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We should be ready to serve others wherever we encounter need, not just when "on duty." Jesus exercised God's power in regular human settings, in this case within the fairly typical living arrangements of a disciple's family.
Donald Hagner (1993:208-9) points out a minor chiastic structure in these verses, in which Jesus first ministers to Peter's wife's mother and she in turn ministers to him. This structure may make emphatic the model for discipleship: after Jesus transforms a person, the person serves him. If so, this is not the only text where Matthew chooses women disciples as a paradigm for discipleship in general (27:55-61; 28:1-10). That Jesus touches her to cure her may also indicate the way he values people over traditions, given some evidence for prejudice against touching people with fevers (Witherington 1984:67); compare 8:3; 9:20, 25.