Exponential Growth #4: Containment (May 23)

In past posts I’ve talked about exponential growth when it’s fast and scary, and when it’s close to flat. But there’s also negative growth, with a multiplier of less than 1.

Right now, the Rt Tracker website shows all but four states with Rt like that, from Arkansas (.99) all the way down to Alaska (.63). If they can stay below 1 for long enough, Covid-19 eventually will reach containment.

Here is a chart of exponential growth rates less than one. It shows how the number of new cases of Covid-19 will decrease for each Rt multiplier. The lower the number, the faster the approach to zero.

Right now there are four states with Rt values under .82: Alaska, Hawaii, Vermont, and Montana. All have relatively small, isolated populations. They never had many cases to begin with, and are close to zero now. With local containment achieved, their biggest worry is new cases that come in from elsewhere.

The next lowest state is Connecticut, with an .83 multiplier. They had over 2000 new infections at the daily peak, but the average is about 600 now. At current rate of decline, it will take roughly 50 days to drop by a factor of 10 (to 60 new cases per day). Another 50 days gets it to 6 new cases. The theoretical curve never reaches zero, but with actual humans it’s possible to get there eventually.

Other states with higher Rt values will decline more slowly. Some will be very, very slow.

Exponential curves and Rt charts are pretty, but they are just theory. Actual containment depends on what people do each day: how much they stay home, how much they congregate, whether they wear masks. Just as important is the work of state and local health departments. They have battled all sorts of diseases over the past century, and this is just another for them.

To contain a disease, health departments do whatever it takes to reduce the infection growth rate to something less than one, then keep it that way.

Vaccines are the best way to contain a disease. Many folks are working on them for Covid-19. Next best is contact-tracing and quarantines. If those aren’t enough, then the only recourse left is massive social distancing. Economically, it’s an extremely painful option, but less bad than having many people suddenly sick and dying at the same time.

The ideal way to conquer a dread disease is to get global containment: already accomplished for smallpox, and almost completed for polio. Total containment is very hard work. Health workers must go into poor and war-torn regions and vaccinate enough people to reach “herd immunity”. It also requires plenty of contact-tracking and isolation until the last cases are completely gone. One sad consequence of Covid-19 is that it sets back the efforts to eradicate polio.

The Rt tracker site seems like a very useful tool. However, Rt is based on actual test results. It lags by at least a couple weeks, because it takes time for infections to develop, tests to be processed, and data to be entered into the pipeline. Today’s numbers reflect conditions from when state just started to reopen in early May. The social distance scorecard is probably the best way to predict the future, but it’s a very crude guide based on smart phone locations. It doesn’t adjust for mask use, indoor vs outdoor contact, or sanitation measures. Lately it rates most of the US at D or F, but I think reality is a grade or so better.

As social distancing relaxes, it will be interesting to see how much it affects the numbers. States will probably jump around with changes in weather, policies and people’s behavior. The risk is always there for an outbreak, with a sudden return to scary exponential growth. A single ‘super-spreader’ event can push any state to well above 1.

SARS and MERS were caught soon enough to be 100% contained. Covid-19 became too global, and it’s unlikely to ever reach full containment. Even with a vaccine. However, it can become like measles, influenza and other diseases that are controlled enough to not cause big catastrophes.

Dennis Kolva
Programming Director
TurtleSoft.com

Author: Dennis Kolva

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