Exponential “stacking” of Coronavirus deaths
Why exponential growth means we can’t reduce the deaths coming in the next 2 1/2 weeks. And why every day matters.
We are committed to almost 200,000 deaths now, today. When I first wrote this essay 4 days ago, before editing and publishing it, that number was 64,000 deaths.
This virus is currently showing exponential growth in most of the places it exists, with a growth rate of 25–35% every day. That means the number of cases doubles about every 3 days — the doubling time. We’ve all seen the curves that result, and how fast we get to terrifyingly large numbers.
What’s not so often appreciated is that counting backward, the cases cut in half with each doubling time. What that means is that hospitalizations and deaths are already determined for the next 2 1/2 weeks, and can’t be avoided.
We have twice as many cases today as we had 3 days ago. That’s what doubling time means.
Because of that, half of all cases were infected within the last 3 days, and the other half of all cases were infected over the entire remaining time of this epidemic, going back to January.
Go back another 3 days, and 3/4 of all cases were infected within the last 6 days.
7/8 of all cases were infected within the last 9 days.
15/16 of all cases were infected within the last 12 days.
This “stacking” of cases with recent dates of infection, is a simple inevitable consequence of exponential growth. The times may change if the growth rate and doubling times are different, but with exponential growth, it will always inevitably be true that 15/16 of all cases will be new within the last 4 doubling periods.
Why does this matter?
Remember that on average it takes about 5 days for people who get this virus to start showing symptoms. That means that almost 3/4 of all people with the virus are “silent” because they’ve gotten it so recently that they aren’t yet or just barely starting to show symptoms.
Remember that on average it takes about 10 days from infection to hospitalization, for the 15% or so of patients who are going to be hospitalized.
10 days is just over 3 doublings. Of the people infected today who are going to need hospitalization, only about 1/10 have had it long enough to currently be in the hospital.
The other 9/0 are not yet hospitalized, but will be within the next 10 days — and this is baked in. They’re already infected. Nothing we can do will stop them from being already infected.
At current rates of growth, For every person in the hospital now, there will be another 9 coming in the next 10 days, and nothing we do now or over the last 10 days can change that.
As long as exponential growth continues at this rate, we can count the number of people in the hospital today and know that 10 times that number will be at the hospital over the next 10 days, needing care, and there is nothing we can do to stop it.
We can slow it down after 10 days from now. But only after that. There’s nothing we can do now about the impact on hospitals for the next 10 days or so.
This is why epidemiologists have been screaming for 2 months that we have to get aggressive NOW in slowing this down.
Every 3 days, those numbers will double. Isolate, isolate, isolate. We have to slow this down.
Remember that on average it takes over 2 1/2 weeks from infection to death, for those who are going to die from COVID-19. We’ll call it 18 days. That’s another 2 doubling periods.
15/16, 31/32, 63/64.
1/64 of the people who have been infected and are going to die, already have died.
63/64 of all people who are already infected and are going to die from this virus, have been infected in the last 18 days and haven’t had time to die yet. That’s a simple inevitable consequence of exponential growth.
The US will cross 3,000 deaths tomorrow, March 31. That is 1/64 of the currently infected people who are going to die. Those 3,000 deaths today, mean that 190,000 more people are going to die in the US in the next 2 1/2–3 weeks, and it’s already too late to do anything about it.
Today Dr. Deborah Birx, the coronavirus response coordinator for the White House, said that if we do everything perfectly, we might keep tjhis to 100,000 to 200,000 deaths. The growth rate through today, coupled with basic facts about for this virus, and the nature of exponential growth, tells us that we’re already committed to almost 200,000, even if we manage to stop the epidemic in its tracks today, and not one more person in the United States gets infected from now. That’s what “perfect” means in this context.
Might these numbers be wrong? Sure. There’s noise in the data. But they won’t be wrong by very much. Maybe half, or twice, at most — which is just one more doubling time. This is the only way we make Dr. Birx ow end estimate of 100,000 deaths — and then only if we stop this virus completely, today.
The only input values we need to arrive at these numbers are the doubling time, the times to hospitalization or death, and the current numbers of hospitalizations or deaths. The only assumption is that the growth rate of infections has remained constant until today. If the growth rate has slowed in the last 2 weeks, the numbers will be smaller.
We expect that death rates will increase as hospitals get over-run, and that would make these numbers worse.
The numbers of hospitalizations and deaths are fixed — we may not know them perfectly accurately, but they are what they are. The times to hospitalization or death are pretty close to what I used — if they’re off, they’re not off by more than a couple days. The doubling time is what we currently see in the US, and it’s been the same for cases since we reached 100 cases, and the same for deaths since we reached 10 deaths.
I desperately want these numbers to be wrong. They aren’t, not by much.
We are committed to almost 200,000 deaths now, today. When I first wrote this essay 4 days ago, before editing and publishing it, that number was 64,000 deaths. The number of deaths that are already locked in and going to happen, because exponential growth means they are already infected, has increased from 64,000 people to 190,000 people in 4 days.
Every 3 days that we wait to take severe restrictions, will cause that number to double. You can do the math. It hurts my heart too much to write it.
We MUST take extreme isolating measures, NOW, to keep this from getting much much worse.
