Thread by @KennethBodin

Multi post about dispersion. The dispersion/inhomogeneity in the reproduction means that ~80% of the transmissions come from 10-20% of the infected. The higher individual reproduction numbers come from superspreading and airborne virus. 1/

If R0 was 2.5-3 early in the outbreak, it was quickly reduced by regulating gatherings and by the use of masks, down to around 1.5 or lower. Most early model studies used R0 =2.5 and did not account for this big reduction down to 1.5. 2/

So, dispersion explains why early modeling went wrong and dramatically over estimated the growth and impact of the pandemic. It was not because of ”bad science”! We learn!
Further, the dispersion also leads to outbreak thresholds and extinction thresholds, respectively. 3/

When few are infected, there is a good chance that the outbreak dies out by itself for stochastic reasons, because the high transmission events are so rare. Dispersion leads to fewer but more aggressive outbreaks. This may partly explain why we get epicenters (eg. Stockholm) 4/

Another consequences is that immunity will first emerge among people with high contact rates and consequently high individual reproduction numbers. Their immunity will become a barrier for second waves of infection. This will raise the outbreak threshold further. 5/

It can also be seen as if the disease induced herd immunity level is lowered below the herd immunity level of homogeneous reproduction (1-1/R0). However, as explained, a chunk of R0 comes from superspreading and is rather stochastic and will not get reduced herd immunity. 6/

The latter effect has not been considered in the papers computing herd immunity with dispersion (Gomes et al; Britton et al) and therefore I believe they over estimate the effect. However, the effect is substantial as long as we have mitigation and regulate gatherings. Good! 7/

It will have less importance if we have gatherings and when R gets much bigger because of (mostly) stochastic superspreading.
Further, dispersion also has consequences for contact tracing. If tracing forward, 80% of the cases will find zero or at most a few cases. 8/

If first tracing backwards, and then forwards, many more cases (2-3x) will be found because there is a higher probability that someone that infected at least one person also will have transmitted to other persons. This can be used in test-trace-isolate to cut more chains! 9/

When designing strategies for vaccination, one can raise the outbreak threshold by first vaccinating people with potentially high individual reproduction numbers. This is intuitive, since it includes personell in health care and restaurants, teachers and taxi drivers etc. 10/

The same strategy can be applied if we would use large scale screening tests. Still quite intuitive, but mathematics now also explains how it can give much better effect if done using a plan. 11/

Sometimes we hear discussions about what ”drives the pandemic”. Well, it seems to be driven by rare events, often called Paretho phenomena. This makes the outbreaks more difficult to understand and these effects were mostly invisible during the outbreak in feb-mar. 12/

They were invisisble because they all overlapped and the outbreak was so fast, and we didn’t test or trace much. This fall, we have seen these effects much more clearly, as local outbreaks and clusters. 13/

As explained, our insights about dispersion can already be used to fight the pandemic. But we also need to know more. Statistical phenomena generally have underlying mechanisms and by understanding these better, we can direct our effort to where we get the best effect. 14/

Some of the high reproduction numbers events from asymtomatic and presymtomatic transmission but it is still unclear to what extent this occurs. Bids vary wildly in the litterature. 15/

Unfortunately, I fear that some of the high reproduction and superspreading events are due to infected people that do not respect isolation. We need to understand this better! 16/

And finally: We must keep superspreading to a minimum. 17/17