NYC analysis: total deaths (red line) are growing at ~10x per week. Because death typically occurs at least +14 days after infection, the behavior of this curve (doubling timescale, or slope of log plot) is mostly baked in for the next two weeks. It depends on the trailing rate of growth of infections, which has not slowed very much, except perhaps in the last week or so.
Only in the last week or less have we seen significant lockdown and isolation in NYC. So I would be very surprised if there were not another factor of 10x growth in total deaths in the next ~10 days. This would mean over a thousand total deaths, and at least roughly five thousand in need of intensive care (i.e., about 5 cases in critical condition for each fatality). This is, I believe, greater than the available ICU capacity in NYC, even including emergency expansion, military hospital ships, etc. (Roughly, 2k base + 1k emergency expansion + 1k hospital ships. Cuomo has talked about this recently.)
With deep sadness, I predict a health system crisis in NYC within a week or so.
The analogous graphs for the US as a whole also have total deaths and total infections growing with a ~3 day doubling timescale. The infection numbers are mainly limited by testing, but there is no reason to expect a significant decrease in slope of the red (deaths) curve. There is probably another 10x growth in total fatalities over the next ~14 days that we can no longer affect -- the infections have already happened.
Figures obtained here.
A week may have been too optimistic...
NYT: ... All of the more than 1,800 intensive care units in the city are expected to be full by Friday, according to a Federal Emergency Management Agency briefing obtained by The New York Times. Patients could stay for weeks, limiting space for newly sickened people.
... At least two city hospitals have filled up their morgues, and city officials anticipated the rest would reach capacity by the end of this week, according to the briefing. The city requested 85 refrigerated trailers from FEMA for mortuary services, along with staff, the briefing said.
... Other doctors said they had tried to resuscitate people while drenched in sweat under their protective gear, face masks fogging up. Some patients have been found dead in their rooms while doctors were busy helping others, they said.