While the play primarily centers around Oedipus's discovery of his own fate, it is very evident that the play also exposes how Oedipus's fate not only affects him, but his entire family as well as his entire city. Therefore, the play does not solely address Oedipus's fate, but the fate of all those around him.
The first thing we learn in the play is that the citizens of Thebes are being directly affected by Oedipus's fate, well before Oedipus even understands his fate. The citizens are being affected by a devastating plague, which includes a famine, and is killing hundreds of people, young and old alike. In fact, we even learn that women are giving birth to stillborn babies, primarily because of the lack of food in the city. We also learn through Creon, who visited the oracle at Delphi, that the gods have sent the plague as a punishment until the city rids itself of King Laius's murderer.
Oedipus's fate also especially affects the fate of Jocasta as well as their children. As soon as Jocasta realizes what has happened, she hangs herself. Oedipus especially expresses concern for his children's fate. He recognizes that his own curse has now cursed his children, particularly his daughters. He recognizes that they will now be ostracized from society and that no one will want to marry them, as we see in his lines:
What sort of company will you keep in town? What festivals will you attend that will not send you home in tears, instead of joy? When you come to the age ripe for marriage, who will he be who will run the risk, children. (1511-15)
Hence, we clearly see that the play does not solely address Oedipus's own fate, but the fates of all that surround him.