Kungfu Pandemic

In my other life, I write academic papers.  Usually, they have to do with clinical biomechanics; occasionally, the topic is growth curves; and once in a very long while, they might actually have something to do with martial arts.  I haven't written one of those martial arts papers in a while.  More and more often regardless of the topic, they involve the use of some pretty fancy statistical analyses. In this other life I tend to rub elbows with doctors of all sorts, and at times, I even have ventured into the area of public health.

In so doing, I've encountered all manners of models that describe how things work.  We've made mathematical models of how people grow, how gun violence propagates, and even how people walk.  So in a number of ways, I'm no stranger to how epidemiology works.  In fact, I often take an active professional interest in what people are doing to model data and better understand how the world around us works.  More on this below the fold.




It is, therefore, of great interest to me to see data like this.  The curve below shows the total number of COVID-19 cases world-wide by date.

From: https://www.worldometers.info/coronavirus/coronavirus-cases/

The bump at February 12 is due to the inclusion of clinical cases (that is those matching symptoms) rather than just confirmed laboratory cases.  Considering this curve is an indicator of who is symptomatic, it suggests that the people represented here had COVID-19 anywhere from 5-14 days earlier, and perhaps had a chance to spread it around a bit first.  Much more on that below.

If we pay attention to the time immediately after February 12, it looks like things are going to be OK.  I've scraped the data from the graph and used a logarithmic fit (green) to represent where the curve seems to flatten out.  (note: it should probably be a logistic fit, but for the sake of argument, a log is close enough).  When we look past the inflection point somewhere around February 28, the curve is best fit by exponential growth (red curve).  In the first case, the behavior of the curve is reassuring - it means that things seem to be under control.  But in the second case, things are spiraling rapidly out of control.

Logarithmic (Logistic) area in green, and exponential area in red.

Now with the fits.  Green is good.  Red is Very Bad.

To understand exponentials, think of them this way.  Today I give you a penny, and every day I say that I'm going to double the number of pennies I give you.  So tomorrow, you get two pennies.  The next day you get four, and so on.  This sequence rapidly grows: {1,2,4,8,16,32,64, 128,256,512,1024,2048,4096,8192...} so that by the end of two weeks I'm giving not mere pennies a day, but nearly $82.  By the end of four weeks I'm giving you 2^28 pennies or $2,684,354.56.

It isn't quite so bad (sort of) in the case of COVID-19.  The doubling time of cases isn't daily, it's every 6 days according to one source.  If we just count what we have here and project our model forward, here's what we find 20 days from now world-wide:

So this isn't looking good, is it?  1500 x 1000 = 1.5 million cases world-wide.

But wait!  This implies that we have accounted for all the cases.  While countries like South Korea are testing something like 10,000 per day, in the US we have, in the last three weeks, only tested about 8,000 people.  I won't start with the politics of this.  This implies that there are lots of silent cases.
 
That same source that gives a 6 day doubling time attempts to account for this fact.  If we just subset our projection to the number of real cases in the US, the projection is that there could be somewhere in the order of 1 million cases by the beginning of April in the US alone.  In other words, the curves thus far are representative of known cases only not true cases.  Ooof!

So this brings me to my point.  You may have already heard about flattening the epidemic curve.  There's a great paper on this "The 1918 Influenza in Missouri:
Centennial Remembrance of the Crisis, part 2" by David S. McKinsey, MD, Joel P. McKinsey, MD & Maithe Enriquez, PhD.  In that paper they examine what St. Louis, MO did before the outbreak was widespread, and there are comparisons to Boston which did nothing until it was apparent that there would be a problem.

Yikes.  Don't hold parades like in Boston.  Practice social distancing.  It works.

The green curve is Boston.  The red curve is St. Louis.  What did they do in St. Louis? Empowered by the mayor, Dr. Max Starkloff:

"began by shutting down the city, by closing schools, theaters, moving picture houses (in the parlance of the day) and places of amusement . Public gatherings of more than 20 persons were prohibited. The
next day closure orders expanded to include playgrounds, library reading rooms, fraternal lodges, pool halls, and Municipal Court. Even churches were closed, for the first time in the city’s history. The use of streetcars was limited. Hours for busy downtown department stores, including Famous-Barr, were restricted. A staggered work schedule was implemented at factories to reduce streetcar crowding"

This is very similar to what is happening now in Italy where at first they didn't take the outbreak very seriously.  It's just like the flu people said.  The problem is that even if our current outbreak was just like the flu, a large number of people die yearly from it even though we have a vaccine.  During 2018-2019, according to the CDC there were

"35.5 million people getting sick with influenza, 16.5 million people going to a health care provider for their illness, 490,600 hospitalizations, and 34,200 deaths from influenza."

Note that this figure will still be with us.  Nearly half a million people in the US will require hospitalization with the flu.  Now add to that COVID-19, and car accidents, and burn victims, etc.  You get the picture.  It is therefore important to "flatten the curve" as St. Louis did to avoid overloading our medical system.

Where's the kungfu in this?  Staying healthy.  We practice gauging our distance from others when we spar.  Now maintaining that social distancing will become just as important as the fancy footwork we use in class.  There will be challenges with working out or practicing when the gym is not available. These will take ingenuity to overcome.  I will attempt to offer some guidance here while we are out as to how you can stay healthy and even improve your kungfu while on your own.

And if you haven't guessed from the tone of this post - do your best to stay home.  Classes at OSW are out until further notice.

Stay safe and healthy,
Sifu Tim Niiler