The COVID-19 Pandemic: Models, predictions, projections, and uncertaintyOct 11, 2021
"Prediction is hard, especially about the future.” This quote, variably attributed to Yogi Berra (what quote isn’t?), physicist Niels Bohr, and a Danish cartoonist, fits well with the pandemic in Colorado at the moment. The number of COVID-19 patients in hospital, used by the Colorado Modeling Group for fitting the epidemic model, has been stuck at a plateau for several weeks and oscillating at around 900. The case numbers are similarly stable while test positivity is rising, now unacceptably over 7%. For the United States overall, the epidemic curve is dropping with a 20% decline in hospitalizations and cases over the last 14 days.
What is happening in Colorado? Our success in vaccinating Coloradans is better than the United States overall with 77% having at least one dose and 71% fully vaccinated (of those eligible). Schools, a locus for mixing and infection spread, are in session across the state, as in other states. We have a patchwork of mask mandates across jurisdictions, comparable to the situation nationally. No single explanation stands out for Colorado’s situation with this continued high plateau; humility leads to “we don’t know.”
A dive into the variation of the pandemic across the state provides some insight but not an overall answer. In the Denver Metro region, the pandemic is tailing off while the curve is rising in several of the more rural regions of the state. The New York Times map shows the hotspot counties. These are more sparsely populated regions of the state and thus, the higher rates in some counties can only partially explain the current statewide picture. Vaccination rates have generally been lower in the more rural regions of the state, but high rates of infection have led to estimates of immunity that are comparable to those in the regions with higher rates of vaccination. The overall state picture is not well explained by the regional pieces of the puzzle. Stay humble.
Another quote that I use often is from the British statistician George Box: “All models are wrong but some are useful.” The Colorado Modeling Group, like others, uses a Susceptible, Exposed, Infected, and Recovered (SEIR) model with the addition of V for vaccinated (SEIRV), as the model now includes a compartment for those who have been vaccinated. We use the model to characterize the direction and trajectory of the epidemic curve by estimating the effective reproductive number (Re) and also the level of transmission control, which ranges from none—i.e., free mixing—to 100% which would be the equivalent to a complete lockdown with people sheltering at home. The high transmissibility of the Delta variant greatly reduces transmission control, compared with the previously circulating strains.
We don’t make predictions (what we think will happen) with the model, but we do make projections as to what might happen under “what if” scenario. We have been making such projections to guide decision-making since the early days of the pandemic. With the current wobbly plateau of Colorado’s epidemic curve, fitting the SEIR model only tells us what see with our eyes: the epidemic curve is more or less flat. I have continued to anticipate that the curve will “declare itself” and take a direction, hopefully downward, but the plateau persists.
Uncertainty bedevils models. For COVID-19, the most critical source of uncertainty is the SARS-CoV-2 virus itself. We continue to be surprised by its behavior as it changes with mutations and other unknowns. Model assumptions, captured in differential equations, are inevitably wrong to some degree, but we and other modelers are continually adjusting them as we learn more. Given known and unknown sources of uncertainty, however, we can still have confidence in the model’s estimate of the direction that the curve will take—just not at this moment.
Jonathan Samet, MD, MS
Dean, Colorado School of Public Health