Recently Germany began to share that they were reopening their economy with an eye on their Rate of Reproduction calculation. They had been seeing Ro in the 0.7 range and decided to back off of some of their lockdown restrictions. Now they were seeing Ro creeping up to 1.0 (edit: I’m calculating their Ro too and I don’t see this movement. Maybe they have data that I don’t) and they were getting concerned. This seems like a data-driven approach to reopening the economy, but is it a good one?
Some Background on Ro
I have published on methods to calculate Ro in previous articles. There may be other ways to do this, but one very simple way is to use the Susceptible, Infected, Recovered (SIR) equations that come from epidemiology. This is why having these three numbers published by a nation or locality is so important (note this, US Governors!). Below is a list of locations where Ro is highest, per my calculations.
The Ro is purported to describe how many people an infected person will transmit the virus to. Therefore, if Ro is over 1, the virus will expand in society. If Ro is 2, one person will transmit to two others, thus creating a non-linear growth pattern. Traditionally, Ro is calculated by multiplying the Transmissibility factor (above on the chart), which is what we actually back out of the SIR equations, by the number of days a person with the disease is infectious.
Problems with this…
- I cannot find any references to what the actual number of infectious days is for COVID-19. In my calculations, I guess at the 14 day number that is all around us and I get the same numbers that I see published for European countries. So I suspect they’re using 14 days too. But I kind of doubt that’s the right number because for other infections the number of infectious days ranges from 2-10. If my assumption is correct, then I suspect that this could be inflating the Ro numbers associated with COVID-19. Not a huge deal (the transmissibility numbers still give an indicator of whether a country is in a highly-infectious period) but might be giving false comparisons to other diseases.
- I also can’t find any data on reinfection percentages for COVID-19. This isn’t surprising, of course, as this is a novel coronavirus, but I also have to assume a value for reinfection in the SIR equations. If it turns out that reinfection is higher than we thought, this will lower our transmissibility values (seems counterintuitive, but it’s complicated).
- Superspreaders are a real problem for Ro. A superspreader is an event or person associated with large numbers of infections. Typhoid Mary, who was a non-symptomatic Typhoid Fever carrier, is a good example. She infected 76 people singlehandedly with Typhoid Fever. Imagine then if the Ro for a disease is 2 and one person infects 100 people? This acts like accelerant on a wildfire! The same applies for an event that acts as a superspreader, such as the Spanish Flu Liberty Loan parade in Philadelphia. Within 72 hours of this superspreading event every hospital bed in Philadelphia was full. Within a week there were 4K deaths. The CDC paper linked above states about this: “SSEs (Super Spreading Events) highlight a major limitation of the concept of R0. The basic reproductive number R0, when presented as a mean or median value, does not capture the heterogeneity of transmission among infected persons; 2 pathogens with identical R0 estimates may have markedly different patterns of transmission. Furthermore, the goal of a public health response is to drive the reproductive number to a value <1, something that might not be possible in some situations without better prevention, recognition, and response to SSEs.” (Frieden and Lee, 2020)
- The Ro measure is being co-opted by researchers who seek to “improve” it. This paper on MedRxiv is non-peer reviewed, but seems to be influencing the German government’s calculation of Ro. A summary of the approach is that the researchers are making assumptions about how to modify the Ro equation to take account of mobility restrictions and quarantines. I’m not a big fan of this paper, as it seems to be more reliant on buzz words and popular assumptions than facts. Also, I see no calibrations for super spreading events. This approach does seem immature, but it does appear that European nations are using this approach in their calculations. If these researchers are wrong in their assumptions on the value of mobility restrictions, of course, or the uniformity of transmission then the whole equation could be off.
Conclusion
This outbreak, because it is a novel virus and a situation we haven’t really been in since 1918, has been a learning experiment. New methods have been tested (nation-wide lockdowns, mandatory face masks), different strategies have been derived (Iceland, Sweden, China, and the US all have very different approaches), and data instrumentation and analysis has been exposed. Using Ro as a single metric to return to economic function seems on the surface to be a good idea, but challenges with the Ro metric itself need to be understood as limitations.