Glass Half Empty, Exponential Growth, COVID-19, Social Distancing

Glass Half Empty:  Exponential Growth 

COVID-19, Social Distancing

This post is motivated by controversy over the wisdom of implementing social distancing and "shelter in place" early in the COVID19 outbreak.  There is an economic impact, and my family and I have felt it.  There are other forms of hardship caused by these precautions.  Why bother when total cases are still relatively low?   The illustration is adapted from a discussion about exponential growth in Geoffrey West's fabulous book called "Scale". 

Glasses representing time-lapse of exponential growth at 0, 50, 60, and 61 seconds.

Snapshots at Zero, Two, Fifty, and Sixty Seconds
These four glasses, with a small bit of imagination, can be viewed as snapshots of a single glass containing a magical liquid that doubles in volume with each passing second.   By starting with just the right amount, it's possible to arrive at the GLASS HALF FULL situation exactly one minute - to the second - after the process begins.   

What does this have to do with COVID-19?
The analogy to COVID-19 cases (or deaths) is important.  Many of you can verify for yourselves using a spreadsheet that after 50 seconds, the second glass is still what you see.  If the liquid is doubling in volume EVERY SECOND, and only reaches the halfway mark after 60 seconds, then you must start with such a small fraction that even after fifty doublings in volume, it's still not visible to the naked eye.  However, moments after the 50s mark, you'll see a layer in the bottom of the glass.  At exactly 60 seconds, you'll have half a glass of magical green liquid.   THE FULL GLASS IS WHAT YOU HAVE JUST ONE SECOND LATER.   

Social Distancing matters - especially while "glass is apparently empty"
Even if you can get the "doubling rate" to slow from 1 second to 3 or 4, you're clearly STILL going to have a lots of green liquid after a few minutes. 

Even though Washington State has decreased the doubling rate from 3 days to 4 or 5, the number of patients and deaths is still skyrocketing.

While you have a few dozen cases, it's like an empty glass 20 or 30 seconds into that process.  If you wait until you have a half-full glass, it's too late for social-distancing to help.  You'll have a flooded kitchen within seconds.  Overwhelmed hospitals within weeks.

Stringent measures are required to avoid those overwhelmed hospitals.  "The Cure" some have been discussing is not a cure at all.  It's an effort to buy time.  Toss it out, and we'll face the fury of an exponential explosion of COVID-19 cases.   That's the big difference between this disease and so many others - or deaths by car accident.   THIS cause of death  is increasing exponentially, the others (such as Dengue in Brazil) is not. 

So what about flattening the curve?  What about a plateau? 
Exponential growth of pandemic cases cannot continue forever.   After a few tens of doubling cycles, you'd have infected the entire planet.   The reality is that once enough people are infected (then either recovered and immune - most cases - or deceased), growth slows down.   The USA, however, has over 300 Million inhabitants.   We've gone from 15 to 60,000 cases, from 1 to over 1,000 deaths in just a handful of weeks.   Unless SOMETHING is done, the plateau will be a sharp peak, not a gentle and broad bump that remains lower than a dashed line indicating the capacity of our health system.