology? Where do you draw the line and how do you decide what is believable and what is not?
It seems to me that some illnesses can be caused by demons or be the physical and psychological side-effects of possession and obsession by demons; but this is rare. Clearly the vast majority of sicknesses, even in the Gospels, are physical ailments plain and simple. What is more, I've seen many holy people physically suffer more than others do and accept it with supernatural peace based on the teaching of Christ that no disciple is greater than his Master and St. Paul who writes: "Who now rejoice in my sufferings for you, and fill up that which is behind of the afflictions of Christ in my flesh for his body's sake, which is the church." (Colossians 1:24)--suffering as a type of intercessory prayer in union with Jesus for the church.
To put it another way, when considering health issues there are three levels to look at: 1. the physical (rule out the obvious), 2. the mental (psychological--i.e. stress can cause heart conditions, fatigue, etc.), 3. spiritual (People living in serious sin cannot be at peace and this will sometimes have physical and psychological ramifications. Then there are those damned spirits themselves--I've seen people who go to fortune tellers or dabble in the occult or open the door directly to evil spirits and later they, or members of their family, have strange, medically unexplainable physcial illnesses--but the root of the problem is not physical, but demonic, and there are usually other strange phenonomen in their houses, dreams, etc. that make this clear. These souls need to get right with God--repent, change their lives, and if necessary seek deliverance). I'm not an expert in any of these fields, but I can certainly say that in our day and age the spiritual is more often than not completely overlooked.
So that's my take on the issue.
Regarding your question: Do you believe medicine belongs in demonology? No. But can men and demons take a good thing and distort and abuse it? Yes. In the name of medicine Doctors kill babies and nurses kill the sick and elderly (overdoses of morphine or depriving the patient of ordinary means of support such as food or liquids). Also, in a materialistic, atheistic society there is an overemphasis on medicine (chemical and surgical intervention) as the remedy to all woes. What I've noticed is oftentimes people suffer more in seeking a remedy for things (bills, hundreds of tests and visits to doctors, medicines with all kinds of undesirable side effects, etc.) than they would have suffered just accepting their cross and saying some prayers :) At any rate, I'm not afraid of going to a doctor and taking some medicine or undergoing a surgery, but in a proper perspective. We're all going to die sooner or later anyway!