Gibbs, Jeffrey A. “Matthew 8:1-4: Jesus Cleanses a Leper." Matthew 1:1-11:1. St. Louis: Concordia Publishing House, 2006, pp. 407-413.
Gibbs observes that in Matthew 8:2 the man with "leprosy" may have had any of a wide variety of illnesses resulting in scaly or scabby skin. The term is not limited to Hansen's disease (Gibbs 2006, 407). When the man has been healed, he is not to go and tell people, but is to see the priests and make an offering. These offerings are not to bring healing but are a response to recovery. They are spelled out in Leviticus chapter 14 (Gibbs 2006, 408).
Gibbs notes that while the crowds were amazed, only the man with leprosy acted in belief. Jesus shows his authority to do good, and works that good by healing the man who believes (Gibbs 2006, 409). The leper's address to Jesus acknowledges him as Lord and also affirms that Jesus is able to heal him if he wishes to do so (Gibbs 2006, 410).
Gibbs points out that Jesus' authority goes beyond that of anyone else. "Any other clean person who would touch a leper would thereby become unclean. However, rather than Jesus himself becoming ritually unclean through contact with the leper, Jesus' touch transmits purity and holiness to the unclean man and restores him" (Gibbs 2006, 411). Though not every person with an illness is healed, Gibbs observes that every person who believes Jesus receives forgiveness of sin, which leads to eternal healing.
Jesus' instructions to the man who has been healed include offering the normal sacrifice. This would permit him to return to life in society. The other instruction, to avoid speakign to anyone, is more cryptic. Gibbs suggests that telling others may have delayed and interfered with the man's re-entry into the community. Therefore, he should go with urgency to offer the sacrifice (Gibbs 2006, 412).