Exponential Growth Part 2 (Apr 3)

Construction estimating uses a lot of math, but it’s simple stuff.  Multiply unit costs times quantities, add them up, and you’ve got a bid.  There might be a little subtraction or division here and there, but nothing more complicated. Construction accounting is even simpler. Thank goodness for sales tax, which at least has percentages to make it more interesting.

As a math nerd, it’s exciting to work with more than just basic arithmetic. So please forgive me as I indulge in a bit more Covid-19 amateur epidemiology.

Recently I mentioned exponential growth, with a series that starts out 1-2-4-8-16-32.  That’s powers of two, which is important for software developers. However, it’s not the only type of exponential curve.

Globally, Covid-19 probably has an R0 basic reproduction number of about 2.7. With that multiplier, the series goes 1-3-7-20-53-143-387-1046. Seven jumps to 1000, not ten. At 4 or 5 days per jump, it’s roughly 1000x per month. Two months makes a million, where we are at now globally. Three months tops a billion.

That R0 value is just an average. The actual growth rate depends on the virus, which can mutate. Usually diseases evolve to become more infectious and less lethal, but that’s not guaranteed. It also depends on the human hosts. If they are densely packed and mobile, the actual R is higher. If socially isolated, it’s lower. The whole point of ‘flattening the curve’ is to reduce R down to something close to 1, so the expansion rate is not so scary.

The series for a R0 value of 1 goes like this: 1-1-1-1-1-1. Still new infections, but they are offset by older cases that either recover or die. Rabies is a disease that acts like that. Nasty, but uncommon. Good thing, because a rabies that spread like Covid-9 would truly be the Zombie Apocalypse, except everyone would end up dead instead of undead.

Unchecked epidemics start out exponential, but eventually they start to run out of hosts. The R value declines to 1, and then all the way to zero.  Overall, the cumulative case count makes an S shape, sometimes called the ‘logistics curve’. It grows steeper and steeper for the first half, then flatter and flatter for the remainder. The number of new cases each day makes a bell curve.

The good news is, the rate of increase globally has started to slow down. Last week I predicted a million cases by Monday, but it took until Thursday instead. Most likely, social distancing is starting to work. Not everywhere, but the data looks promising for much of Europe, and a few parts of the US.

Sadly, much of the US is still in the early growth stage, where it looks easy peasy. In a week or two or three it won’t be.

Dennis Kolva
Programming Director


Author: Dennis Kolva

Programming Director for Turtle Creek Software. Design & planning of accounting and estimating software.