What is the Most Important Question in the World?
There is a
great deal of talk about Herd Immunity. Social Distancing absolutists poo poo
it as Pollyannaish: "let's just all go inside for 30 days and kill this bastard once and for all!"
Unfortunately, mass quarantine won't work. It flattens the curve, but doesn't get us past the pandemic. We will be trapped inside for a year, which would be certain to make the cure worse than the disease, as the global economy implodes, destroying the lives not just of those that die, but of those that live.
Many of the social distancing absolutists do not understand the unbelievable
power of compounding. Even those that do appear to think we should treat all people
as equally risky - "everybody go inside!". Both of those are terrible underpinnings for making rational
decisions.
Those that follow me on Twitter know that the
number of “Cases” of CV19 is a terribly misleading statistic, because it
depends largely on self-reporting and testing breadth.
Unlike Cases, "Deaths" is an extremely reliable number. While Deaths is not perfect (due to its
lag and the fact quality of treatment impacts it), Deaths is objective,
comprehensive, and easily measured. It helps us understand what is really happening in the world.
According to
this article
in the WSJ yesterday, the number of Deaths in the US “quadrupled” in the past
week. In Spain, the article mentioned that Deaths jumped by “a third” in one day (from ~1,000 deaths to 1,326). Both of those are staggering growth rates. While the growth rate differences are wide, in both cases we know it is very high. These differences make sense, because growth in Deaths will vary by geography depending on the quality of care available, how “seasoned” the ill are, overall population
health and age, social response, population density, quickness to diagnose, etc. Different growth rates are to be expected.
33% growth
per day is horrifying. It implies more than a septupling (7x) every week or so.
If that you think that sounds like a lot, it's because it is!
Using Spain’s
33% daily growth as the benchmark, each infected person would lead to six new
people infected each week (leading to a 7x - going from one infected person to that one person plus six new people). That does not mean the six people
were directly infected by the first person. Rather, the people the first
person directly infected went on to infect other people, and so on and so
forth.
Why is herd
immunity important? One might think that 20% herd immunity would only reduce
the number of infections by 20%. One would be wrong. Welcome to the world of
exponential math. Exponential up, but also exponential down. We will get into that in a moment.
I created a
simple exponential growth weekly table below. You can see the Spain example in
the top “0% Herd Immunity” row below. I set that row at approximately 33% growth per day.
Importantly,
Deaths are on a lag to initial infections (Cases). If you make a table that has
33% daily growth, and we assume the Infection-to-Death lag is 12 days (that’s
an educated guess), that means Deaths are somewhere in the 26th day
and infections are in the 38th day (i.e., it arrived in Spain around
February 12). If we assume Spain began with a single true Patient Zero, which
is a bad assumption, that would imply ~38,000 infections currently, 3.4%
of whom are dead now but more of whom will die over the coming week.
My guess is there are many many more infections than that. It is much more likely that there were multiple Patient Zeros that returned
from China or other countries with CV19 (not necessarily all arriving at the same time - some earlier, some later). In that case, there could be many multiples
of 38,000 actual infections in Spain. All else equal, I view that as a positive
(it implies lower Mortality Rate and future higher herd immunity). Also, the real growth rate may be higher or lower - but we're using 33% per day for these purposes.
So, we have no idea how many Cases there really are. But we do know the number of Deaths and we know
that Deaths is going to keep growing dramatically, as the social distancing
didn’t begin en masse until the past week. Recall Deaths are a lagging indicator. If we assume social distancing causes Cases
to plateau and then decline, Deaths should plateau around 12 days after Cases, which
gives another week of exponential Deaths growth.
Unfortunately,
7 days from yesterday, if the 33% growth per day continues, over 9,000 people will
have died in Spain, with 2,200 people dying on the last day alone (a septupling'ish from the 330 people that died yesterday). If, at that
point, the curve has flattened, then it will continue at 2,200 Deaths per day for a
period. The virus will work its way through the quarantine over the
subsequent 2-3 weeks, declining rapidly throughout.
But what
then? If even one person unknowingly remains infected and at large, when people go back out into the
world, won’t we just start over again? Yes.
This is why we
care about Herd Immunity and compounding.
If Spain is going to max out at 2,200 Deaths per day, and we assume a 1.5% Mortality Rate, we could assume that there were also 147,000 new Cases per day (12 days prior) that were leading to those 2,200 deaths. If one Patient Zero would have led to 38,000 new Cases per day, to get to 140,000 Cases per day, it actually requires about 14 Patient Zeros (don't put too much weight on that number). Let’s also assume that yesterday,
Spain shifted from exponential growth to linear growth based on Social Distancing (i.e., the number of new Cases per day flatlines).
Its new Cases would stabilize at 147,000 per day, then begin to decline rapidly.
If we assume the linear growth for the next 2-3 weeks averages half that max growth,
then 147,000 * 21 / 2 = 1.5 million additional new Cases during that period. This would be in addition to the over 500,000 people that were infected before the end of exponential growth, giving the world around 2.0 million infected Spaniards. Spain has 49
million people and unfortunately only 2.0 million will be immune (most of whom won't even know they are immune). 2.0 million is around 4% of the Spanish population. 4% does not provide the necessary herd immunity to cut the transmissions
down dramatically. Crazy as it sounds, Spain may have achieved 25%+ if Social Distancing measures had waited another week (my math becomes even less sciency as the number of Cases grows to very large numbers, because some benefits of Herd Immunity would slow down the contagion rate along the way and small changes in growth lead to big differences in ultimate outcome).
Why does herd immunity matter? Each person
that gets infected and recovers becomes immune. These immune people begin to
break the chain of contagion. Those immune people are protecting the rest of us - silent heroes.
Two Scenario Examples:
1: Zero Herd Immunity: assume you personally would have given the infection to two
people, and then they do the same, so on and so forth;
2: Same as #1, but the herd is 50% immune
In Scenario 1, after you get infected, you give it to two people. Then they each subsequently give it to two
more people (you + four people). In Scenario 2, you try to give it to two people, but one of them is immune. So only one new person gets it. Likewise, the one new
person gives it to one additional person (you + two people). Take it two steps farther and it’s You + 16 People
vs. You + 4 People. Another step, You +
32 vs. You + 5. You + 64 vs. You + 6. Hopefully you get the point.
So, a 50%
herd immunity doesn’t reduce the number of new infections by half, it reduces
the exponential factor by half, which reduces infections exponentially. It basically breaks the chain. Barring an effective treatment, this is the primary path to saving lives. We must get herd immunity up while also protecting
lives on the journey.
This becomes
the most important question in the world today: how do we get to maximum herd
immunity with minimum Deaths? My next
post addresses that.
