In a Pandemic, Little Things Matter a Lot

 

There is a branch of complex dynamic systems theory called global cascades modeling that tries to explain things like avalanches and sand piles. In both cases, everything is fine, and you have a coherent snow load or sand pile. 

Then, suddenly and spontaneously, the structure collapses. The snow comes crashing down the mountain or the sand pile collapses for no apparent reason. Of course, there is a cause, but it's some very small change too small to notice in a big system of snowflakes or sand grains.

Researchers in Austria are applying a different but similar approach to the COVID-19 pandemic. Borrowing ideas from fluid dynamics, normally used to study turbulence in things like pipes, they are showing why COVID-19 infection rates are either boom or bust (from the virus's point of view). 

You want to avoid turbulence in pipes because it increases resistance, slowing down the flow of whatever liquid you're trying to move. As with cascades, turbulence is initiated by very small changes in the system, and you get a sudden, overwhelming change from smooth flow to turbulent flow.

In this paper the change is an increase in cases to the point where mitigation measures can't keep up. They did a simulation using the reproduction number, also called R₀. This is a measure of how many people will be infected by someone who has COVID-19 in a given period of time.  

When R₀  is less than 1, every infected person infects fewer than on other person on average and the infection rate dwindles.  For R₀ greater than 1, every infected person infects more than one other person on average, then they each infect more than one other person, and so on.  That's bad.  

The researchers' simulation found a tipping point at R₀ = 2.5, illustrated in this chart from their paper:

Here the y-axis shows Rt, the actual infection rate at a certain point in time. When the underlying R0 = 2.3 (black dots), mitigation measures can beat back the spread. In a few days the actual infection rate declines to below 1 and the outbreak is controlled. 

But when the underlying R0 = 2.7 (red dots), mitigation measures can't keep up. Rt decreases for a few days but never goes below 1. Each case causes more than one new case. Those cases cause more than one case, and so on, and you're off to the races with actual infection rates accelerating out of control.

This illustrates why, during the winter surge, public health people kept saying that if everyone would just wear masks, we could get the infection rates under control.  It's a small thing that can make a big difference.  But enough people didn't listen or didn't care that we got on that red track and a bunch of people got very sick and some died.

Header image by Jacky Barrit from Pixabay