# COVID-19 herd immunity? Not so fast.

Herd immunity (or community immunity if you like rhymes) is the point when enough of the population has been immunizes so that a disease can’t spread much. Maybe only a few people get sick, but outbreaks are stopped because there just aren’t enough vulnerable people around for the disease to spread.

And boy, would we just love to get to that point with COVID-19. But at least in the USA it doesn’t look like we’ll get there. Why? Because you need enough of the population immunized. Something around 80% is needed(it varies depending on each disease’s R number). But with about 25% of the population here refusing to get immunized, we may never reach it.

Anthony Fauci isn’t talking about getting there anymore. He’s shifted to trying to get as many people immunized as possible. Others are more explicit:

“It’s theoretically possible but we as a society have rejected that,” said Dr. Gregory Poland, director of the Mayo Clinic’s Vaccine Research Group. “There is no eradication at this point, it’s off the table. The only thing we can talk about is control.”

— Dr. Gregory Poland from an article in USA Today

Control. Not the nice kind where we’ve beaten the disease. The kind where we have to be careful for a long time. These anti-vaxers are just making things worse. It’s called a conspiracy theory for a reason: it’s like circular reasoning and non-falsifiability. i.e. not science, and not trustworthy. It’s like these people are afraid of critical thinking.

Sigh.

Let’s just hope we get there in spite of them. Maybe some parts of the US will get herd immunity while others just won’t have enough people who believe in science.

# Fundamental Equations, Chaos, Fractals, and Leaky Faucets

It’s been a while since I’ve written here. Busy teaching. (I know, lame excuse).

So I go and watch some video on YouTube, and on the side is the list of suggested videos. For a while there’s been this one by Veritasium (Derek Muller). Now, Derek is a fantastic science educator, and is who I want to be when I grow up. One problem is he’s younger than me by over a decade. Hmm. Have to work on that somehow.

Anyway, the video that was just waiting for me to finally click on it was this one. It’s about an equation that will change how you see the world.

## The Logistic Map

The math is very simple: $x_{n+1}=r x_n(1-x_n)$ where $r$ is the growth rate. This is a very simple equation with a negative feedback loop.

When you graph $r$ by the equilibrium population, you get this:

What!?

Once the growth rate hits 3, the equilibrium population splits, and oscillates between two values. Then just after 3.4 it splits again. And very soon it becomes chaotic. Oh, and fractal. The chaotic nature was used for pseudorandom number generators.

## The Mandelbrot set

Does mentioning fractals make you think of the Mandelbrot set? If it doesn’t, then you have some research to do.

It’s probably the most famous fractal out there. Heck Johnathan Coulton has done a song about it.

But evidently if you somehow rotate the Mandelbrot Set along it’s real number axis, you get this:

Look familiar? At this point I started getting a headache, but it was one of those good, excited headaches that come from having your reality twisted about.

## Leaky Faucets

Oh yeah, leaks. Derek then mentions that if you get your faucet going drip, drip, drip, and then increase the water pressure just right, it will start doubling: drip drip, drip drip, drip drip. Push it a little more, and you get chaotic behavior.

Of course the YouTube video is so much better than my explanation. Go watch it.