Friday, April 3, 2020

I can help

This NY Times piece seems to make an important point that has not received much attention:
From a policy perspective, we need to consider that not all exposures to the coronavirus may be the same. Stepping into an office building that once had someone with the coronavirus in it is not as dangerous as sitting next to that infected person for an hourlong train commute.... 
Low-dose infections can even engender immunity, protecting against high-dose exposures in the future. Before the invention of vaccines, doctors often intentionally infected healthy individuals with fluid from smallpox pustules. The resulting low-dose infections were unpleasant but generally survivable, and they prevented worse incidents of disease when those individuals were later exposed to smallpox in uncontrolled amounts. 
Despite the evidence for the importance of viral dose, many of the epidemiological models being used to inform policy during this pandemic ignore it. This is a mistake.

Says Mankiw.

The unit I use is one spreader in a card game with 150 other in a ball room at a hotel.  If the atmospheric properties are assumed constant, then this unit encompasses density and thus dosage. The I estimate a particular metropolitan area according to how much of their daily life resembles a card game.  NYC is doomed in my model, they are nothing but a packed set of card games.

But the model performs a probability transformation numerically.  Take the distribution in a uniformly spread finite space and transform that into the probability distribution of NYC. The card game unit was an actual human experiment with 150 subjects in a known finite space over eight hours.   Insert in  the transmission constant, which scales the power spectrum,  and get the equilibrium curve. It has a very sharp peak for NYC.

So if one created a monte carlo sampler from a histogram of new cases in NYC one would pull out sample of large numbers, more frequently because the economies of scale in new york require mass gatherings.

If the monte carlo sample was adaptive, that is the histogram was updated as the sequence proceeded, then the large mass gatherings show up first in the histogram, it is heavily skewed. NYC is the extreme case in that it is packed precisely so it can support mass meetings, concerts, market, restaurants,  and ports or entry. It has been the meeting place of America since the founding.

I think Cuomo is right. If we focus on treatment, right now, in New York we minimize hospital shortages over all because most of the shortage rates will be NYC.  This sudden stop is likely as bad as the 1929 sudden stop in any event. We are kiind of screwed.

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