What is the main conflict in Brief Lives by Neil Gaiman?

Delirium, the youngest of the Endless, is seized with the idea of finding her older brother Destruction, who abandoned his duties and has kept himself hidden from the family for 300 years. Delirium asks Desire and Despair to help her find Destruction, but they both refuse. She then asks Dream. Dream is heartbroken by the recent breakup with his mortal lover Nada, but he agrees to accompany Delirium. He tells his librarian Lucien that he has no wish to find his brother, who expressly told them not to come looking for him, but that he would be going on the search solely to spend time with Delirium.