So, for a fun clock. The end point is "you have 10,000 cases in your community in the wild", assuming no measures as extreme as Italy (local travel bans, social distancing).
- First community transmission detected because someone went to the hospital feeling unwell: 32 days
- First community-infected death: 16 days
- 10th community-infected death: 0 days, roughly 10,000 people in community infected
- 100th death: -16 days, roughly 100,000 people in community infected
- You need 500 new free ICU, 1500 Oxygen beds: -20 days
- You need 1000 new free ICU, 3000 Oxygen beds: -26 days (total 1500)
- You need 2000 new free ICU, 6000 Oxygen beds: -32 days (total 3500) about 1 million infected
- You need 4000 new free ICU, 12000 Oxygen beds: -38 days (total 7500)
- You need 8000 new free ICU, 24000 Oxygen beds: -44 days (total 15000; first few patients are now stable)
- It is everywhere. -48 days
- You need 16000 new free ICU, 48000 Oxygen beds: -50 days (total 30000)
- ICU need reaches steady state, way over supply. -68 days
USA as a whole has 65,000 ICU beds, or 1 per 5000 people. They tend to be in 80%+ utilization, so you have 1 "free" ICU bed for every 25,000 people. So, in a region of 25 million people, you might about 1000 beds they can free up at this moment. It is probable they can cobble a few more together by turning surgical equipment into ICU beds or similar.
When you introduce drastic measures, the number of new beds needed levels off
3 weeks later. Patients needing beds need them for up to 4 weeks.
This kind of curve hasn't been flattened without drastic measures.
Patients who need ICU/Oxygen basically die if they don't get it. Some that need it die anyway. You get a <1% death rate if you have enough ICU/Oxygen/etc. You get a 4%+ death rate if you don't.
So suppose modest measures are taken at the 10,000 people infected mark.
- First community transmission detected because someone went to the hospital feeling unwell: 32 days
- First community-infected death: 16 days
- 10th community-infected death: 0 days, roughly 10,000 people in community infected
- 100th death: -16 days, roughly 20,000 people in community infected
- You need 500 new free ICU, 1500 Oxygen beds: -20 days
- You need 650 new free ICU, 2000 Oxygen beds: -26 days (total 1150)
- You need 850 new free ICU, 2500 Oxygen beds: -32 days (total 2000)
- 40,000 people infected: -32 days
- You need 1100 new free ICU, 3300 Oxygen beds: -38 days (total 3100)
- You need 1400 new free ICU, 4300 Oxygen beds: -44 days (total 4000; first few patients are now stable)
- 80,000 people infected: -48 days
- You need 1800 new free ICU, 5500 Oxygen beds: -50 days (total 5150)
Suppose drastic measures are taken at the 10,000 people mark.
So suppose modest measures are taken at the 10,000 people infected mark.
- First community transmission detected because someone went to the hospital feeling unwell: 32 days
- First community-infected death: 16 days
- 10th community-infected death: 0 days, roughly 10,000 people in community infected
- 100th death: -16 days, roughly 20,000 people in community infected
- You need 500 new free ICU, 1500 Oxygen beds: -20 days
- You need 450 new free ICU, 1350 Oxygen beds: -26 days (total 950)
- You need 400 new free ICU, 1200 Oxygen beds: -32 days (total 1350)
- 12,000 people infected: -32 days
- You need 350 new free ICU, 1000 Oxygen beds: -38 days (total 1700)
- You need 300 new free ICU, 900 Oxygen beds: -44 days (total 1500; first few patients are now stable)
- 7,000 people infected: -48 days
- You need 250 new free ICU, 750 Oxygen beds: -50 days (total 1200)
A downslope starts. But it starts ~10-20 days after measures start, because the people in hospital are the people infected 2-3 weeks ago.
Model: 5% of sick need a ICU in 20 days, 15% need oxygen, and they need it for 4 weeks. Base is 10x new cases every 16 days. Modest intervention makes it 2x new cases every 16 days. Serious intervention makes it x0.7 new cases every 16 days.