The Chicago story also caught my eye. It is sensational and does suggest that super spreaders can have disproportionate effect during bootstrapping. Later if 30,000 people are infected per day, an anomalous high individual rate shouldn’t matter as much (assuming few superspreaders). Your intuition sounds right to me, and I would add that PDEs are really a better description of the process than an ODE. Once there is an epicenter, it looks more like a heat equation with sources and sinks. Presumably if an ODE applies to a gross metric, it could be derived from the PDE. Epicenters combined with massive transit allows spawning of new epicenters as we have seen, and it probably is fractal in the sense that any city can become an epicenter. The other sensational story (in my region) was about Mardi Gras, which may have created case 1 in Arkansas and Tennessee. Yet again the problem is changing one ODE model with too many parameters for another PDE model (or better) with too many parameters. Epidemiologists might claim to know how to set these parameters, but most of us won't know if our trust is misplaced until after the fact. We can sit here all day and debate what the best possible theory is, but that speculation is useless unless it generates hypotheses to answer questions: - Is U.S. at peak infections / day? If not when? - Is U.S. pandemic duration relatively long? If so, by how much? When you can't trust the politicians and the talking heads on television, you have to look at the data and make a few assumptions. I don't know the answers, but at least was able to make a few suggestive plots of available data in the other thread from today. If you have any of your own estimates, I would be interested to hear. --Brad
On Apr 11, 2020, at 12:52 PM, Henry Baker <hbaker1@pipeline.com> wrote:
I've been reading about Covid19 and listening to a number
of professional podcasts about Covid9 -- e.g., "This Week in Virology", which amazingly enough, is entertaining enough not to be a soporific.
Reading between the lines, I'm coming to the conclusion that the concept of "R_e" ("effective" R), may be fatally flawed, as it tries to capture some sort of "mean" or "average" R in an inherently exponential setting.
Thus, if one person has an R_e of 0.9 and another person has an R_e of 40.0, there isn't a good way to average the two R_e's to compute a composite R_e. What if a vanishingly small fraction of infected people induce the vast majority of cases? We know that spreading is a *network* phenomenon which means that it is highly likely to have a *fat tail* distribution.
If I'm correct about this, then the standard epidemic model is also fatally flawed, and hence unreliable for making trillion-dollar decisions. What won a Nobel prize a century ago is today an undergraduate homework exercise. We desperately need a better class of models for today's pandemics.
For example, in Massachusetts in the early going, almost 100% of the confirmed cases stemmed from a single meeting of a single company in a single downtown Boston hotel.
As another example, in Chicago, most of the early cases stemmed from a single funeral and a single birthday party.
So if it is true that there are "super spreaders", both in terms of individual people and/or individual events, there must be a better way to quickly identify and isolate these people and events other than putting the entire world on lockdown.
I would imagine that some of the work on fractals should be useful to look at this superspreader phenomenon.
Perhaps fractures in glass or metal may have relevance, as it may only take a single flaw in a crystal structure to destroy the entire structure.
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