There are two views of what Jesus healed according to Matthew 4:24:
Matthew 4:24 mentions three specific illnesses: possession by demons, epilepsy, and paralysis—all considered untreatable at that time. The Greek word used here, seléniazomenous, literally meaning moonsick, refers to suffering from epilepsy, an illness thought to be caused by the moon’s motion.
Matthew 4:23 says that Jesus healed every disease, and the next verse lists three specific diseases, but still says that he healed
all the sick,
including people with a handicap rather than a disease.
Interpretation 1:
After a general indication of illness in Matthew 4:24, three illnesses are mentioned by name: those possessed by demons, epileptics, and those who have been paralyzed. These were probably the illnesses that at the time were considered to be untreatable. The Greek word used here, seléniazomenous, which literally means being moonsick, refers to those who suffered from epilepsy, an illness that men in ancient times thought had to do with the movements of the moon.1
Interpretation 2:
Jesus heals every disease and every affliction among the people (Matthew 4:23). This can be understood literally, for the varieties of diseases were limitless (Matthew 4:24). The people truly brought to him everyone who was in a bad way and afflicted by all possible diseases and pains. They also brought him people who could not really be described as ill, but as handicapped (and suffering from a problem that could not be treated). These include people possessed by a demon, epileptics, and those who were paralyzed. Jesus heals them all.2
24 Sa renommée se répandit dans toute la Syrie, et on lui amenait tous ceux qui souffraient de maladies et de douleurs de divers genres, des démoniaques, des lunatiques, des paralytiques; et il les guérissait.