COVID-19 Model and Projections Rationale (from Daily Report on 4/2/2020)

By Dan Reichart, Nick Konz, and Adam trotter

Let’s spend a moment reviewing our general approach, and why we chose it.

Our page features two separate models. The first is a purely empirical model of the daily doubling-time measurements. We take a purely empirical approach — i.e., what is the doubling-time trend line and what is its uncertainties? — because (1) this doesn’t require any specific knowledge of epidemiology (we are astronomers after all!), and (2) the alternative is nearly impossible, even for professional epidemiologists.

What is the alternative? A first-principles approach: What is the specific effect of more widespread, faster case identification and isolation? What is the effect of social distancing? What is the effect of stay-at-home orders? What is the effect if these (and many, many, many other factors!) are not applied uniformly? What is the effect of wearing vs. not wearing masks? Etc., etc., etc. Many, very smart, very experienced, professional epidemiologists are taking such, first-principles approaches — and their projections are all over the place (for example).

Why are they all over the place? There are simply too many variables, and too many unknowns. The result is a model for everyone: Optimists can find an optimistic model. Pessimists can find a pessimistic model. Politicians can find either, depending on what they hope to achieve, or on how they hope to appear.

This is why we chose to take the opposite approach. We do not know how all of these efforts that everyone is making translates into changes in the doubling time…but we can measure these changes. And we can measure them well — in near-real time, and without underestimating the uncertainties in the implied parameters. (The latter in particular is actually our little group’s area of expertise.)

The second model that our page features is the projection model: Given this doubling-time trend line, and its uncertainties, how many people will become infected and when? This (unlike the challenging epidemiological questions above) is actually a fairly easy problem to solve. Similar questions are assigned to students in introductory calculus classes.

And with not much more information, we can also project how many of the infected will be symptomatic, and how many of these will die. Each of these additional steps comes with additional uncertainties, but we are careful to propagate these uncertainties through to our final projections.

The only assumption that this approach makes, that is not reflected in our uncertainties, is that the doubling-time trend line continues to hold into the future. That is why we are always careful to emphasize that we are not projecting what will be, but what will be if we cannot make the doubling trend increase faster than it already is.

In this sense, the true goal of our little project is to give us all near-real-time feedback as to whether or not our collective actions are making a difference, and if so to what degree. When fighting an invisible enemy, it is hard to know if we are winning or losing, or at least turning the tide. But each time our projections improve, we know that at least some of the things that we are doing are having an effect. In that sense, this page is meant to be encouraging, and even empowering.