In Oedipus Rex, how does the metaphorical decay of morality, social convention, and so on connect to the literal decay caused by the plague?

When the text begins, the city of Thebes is afflicted by plague. Supplicants apply to Oedipus to help alleviate their suffering, and he promises to do so. They reference his past success in saving them from the curse of the Sphinx, and he lauds his own success, confident that he will be able to relieve them of their current ills.
The irony, however, is that even as Oedipus promises to cure the illness of his city, he is its cause. He is informed by the oracle of Apollo that his city will be cured when the former king Laius's murderer is rooted out. What Oedipus doesn't know (but that we, as an audience, do), is that Oedipus himself is Laius's murderer.
This, in and of itself, isn't a problem. Killing an enemy would have been seen as a socially acceptable, if not entirely polite, manner of solving a dispute on the road. It is because this murder leads to the subsequent corruption of the family structure, of the monarchical structure, that it is seen as a blight. The social construct of family decays as a result of this murder—Oedipus has unknowingly killed his father, married his mother, and fathered his siblings—each a heinous and sick action. This is a complete degradation of acceptable social institutions—both at the micro level of the family and the macro level of the government. As such, the decay of the home that results from Oedipus's choices manifests in the decay of his city.