Up or down?

Having been exposed for the past year and half to stories about the ‘basic reproduction number’ and ‘effective reproduction number’ of Covid, you might ask ‘what is R_eff at the moment?’

It’s hard to say. Firstly, it’s not really Covid that has an effective reproduction number but SARS-Cov-2; not the disease, but the virus.  The reproduction number is a feature of models for infection, not models for illness or even for confirmed cases.  Trends in illness or in the number of confirmed cases are important, but they are separated from trends in infection by the whole process of diagnosis, testing, and tracing. Right now, testing is on overdrive: people with minor symptoms are tesing (yay them!) and people with no symptoms but even minor contact with a case are testing (yay them, too!). As a result, cases are much more likely to be diagnosed than they were, say, two weeks ago.

In the long run, under constant conditions, the outbreak will have exponential growth or decay. In the long run, even quite large changes in the diagnosis, testing, and tracing process will be swamped by the much larger changes in the underlying infection rates. In the long run it will be obvious if total infections are going up or down and the rate can be estimated fairly well from confirmed cases. But in the long run we are all in level 1, so that’s not very satisfying.

At the moment, we have a reasonable hope that the population is effectively partitioned into bubbles, with much lower spread between bubbles than within bubbles.  If so, new confirmed cases will mostly either be new diagnoses of cases infected a while ago, or cases who got it from someone in their bubble.  For example, a lot of people who work in the same building as the Stats Department were being tested yesterday, in case they had been infected on August 17.

The number of cases like these is important, because we care about their health, but doesn’t really tell us about the effectiveness of level 4 lockdown, which is about the relatively small number of new between-bubble transmissions from people who were not yet diagnosed.  Calculating effective reproduction numbers from the number of observed cases isn’t going to be very accurate.

All this goes to say that, yes, we have good reason to hope the out-of-bubble reproduction number is well under 1, but the actual value genuinely is hard to estimate — and it’s particularly hard to estimate just from public data on numbers of newly confirmed cases.