Spirits of infirmity are spirits that afflict the bodies of believers as well as unbelievers.
Read Luke 13:10-17:
10 And he was teaching in one of the synagogues on the sabbath.
11 And, behold, there was a woman which had a spirit of infirmity eighteen years, and was bowed together, and could in no wise lift up herself.
12 And when Jesus saw her, he called her to him, and said unto her, Woman, thou art loosed from thine infirmity.
13 And he laid his hands on her: and immediately she was made straight, and glorified God.
14 And the ruler of the synagogue answered with indignation, because that Jesus had healed on the sabbath day, and said unto the people, There are six days in which men ought to work: in them therefore come and be healed, and not on the sabbath day.
15 The Lord then answered him, and said, Thou hypocrite, doth not each one of you on the sabbath loose his ox or his ass from the stall, and lead him away to watering?
16 And ought not this woman, being a daughter of Abraham, whom Satan hath bound, lo, these eighteen years, be loosed from this bond on the sabbath day?
17 And when he had said these things, all his adversaries were ashamed: and all the people rejoiced for all the glorious things that were done by him.
This woman was afflicted with a spirit of infirmity. She was present in the Sabbath services and Jesus called her "a daughter of Abraham." Both of these facts indicate she probably was a follower of God, yet satan had afflicted her body for eighteen years.
Other examples of demonic powers afflicting the body:
Matthew 12:22:
Then was brought unto him one possessed with a devil, blind, and dumb: and he healed him, insomuch that the blind and dumb both spake and saw.
Matthew 17:15-18:
15 Lord, have mercy on my son: for he is lunatick, and sore vexed: for ofttimes he falleth into the fire, and oft into the water.
16 And I brought him to thy disciples, and they could not cure him.
17 Then Jesus answered and said, O faithless and perverse generation, how long shall I be with you? how long shall I suffer you? bring him hither to me.
18 And Jesus rebuked the devil; and he departed out of him: and the child was cured from that very hour.
2 Corinthians 12:7:
And lest I should be exalted above measure through the abundance of the revelations, there was given to me a thorn in the flesh, the messenger of Satan to buffet me, lest I should be exalted above measure.
