Exponential Growth Part 3 (Apr 27)

In past posts I’ve talked about big exponential growth. The scary kind. Covid-19 was like that for most of the world in March. Multiplying by 2 or 3 every 4 or 5 days makes rapid changes.

Fortunately, thanks to social distancing, the pandemic settled down in April. People are still being infected, but in most places the number of new cases is close to constant. That means the Rt growth rate is about 1 (with some exceptions).

Here is a chart of small exponential growth rates.

Back when humans went to work, parties, restaurants and sports arenas, the Rt growth rate for Covid-19 was mostly between 2 and 3. Those would be almost vertical on this chart. The more horizontal curves come from a world that still has social distancing. Their shape depend on how much it reduces the infection rate. If the rate is more than 1, cases increase. If below 1, they gradually subside.

Small changes in the rate have a big impact. For example, if a region has hospitals currently at half-capacity, then an Rt of 1.05 overwhelms them in June. 1.04 hits crisis in July, 1.03 in August, 1.02 in October, and 1.01 postpones it til early 2021. 1.0 prevents it entirely.

One challenge is, there’s no way to know the current exact Rt number. The Rt Tracker website calculates a value for each state based on testing data and other factors, but their model is based on a lot of guesswork. The site include error bars above and below each estimate, to show how much uncertainty there is.

Even worse, there’s no way to know the impact each policy decision has on Rt. If everyone wears masks in public, the infection rate surely goes down: but how much is just a guess. Ditto for every other change in daily life. In a year or two there will be tons of data to help calculate impacts, but right now we’re on brand new terrain.

Even more worse, the system is complex and sensitive. The drastic changes in March dropped Rt all the way from 2.7-ish to 1.0. Small decisions like mask-wearing or opening restaurants could easily shift the Rt value up or down by several or many times .01. After a few months, that makes a big difference.

Governors, mayors and local health departments will make policy decisions. Individuals and business owners will make personal decisions. The net result will be some Rt number that won’t be known until infection data comes in, several weeks or a month later. That feedback delay can make the ride even bumpier.

If you’ve ever lost control of a vehicle on snow or ice, you probably experienced a feedback/delay loop. Skid to the right so you steer left, but there’s reaction time so you over-compensate. That leads to a few left/right cycles of increasing magnitude, until you’re backwards in a ditch.

Covid-19 will probably be similar over the next year or two. Odds are good there won’t be a whole giant pandemic again, but expect lots of little outbreaks. Local ones on the scale of factories or cities. Maybe some on the scale of states or countries or continents. The rules will need constant tweaking. Fasten your seat belts, folks.

Dennis Kolva
Programming Director

Author: Dennis Kolva

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