Unstable Focus

There has been quite a bit of debate about the “dire” predictions that COVID-19 models have made and are making for infections and, especially, deaths, and how those predictions are being used to scare people.  I can say with a great deal of certainty that scientists making these models and doing the simulations are not intentionally trying to scare anyone.  (The only “scientists” I am skeptical of are the ones trying to sell books or market themselves for something.  The “Plandemic” woman is in this category.  She’s been peddling false hope to people with chronic illnesses for a long time.)  On the other hand, in the hands of the media and politicians the predictions can be used in many different ways.  I think many of the early models used a few different scenarios:  we do nothing, we socially distance and/or shutdown, we discover a vaccine, etc.  If you want to scare people, the predictions from the models in which we do nothing can certainly be used, and I believe that if we had done nothing we would be in a very serious situation.

I’ve spent most of the last 30 years developing and analyzing models, mostly trying to predict how physical systems will respond.  Physical system models are not hard to develop if you understand the physical laws that govern them (and the mathematics needed to study them).  There have been very few advances in modeling physical systems at scales visible to humans in nearly a century.  That is why physicists rightly say that most of what engineers do is classical physics.  One nice thing about physical systems is they are not alive to change their behaviors to something not included in the model.  (Note, “smart” materials on which I did a lot of research are not actually smart. [1])  Another nice thing is you can do controlled experiments to validate your model.  Finally, you have a lifetime of experience and intuition to use to see if the results make physical sense.  However, I think the best results are the ones that do not initially make intuitive sense and require you to adjust your intuition.  See footnote [2] for a great example of this and footnote [3] for my experience trying to get engineering students to use their intuition and common sense.

The basic model for disease spread is what’s called the SIR (susceptible/infected/recovered) model; there are many variations and extensions of this.  There are also many good explanations of this model online so I won’t go into details about it here.  I would recommend watching the YouTube video I’ve embedded at the end.  One thing to know about these models is that they are statistical and have many parameters that people can “tweak” and many “features” that can be added.  Being statistical, they will only give you an “average” sense of what might happen.  Likewise, you can adjust the parameters to get almost any prediction.  This is where so-called fitting comes in.  Scientists will tweak the parameters until they fit known cases and hope those parameters will predict what will happen in the future.  When scientists share these models they usually provide the parameters they’ve used and what “ingredients” have been included.  Although some people want to keep their models proprietary, and I would be skeptical of them.  The problem here is that by the time the predictions hit the media and politicians all those details have been stripped away to make it more digestible for the general public.

Statistical models have been used in physics for over a century, and from basically the time we realized matter was made of atoms but we could still measure properties of matter without having to keep track of every atom.  For example, the temperature of something basically measures on average the energy contained in the atoms/molecules comprising the material.  We don’t need to track every atom to get this average.  Likewise, the pressure from the air you feel is the forces of all the molecules in the air hitting you.  If the wind hits you from one side you notice a net force acting to push you in the direction the wind is blowing.  This is simply because more molecules are hitting you on one side than the other creating a net force that wants to move you.  Again, we do not need to keep track of every molecule/atom to determine what this force is.

Statistical models in physics (a subject called statistical mechanics) work extremely well and are used extensively.  Like SIR models statistical mechanics models can be more or less complicated by adding or removing ingredients.  For example, the “ideal gas law” that relates pressure, temperature, and volume was known long before we understood anything about atoms, and we now know that it can be completely derived by averaging the motion of atoms and molecules modeled as balls bouncing around.  However, there are cases when the ideal gas law doesn’t work well.  For example if the gas is made from molecules you can include the rotation of the molecule as an ingredient.  It turns out that under “normal” conditions this ingredient isn’t needed, but under extreme conditions it helps explain why the ideal gas law fails.  The other time statistical models don’t work well is when you don’t have enough particles (i.e. atoms or molecules) to average over.  If you only have, say, one thousand atoms bouncing around in a box, statistical averaging starts to not work so well.  Fortunately, with modern computing power, we can model billions of atoms moving around using molecular dynamic simulations.

One reason statistical models and molecular dynamic simulation work so well is that atoms do not have free will, i.e. under the same situation they will all act the same.  People on the other hand are very different.  It’s this behavior and the feedback causing that behavior that makes modeling populations so hard.  If you have millions of people you can try to estimate how the average person will behave and include that in a statistical model.  Most of the variations of the SIR are doing just that, but modeling behavior even on average is very difficult.  While we could theoretically model every person in the United States acting in an average way, we know this would provide the same results as the statistical model.  We could include some randomness in the every-person model, but again with enough people you’re still going to get the average result.  What an every-person model may help predict is how a very non-uniform population density plays a role.  However, SIR models can be adjusted for this too.

To help explain the SIR model, the creator of the two videos below basically does molecular dynamics simulations with people replacing the atoms and behaving in different random ways.  Note the Twitter screenshot he includes around the 2:14 mark with someone responding to him, “Im not a gas in a box :'(”  Because he is only using around one thousand people walking basically randomly he makes many runs and averages the results.  To try to model the variation in people’s behavior he uses various percentages and looks at how these percentages change the results.  For example, he varies the percentage of people infected that get quarantined or the percentage of people traveling from one community to another.

When you’re modeling things with algorithms instead of equations you can play around with all kinds of probable behaviors and actions.  Things can get extremely complicated and often you have no idea what the result might be.  There is actually a scientific/mathematical buzzword for this called “emergent behavior.”  According to Wikipedia, “emergence occurs when an entity is observed to have properties its parts do not have on their own.”  You can think of your body as the emergence of all the individual cells doing their own thing.  Scientists and mathematicians are enamored with emergent behavior because you often see very interesting and realistic behaviors emerge from very simple models of how the parts interact.

While I am certainly biased, I believe the scientific community is doing a great job simply trying to keep people informed.  Unfortunately, their messages can get distorted and used politically.  Plus, scientists usually avoid words like “never” and “always” so when someone asks them if it’s possible 10 million people will die, they’ll simply answer, “Yes.  It’s possible.”

 

Footnotes

[1]  Playing with a dielectric elastomer “smart” material water balloon in the lab of my former student Nakhiah Goulbourne at the University of Michigan during the summer of 2010.  What makes this material “smart” is a crazy-stupid 5,000V being applied across the membrane, although there is very little current so not much power.

 

[2] A great example of needing to adjust your intuition based on strange results from a model is a model/simulation I worked on with Elaine Serina when we were graduate students.  Elaine wanted to understand how forces on your fingertip get transferred to tension in the skin and stresses on the bone as part of a larger study on carpal tunnel syndrome.  As a simple first step, we decided to model the fingertip as an ellipsoid (think of a plain M&M) inflated by water and then compressed between two plates.  We wanted the initial inflation because there is usually tension in your skin (unless you’ve been soaking in water and are all “pruney”).  However, when Elaine took the equations I derived and wrote code to solve them she kept getting strange results that we were both convinced couldn’t be correct.  The simulations were showing that when you inflated the skin membrane you would get compressive stresses.  Our intuition said, “You can’t inflate something and get compression.”  We spent at least a month trying to figure out what was wrong with the model and/or the code to no avail.  After a meeting with our thesis adviser in which he concurred with our intuition that something must be wrong, we were walking back to our lab through the student union and noticed the inflated mylar balloons.  One of us (likely me because I was the one studying wrinkling caused by membrane compression) realized that all the mylar balloons were wrinkled around the edges, just where our model was predicting compressive stresses.  The only way you get wrinkles is when you have compressive stresses.  Thus, we realized our intuition was wrong!  As you inflate a mylar balloon the edges want to pull in towards the center.  This creates the compression.  If you have a rubber balloon of this shape, adding more pressure will eventually cause the wrinkles to disappear.  However, because mylar is so stiff you can’t pressurize it enough to remove the wrinkles without it rupturing.

[3] I was always a bit disheartened with how many mechanical engineering students did not seem to have this intuition when they got to the junior-level class I regularly taught.  To address this, part of every homework problem was a statement about why they felt their answer was correct or incorrect.  Early in the semester I would get answers like, “Because I followed all the steps and checked the math.”  I was constantly shocked at how many mechanical engineering students did not come into the class with the skill of looking at the result they got and evaluating if it made physical sense.  Every semester I talked a lot about “sanity checks.”  Plus, I wanted to know if they suspected their answer was not correct, as it’s much better in the real world to know a result is likely not correct than to think it is.