The God as perceived by the Jews in the OT does. In the NT, God heals the sick. What a difference! In fact, healing involves driving out evil spirits. And Christ says that He couldn't possibly be the devil because, by healing the sick, that would make Satan divided. Obviously, God and Satan are not both the cause of illness in the NT. In the OT, that's a different story: Satan works for God, and angles do all the killing in the name of God. It's like night and day.
God clearly diseased Herod with worms.
"Acts 12: 21 On the appointed day Herod, wearing his royal robes, sat on his throne and delivered a public address to the people. 22 They shouted, "This is the voice of a god, not of a man." 23 Immediately, because Herod did not give praise to God, an angel of the Lord struck him down, and he was eaten by worms and died.
My memory of the verses you cite says that they involved the casting out of demons. Therefore, Satan would not cast out Satan. A house divided cannot stand.
In the Revelation, God uses the bowl (vial) judgments, and those include disease.