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Coronavirus hospital capacity math is brutal.

Consider Osaka, which had 674 beds as of as of 4/17. They are urgently adding capacity, expanding to 888 by 4/27 and 1,008 by 5/1, per the prefecture. pref.osaka.lg.jp/attach/37375/0…

22% WoW growth, through extraordinary measures.
Osaka has stopped sending low- and medium- severity patients to hospitals. Approximately 450 of them are waiting it out in dedicated semi-medical facilities or at home. Some of those will need to go to the hospital soon.

But higher-severity patients can't wait.
Osaka had 472 patients hospitalized as of 4/24, and another 107 which were in the process of negotiating placement with a hospital. (e.g. "Sure, we will have a bed for you in 48 hours, please come in then.")
That count (hospitalized plus waiting on a bed) is experiencing 6% growth.

Day over day.
It's worse than the aggregate stats would imply, too, because hospital beds aren't simply a fungible burst capable resource. Having an open bed on the other side of the prefecture doesn't help you.

Stats on patients:

pref.osaka.lg.jp/hodo/attach/ho…
If you want a single-page look at hospital capacity relative to utilization, see stopcovid19.jp

The view of current state reported there broadly tracks the one reported by NHK:
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