Solving a Real Problem — with math.
The COVID-19 pandemic was a world-changing madhouse of a contagious disease. People got sick and shared the virus with others, and there we go, off to the races. I mean hospital.
We have mathematical models for disease spread, so of course we could predict the number of cases! It’s a tough problem but not unsolvable. The most common model is called the SIR model, for Susceptible, Infected, and Recovered. It’s a spiffy model that works well … in certain situations. Situations that look like this:
The model expects that in a perfect world, you would catch it, recover (hopefully!), become immune, and the curve of cases would flatten just like you see here. That’s why at the beginning of the pandemic there was a lot of talk about flattening the curve. We all expected (and hoped!) that COVID-19 would act just like these theoretical models. We would flatten the curve, and it would go away, and we would get back to normal quickly.
Reality, and COVID-19, had other plans for us.
We had multiple surges caused by people acting like people (what, me quarantine? HAH!), by multiple mutations in the virus, or by the fact that you could have the disease and not be aware of it, or that you could catch the disease more than once. It was a very impolite disease.
We ended up with disease counts that looked like:
These were the cases in Los Angeles over time. You can see the surge, a slowdown in the number of cases, a surge, another slowdown, and whatever that last bit of the curve was. SIR isn’t designed for this case at all. Predicting the number of cases using it isn’t going to work. At all.
So the theoretical method was originally SIR, the applied version was when people wrote code to implement it, and we, the practical mathematicians, said, “We need a plan B!”
We looked at the Los Angeles cases, and we saw that it looked like someone had taken multiple SIR curves and stuck them together. There’s a simple curve, like the SIR model, and it flattens out, and then there’s another surge. After much thought and discussion, we came up with what we call the ALM model.
We even published a paper found here. It’s a mathy paper, with both theoretical and applied mathematics, but the end result is a method that’s very practical.
