The Lord Jesus affirmed the existence of demons and often commanded them to leave the people that they were afflicting. In the gospels we can see that demons at times are the cause of sicknesses, infirmities and insanity. At times, Jesus healed people that were sick and at other times, He healed by commanding demons to leave; such as deaf spirit etc. It's apparent that there are some sicknesses that are caused by demons and some that are caused by disease, etc.

A small sample of scriptures from the Gospels.

Matthew 4:23-24 And Jesus went about all Galilee, teaching in their synagogues, and preaching the gospel of the kingdom, and healing all manner of sickness and all manner of disease among the people.
24. And his fame went throughout all Syria: and they brought unto him all sick people that were taken with divers diseases and torments, and those which were possessed with devils, and those which were lunatick, and those that had the palsy; and he healed them.

Matthew 8:16   When the even was come, they brought unto him many that were possessed with devils: and he cast out the spirits with his word, and healed all that were
sick:

Matthew 9:32-33   As they went out, behold, they brought to him a dumb man possessed with a devil.
33. And when the devil was cast out, the dumb spake: and the multitudes marvelled, saying, It was never so seen in Israel.

Mark 16:9   Now when Jesus was risen early the first day of the week, he appeared first to Mary Magdalene, out of whom he had cast seven devils.

Luke 9:38-42   And, behold, a man of the company cried out, saying, Master, I beseech thee, look upon my son: for he is mine only child.
39. And, lo, a spirit taketh him, and he suddenly crieth out; and it teareth him that he foameth again, and bruising him hardly departeth from him.
40. And I besought thy disciples to cast him out; and they could not.
41. And Jesus answering said, O faithless and perverse generation, how long shall I be with you, and suffer you? Bring thy son hither.
42. And as he was yet a coming, the devil threw him down, and tare him. And Jesus rebuked the unclean spirit, and healed the child, and delivered him again to his father.

Jesus gives His disciples authority over demons.

Luke 9:1-2 Then he called his twelve disciples together, and gave them power and authority over all devils, and to cure diseases.
2. And he sent them to preach the kingdom of God, and to heal the sick.

Luke 10:17-18 And the seventy returned again with joy, saying, Lord, even the devils are subject unto us through thy name.
18. And he said unto them, I beheld Satan as lightning fall from heaven

Mark 16:17 And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues;

Acts 8:6-7 And the people with one accord gave heed unto those things which Philip spake, hearing and seeing the miracles which he did.
7. For unclean spirits, crying with loud voice, came out of many that were possessed with them: and many taken with palsies, and that were lame, were healed.

Acts 16:16-18 And it came to pass, as we went to prayer, a certain damsel possessed with a spirit of divination met us, which brought her masters much gain by soothsaying:
17. The same followed Paul and us, and cried, saying, These men are the servants of the most high God, which shew unto us the way of salvation.
18. And this did she many days. But Paul, being grieved, turned and said to the spirit, I command thee in the name of Jesus Christ to come out of her. And he came out the same hour.

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