UA has stated that they intend to be aggressive about restoring capacity as soon as they see enough demand to justify it. However, they've also cut their May schedule by 90% vs. what they were originally planning to operate, and have suggested that they expect similar, or deeper cuts in June and possibly July.

While the passenger counts are rising, they're still nowhere near enough to make even these reduced schedules profitable. I believe that UA is scheduled to release its earnings after-hours today, at which point they will presumably schedule an investor conference call in the next few days. You may be able to get an idea what the reopening plan is from that.

Realistically, though, I don't expect things to change much for at least six weeks, if not longer; even if UA sees promising trends, it will take some time to get flights scheduled and crewed. (Crews normally bid on their schedule for a given month at some point during the previous month, IIRC -- so, May's crew schedule has already been filled, and June's will be bid sometime during May).