It’s not like the literature hasn’t discussed these:

Russell Timothy W , Hellewell Joel , Jarvis Christopher I , van Zandvoort Kevin , Abbott Sam , Ratnayake Ruwan , CMMID COVID-19 working group , Flasche Stefan, Eggo Rosalind M , Edmunds W John , Kucharski Adam J . “Estimating the infection and case fatality ratio for coronavirus disease (COVID-19) using age-adjusted

data from the outbreak on the Diamond Princess cruise ship”, February 2020. Euro Surveill. 2020;25(12):pii=2000256. https://doi.org/10.2807/1560-7917. ES.2020.25.12.2000256.

T. Jombart, *et al*, “Inferring the number of COVID-19 cases from recently reported deaths” [version 1; peer review: 2 approved], Wellcome Open Research 2020, 5:78 Last updated: 26 MAY 2020.

T. W. Russell, *et al*, “Using a delay-adjusted case fatality

ratio to estimate under-reporting”, https://fondazionecerm.it/wp-content/uploads/2020/03/Using-a-delay-adjusted-case-fatality-ratio-to-estimate-under-reporting-_-CMMID-Repository.pdf.

Given that infections are far from Poisson events, being overdispersed because of the superspreader phenomenon, it seems a good deal more investigation of those long tails would be warranted. After all, the nice thing about Poisson statistics is that they imply a certain stability and predictability in outcome. Forcing a Poisson model on top of an actually Negative Binomial model with a big variance means the of the Poisson is going to be exaggerated. Sure, it looks like the Poisson is exaggerating. But, in fact, there’s bigger latent risk: Can’t know how the big tail events are going to behave.

Indeed, if there’s anything specific to be criticized about Imperial College is that they did not acknowledge this feature of epidemics in their analysis. The superspreader phenomenon has been known for a while, since 2000 at least. See

J. O. Lloyd-Smith, S. J. Schreiber, P. E. Kopp & W. M. Getz, “Superspreading and the effect of individual variation on disease emergence”, *Nature*,438(17), November 2005, doi:10.1038/nature04153.

And see its references.

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]]>@Yves Moreau,

Some of your puzzlement may be explained by the attendant simplified model of transmission. Reproduction number is essentially a Poisson lambda mean. In fact, disease transmission is characterized by that parameter, and a variance, variously called a concentration or a dispersion parameter, and the distribution is the Negative Binomial. So it can be overdispersed.

See:

J. O. Lloyd-Smith, S. J. Schreiber, P. E. Kopp & W. M. Getz, “Superspreading and the effect of individual variation on disease emergence“, Vol 438|17 November 2005|doi:10.1038/nature04153

]]>Peter McCluskey makes an interesting comment on this post at lesswrong pointing out that after restrictions start, there will still be transmission within households for a while. Since most households have only two adults (and children will probably not be noted as having covid-19), this would for a while lead to R seeming to be 1. So we can hope that that’s why getting it below 1 seems to be difficult at the moment.

]]>Saw today that Germany had their transmission rate down to 0.7 but then relaxed their restrictions and it is now 1.0. It does seem that it is quite difficult to get it below 1.0. In Australia we are seeing that people make their own decision on what they think is appropriate levels of restrictions, as the rate of new cases declines to low levels. The good news is that if we go to a transmission rate of 1 then it won’t be a problem, as we are at under 20 cases per day.

]]>Another interesting feature of the data is that often case rate curves will rise very rapidly early, as a country realises that they have an epidemic and will put resources into finding cases, so will find existing as well as new cases.

]]>Yes, it could be that the curve is bending down from exponential growth to horizontal, but slowly enough that for a while it seems to be going up linearly. This might be more likely given the variable incubation time (and time to death when fatal), which would have the effect of smoothing out the impact of a sudden “lockdown”.

But if you look right now at the world totals for cases and deaths at https://www.worldometers.info/coronavirus/ it’s really hard to think that the strikingly linear growth since about March 30 can be explained so simply. Perhaps the staggered timing of interventions that you mention could explain this, if they just by coincidence have the combined effect of producing a linear curve (for a while), but this seems a bit unlikely.

]]>I’m curious if the apparent linear rise of cases (actually confirmed cases as per testing) may be an artifact of both the lag time from the moment individuals are actually infected to where they may be exhibiting symptoms or are tested, given an incubation estimated to be about 5-14 days.

If so, and given the inconsistent timing of government interventions across the globe, we might expect to see a “bending” of the rise in cases into a more horizontal line in, say, around May.

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