Gibbs, Jeffrey A. “Matthew 4:23-24: Summary of Jesus’ Ministry.” St. Louis: Concordia Publishing House, 2006, pp. 221-225.
In Matthew 4:23, Jesus “went around.” Gibbs sees the verb as inceptive in nature. He also asserts that the present participles “after a main verb of coming or going” likely show purpose (Gibbs 2006, 221). So Jesus’ purpose is to teach, preach, and heal.
The activities of preaching and teaching in Matthew are used in very similar ways. Gibbs does observe that perhaps preaching is aimed more at bringing a message to those in need of conversion (Gibbs 2006, 222).
Gibbs does note that in his opinion 4:25-5:2 serves as an opening bracket for the Sermon on the Mount, with a closing bracket at 7:28-8:1 (Gibbs 2006, 223). Matthew 4:23-24 thus serves to conclude the portion before it.
Gibbs sees the purpose of Jesus as saving people from sin. He accomplishes that purpose by preaching, teaching, etc. (Gibbs 2006, 224). This is the work of God’s reign in the world. Gibbs does observe that the biblical text is clear that not all sickness is demonic and not all is natural. We should expect the same kind of pattern in our world today (Gibbs 2006, 225).