The actual assumption is that with current social distancing, any outbreak will die down on its own on approximable dynamics. There is good evidence that this is so.

When we end social distancing, all bets are off. See http://www.healthdata.org/covid/faqs#length%20of%20the%20epi... to see that they are painfully aware of this and are explicitly not trying to model that.

All right, that seems much more reasonable to me. Thought you said the peak for the USA in general was imminent, and that's not at all obvious given that the social distancing policies going forward have yet to be decided.

It might be the case, but that assumes that effective measures to control the epidemic will keep being applied everywhere.