COVID-19 March 25, 2020

Some good news? We're still closing in on the 100,000 mark in just a couple of days from now, BUT take a look a the second graph below--the daily rate of change. Yesterday's total showed a drop in the number of infections compared to the day before: 9,905 vs. 10,408. It's hard to say if that is real, which would be good news, or a change in testing, which would not be good news. A closer inspection of the numbers indicates that the drop is largely due to a drop in new cases for NY. The number of daily new cases in NY fell by almost 1,000. Are the social distancing and lockdown policies in NY showing? At the same time, other states are exploding. For example, MA went from 131 to 382. Is that due to increased testing or is it real? And then some states still seem wonky, as I indicated yesterday. Did LA really drop from rising numbers up to 335 the day before down to 216? Seems unlikely. So, the nationwide total could be good news, or it could just be bias in the measurements. We'll have to wait a few more days to see how things go. I do find it interesting that I haven't seen the drop in numbers in the press.

Nerdgasm alert for what follows:

There is no need to be a medical professional or epidemiologist to understand and then predict what is happening. It's simple mathematics that emerges in countless natural systems. If you tell me that the change in some quantity is proportional to the amount of that quantity, I can write down a simple ordinary differential equation (ODE), the solution to which has been known since Newton invented calculus: an exponential function. I could be totally ignorant of the origin of the data I've been plotting, but if you told me that the next number in a sequence of numbers was proportional the current number, I'd know exactly how to model that series without any knowledge whatsoever of the physics behind the numbers. In this case, the number of new infections is proportional to the number of existing infections, at least initially. Thus, it can be described by an exponential function. Similarly, the change in the intensity of light passing through an absorptive medium is proportional to the amount light (a.k.a. Beer's Law) and is described by the same exact ODE with the same exponential solution. It's just math.

Eventually, other things will begin to influence the growth rate besides the existing number of cases. For example, the number of people that have died could start to matter. Those people cannot pass on the infection nor get reinfected (because they're dead). For now, we can ignore them with only a small error, because they are a small fraction of the total population that is alive. But, that may not always be the case, and thus the error of using a pure exponential function will grow with time. And the number of people that have been infected but are fully or at least partially immune to reinfection can also come into play. And there can be subtleties, like having some fraction of the population be more susceptible than others or more likely to pass an infection than others. Or the virus could mutate and change its lethality, viability, or transmissibility. Each of these effects, and others, can be described by other ODEs, all of which then become a coupled system of equations. But, in the end, it's still just math, and there are analytical and numerical ways to solve those coupled equations. My area of expertise requires me to solve even more complex coupled partial differential equations (PDEs), but the techniques for solving ODEs are a simplified subset of the PDEs. It's all just math.

For the analyses I've been doing, I'm only comparing the data to the simple exponential model. The data fits. It works. When the data starts to diverge from an exponential function, as it eventually must, I can try to include the additional complexities that are making it do so, and then project those data forward (I *may* do that, but it's more time-intensive), or I can just note the degree to which the exponential model fails, which is still an informative metric. We aren't there yet. I hope the data will diverge from the exponential model sooner rather than later, and in the correct direction (downward). The sooner the simple exponential model breaks the better.

One of the flies in the ointment (there are many) is that the exponential model can appear to break when it shouldn't. That can happen when the input data is bad. If consistent reporting fails or testing protocols change that will cause a change in trends that is due entirely to how the data is obtained; the data is no longer purely a metric of how infections are changing over time. Unfortunately, this particular fly seems to be increasingly bathing in the ointment.

/Nerdgasm