Lot of people disappointed that Melb isn't relaxing restrictions despite low numbers today. But it was never about the total or the R, pace John Quiggin's musings. It's about the structure of the local epidemic that generates those averages. A dispersed structure is a concern.

Imagine two outbreaks, each 100 cases resulting from a superspread event. Both have the potential to generate 250 cases if unchecked. One outbreak is tightly clustered – a meatworks, say. The other is highly dispersed – all the families that intersect with a megachurch, say.

As far as an economist is concerned, these two outbreaks generate the same average numbers and are therefore equivalent. But the dispersed outbreak poses MUCH higher *uncertainty* — you can't be sured you've found every case, so the chances of further spread are higher.

In addition, the dispersed outbreak is more socially diverse, which means there are more of those long ties between otherwise-distinct social cliques — ties that facilitate the spread of contagion along pathways that are improbable and by definition less easy to trace.

We call these 'small world' network dynamics. Look up the work of Duncan Watts for a good introduction. They don't generate exponential decay curves — they produce a power law distribution: v. steep initial drop-off then a long tail of low level numbers.

If your contact tracing data is telling you those low numbers are coming from a whole bunch of different places, that's a warning sign that you have a highly dispersed outbreak. Uncertainty correlating with risk is BAD NEWS. So you might lock down for longer.