This chapter of Matthew forms a chiastic structure:
1a) Mat 8:2-4, Jesus cleanses leprosy;
1) Mat 8:2, Jesus receives a leper’s worship;
2) Mat 8:3, Jesus cleanses leprosy;
3) Mat 8:4, See that you tell no one;
1b) Mat 8:5-13, The centurion’s great faith;
1c) Mat 8:14-16, Miracles of healing spread His fame abroad;
central axis) Mat 8:17, That the word of Isaiah the prophet might be fulfilled: “He Himself took our infirmities and bore our sicknesses;”
2c) Mat 8:18-22, Multitudes follow Him (because of the healings) without counting the cost;
2b) Mat 8:23-27, The disciples’ little faith;
2a) Mat 8:28-34, Jesus cleanses demoniacs;
1) Mat 8:28-29, The demons proclaim Jesus the Son of God;
2) Mat 8:30-32, Jesus casts out the demons into a herd of swine;
3) Mat 8:33-34, The swineherds went their way and told everyone.
In the last three chapters we saw that Jesus taught the word of the God with authority. In this chapter, the matching pairs that lead up to the central axis proclaim who Jesus is, by showing His power and authority over the spiritual and natural worlds, which only the Creator and Ruler of the universe can wield.
The cleansing of leprosy is a different type of healing than the healings mentioned in the 1c pair. The condition translated as “leprosy” in English is the spiritual condition of tsara’ath described in Lev 13-14. This condition, and its purification, is a proclamation of the gospel of salvation by faith from Torah (see the explanation here).
Likewise, the cleansing of demoniacs is the cleansing of a spiritual condition rather than merely a physical one. The Son of God has power over uncleanness, whether of the body or the spirit, because He is Himself under the authority of God. Because He is sent by God and acting in accordance with God’s will as the prophets have proclaimed, those who are under Him (uncleanness, demons, sicknesses) must obey His word.
His power and authority extends to the natural world, so that even the winds and the waves obey Him. This chapter is answering the question, “Who can this be?” (Mat 8:27).