I am Confused

When people give numbers I always try to go back and do a sanity check. Does it make sense. Well here are two simple checks.

First the distance a sneeze travels. An MIT type published in JAMA a piece saying a sneeze goes 27 feet. Specifically:

Owing to the forward momentum of the cloud, pathogen-bearing droplets are propelled much farther than if they were emitted in isolation without a turbulent puff cloud trapping and carrying them forward. Given various combinations of an individual patient’s physiology and environmental conditions, such as humidity and temperature, the gas cloud and its payload of pathogen-bearing droplets of all sizes can travel 23 to 27 feet (7-8 m). Importantly, the range of all droplets, large and small, is extended through their interaction with and trapping within the turbulent gas cloud, compared with the commonly accepted dichotomized droplet model that does not account for the possibility of a hot and moist gas cloud. Moreover, throughout the trajectory, droplets of all sizes settle out or evaporate at rates that depend not only on their size, but also on the degree of turbulence and speed of the gas cloud, coupled with the properties of the ambient environment (temperature, humidity, and airflow).

But let us do a simple check. If one fires a ball from a cannon at some exit velocity as described in the paper the ball drops 3 feet, a reasonable distance to make a sneeze deadly, only 4 feet, not 27.  That is 7 time more distant. Now a cloud is a mass of particles so the dynamics are no different for any. Unless there is some cohesive lift effect. Unfortunately the author does not explain this almost order of magnitude difference.

Now to the doubling time. The equation below calculates the doubling cycles, not days, needed to get from 4,000 (now) to 200,000 in 15 days.

 

To get the doubling days we take the number of days and divie by the doubling cycles needed. Thus we get 5.64 for the number of cycles and 2.66 for the number of days. Now when we look at the actual data we calculate the doubling time as follows. We determine the daily growth rate. Then we calculate it as follows;

Now Item 2 is the NY Times and the presentation today. In that piece they say we are going from 4,000 deaths today to 200,000 by April 15. We showed today that the doubling time for NJ is 5.5 days or less than three doubling cycles in 15 days. The doubling time. However if you use the Government's numbers you go from 4,000 deaths today to 200,000 by April 15 then the doubling time is 2.66 days or more than six doubles. Close but it assumes a fixed and non decreasing doubling. Also when you see it is a difference of almost 3, that is a fantastic difference in the final result. But we have seen an elongation of the doubling time. Given mitigation we expect that to continue. We seem to have projections based on nothing changing. Then why is the facts on the ground so disparate from the model being used? So I am confused. The facts show 5.5 the model says 2.6 and when you exponentially look at the difference it is fantastic! Yes, I am comparing mortality with reported infection rates but if one assumes a constant mortality rate per infection we are close. So what's up.

Since the Washington group has not revealed anything about the model we are back to the Three Card Monty world.

I have always done checks like this with business plans. Somehow when there are issues like this I don't invest. But somehow we have a group betting our entire country with a model hidden in a vault somewhere. Transparency anyone.

This problem requires the insight of Richard Feynman. Remember the Shuttle disaster!