Overall numbers won’t show the English strain coming

Here is a plot of daily new positive COVID tests in the U.S. in the first half of March 2020.

It’s no surprise that by mid-March, most people were worried: the virus was here and was growing fast. This was evident by the time there were 1,000 new positive tests per day. The lockdown began around mid-March — way worse than if it had begun in early March, but much, much better than if it had begun in late March, when we had tens of thousands of daily positive tests.

Meanwhile, a new strain of COVID first discovered in England looks to be substantially more infectious (two figures being thrown around are 56% more and 70% more; epidemiologist Trevor Bedford’s best guess is 50%). If these numbers are anywhere close to right, the new strain will grow rapidly and exponentially until and unless we react and dramatically increase our levels of precaution. (See here for further discussion.)

The question, then, is: when will we react? In my mind, there’s reason to believe that we will react slower this time than we did in March.

The reason COVID (correctly) felt scary in March is that on any given day there were many times more positive tests than just a week before. For example, on March 12th there were 7 times more cases than on March 5th. This trend was really clear because the exponential growth drowned out any day-to-day noise.

With the new strain, if the general public (or public officials) use overall case numbers to guide their planning, this won’t be the case. Positive tests in the first half of March (above) could have been modeled as something like \text{pos\_tests}(t) = 1.36^t plus random noise (where t was the number of days since February 20th). For the sake of comparison, let’s say the English strain were to increase at the same rate. The overall daily case numbers would look something like this.

\text{pos\_tests}(t) = 200,000 + 1.36^t plus Gaussian random noise with standard deviation 25%

This is a simulation of daily positive tests, modeled as \text{pos\_tests}(t) = 200,000 + 1.36^t plus random noise. The 200,000 is the baseline rate of new cases due to the old (currently dominant) COVID strain. The 1.36^t term is the contribution of the new strain.

Remember that people started reacting to COVID around when there were 1,000 new positive tests per day. In the previous chart, on what day would you guess that the new strain first contributes 1,000 new positive tests per day? The answer (in white, highlight to see):

Day 23

Instead of exploding relative to a baseline of 0 cases (like in March), the new strain will be exploding relative to a baseline of around 200,000 cases per day. As a result, day-to-day random noise will completely mask any increase in infections from the new strain until it becomes dominant — around day 40 in the above chart. This means that if people use the overall numbers to guide their levels of precaution, our reaction time could lag by two or three weeks compared to March — as if we had locked down in early April instead of mid-March.

Now, this isn’t entirely a correct comparison because the rate of exponential growth will be much below 1.36; a reasonable guess might be 1.12. (You can get this by assuming R = 1.6 and assuming a generation time of 4 days.) But the overall point is the same: because any increase in the prevalence of the new strain will be masked by noise in current COVID levels, the new strain won’t be evident in overall numbers until it starts contributing hundreds of thousands of daily infections.

The current situation isn’t perfectly comparable to last year’s for a number of reasons. On the one hand, we’re already exercising our quarantine muscles: we won’t have to re-learn everything (e.g. “wear masks”) from scratch. On the other, people may be complacent because COVID already feels like a known quantity. But regardless of specific differences, the fact that baseline noise will mask numbers from the new COVID strain until really late is a major reason to expect our reaction to the new strain to be slower, and that’s pretty scary.

3 thoughts on “Overall numbers won’t show the English strain coming

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