Modeling an exponential process necessarily produces a wide range of outcomes. In the case of COVID-19, that’s because the spread of the disease depends on exactly when you stop cases from doubling. Even a few days can make an enormous difference. In Italy, two similar regions, Lombardy and Veneto, took different approaches to the community spread of the epidemic. Both mandated social distancing, but only Veneto undertook massive contact tracing and testing early on. Despite starting from very similar points, Lombardy is now tragically overrun with the disease, having experienced roughly 7,000 deaths and counting, while Veneto has managed to mostly contain the epidemic to a few hundred fatalities. Similarly, South Korea and the United States had their first case diagnosed on the same day, but South Korea undertook massive tracing and testing, and the United States did not. Now South Korea has only 162 deaths, and an outbreak that seems to have leveled off, while the U.S. is approaching 4,000 deaths as the virus’s spread accelerates.
Exponential growth isn’t the only tricky part of epidemiological models. These models also need to use parameters to plug into the variables in the equations. But where should those parameters come from? Model-makers have to work with the data they have, yet a novel virus, such as the one that causes COVID-19, has a lot of unknowns.
For example, the Imperial College model uses numbers from Wuhan, China, along with some early data from Italy. This is a reasonable choice, as those are the pandemic’s largest epicenters. But many of these data are not yet settled, and many questions remain. What’s the attack rate—the number of people who get infected within an exposed group, like a household? Do people who recover have immunity? How widespread are asymptomatic cases, and how infectious are they? Are there super-spreaders—people who seemingly infect everyone they breathe near—as there were with SARS, and how prevalent are they? What are the false positive and false negative rates of our tests? And so on, and on and on.