Can someone explain "herd immunity" to the rest of us?

[Bernardo de La Paz]

15. It is the logistics curve. Think an exponential and a reverse exponential glued together

Basically it is exponentially increasing until 50% and then exponentially decreasing, which means a long taper as the human population gets saturated with infection. It describes in a way the population growth of antibodies in the human bio-culture. https://en.wikipedia.org/wiki/Logistic_function#In_ecology:_modeling_population_growth

What is the intuitive explanation? We all know that it seems like infections (unchecked) blow up in an area. This is because from this virus's point of view new hosts are easy to find and you're only killing off something from 1% to, say, 5% of hosts. But at the halfway point, infected people start to outnumber uninfected. It gets increasingly harder to find hosts. So the curve slows down and starts running out of steam. At some point like, say, 90% infected, what remains are pockets that don't communicate much with others. So the top flat part of the curve is never really 100%. This is effective herd immunity. The herd is essentially immune and its as if the infection has died out.

Now there are many confounding factors at play, but basically it is a logistic curve. For number of infections think of the vertical as 0.5 = 50%. Think of the horizontal as time. You can think of Month 0 as the worst month of the epidemic.

Logistic curve (Wikipedia):


The rate of change of the curve is the famous Curve We Are Flattening, because that is the rate at which we adding new cases. Technically it is called the logistic distribution (though it is not a probability distribution). https://en.wikipedia.org/wiki/Logistic_distribution As you lock down, you slow the rate of infection, which flattens the curve and spreads it out so that hospitals and health care workers are not overwhelmed.

The logistic distribution is the derivative (slope) of the logistic curve.
The logistic curve is the integral (area under) the logistic distribution.

There. You've just learned a bit of calculus. An example of the Fundamental Theorem of Calculus.

Logistic distribution (Wikipedia):