Linear Models

The linear model continues to preoccupy my mind. Today confirmed for me that many of these countries and states are now behaving as a linear model, by successfully predicting the numbers for the selected regions. Comparing against eight different models, the linear growth was consistently the best predictor. See the comparison numbers in the charts above.

The good news out of these numbers is that Switzerland is continuing to slightly reduce their active cases of COVID-19, as people are recovering faster than it is spreading. This marks three days in a row, establishing a clear pattern of slow recovery. Also providing hope, the Mideast seems to be improving, as all three tracked countries seem to be switching over to a linear model now.

I am still puzzling over how a region can maintain a linear growth rate, regardless of the size of the region or the number of infected. This means that a roughly constant number of new people are confirmed each day. In looking deeper, it turns out this is not strictly constant after all. All across the world, there is a week long cycle of ebb and flow within that linear growth, so that growth peaks in the latter half of the week around Thursday, and reaches a consistent low around Sunday/Monday. This is most easily seen in South Korea, which has been holding a roughly steady rate of new cases for almost three weeks now. This could be a reporting anomaly, the result of testing or results availability, but it was interesting to see anyway.

Day-to-day changes can make it easy to lose the significance of this model change within the background noise. To see how different a linear model is from the exponential, consider projections of active cases in the UK. In the first graph, you can see that the country switched over from exponential growth to linear growth on March 29th (five days after the stay-at-home order was issued, which happens to be median time from infection to symptoms). The difference between the two models over the period of March 29th to April 3rd is distinct. However, continuing this trend out just one more week can make a huge difference, as the next chart shows. You can imagine what happens after that.



This has important implications on how the pandemic plays out. On one hand this is great news, as it means the pandemic can be contained and the curve can be flattened much more effectively than we had hoped. However, if the linear model continues indefinitely, as South Korea suggests might be the case, then the lockdowns may need to stay in place much longer than anyone is anticipating. Returning to life as it was before the spread of COVID-19 would restart the exponential growth again. Until something changes on the healthcare side, such as a vaccine or a realistic implementation of an aggressive test-track-isolate strategy, the regions willing to enforce stay-at-home orders may be in a bit of a stalemate.

In other news stateside, Alabama has issued a stay-at-home order starting on April 4 and Missouri has decided to start one April 6. South Carolinians may be feeling a little left out at this point. Fear not, though, for neighboring Georgia has effectively weakened their stay-at-home order and reopened the beaches, as Governor Kemp took inspiration from Governor DeSantis (FL) and decreed that state law overrides any local regulations that might be more restrictive.