CoViD-19: A Follow Up

Words of Caution:

See the post below.  They all still stand!

Background:

Last week I presented some results from a quick and dirty model, utilizing the best parameters I could find, and the simplest assumptions that allowed me to fit the data.  Well it's been an interesting week, to say the least.  I have had to make a few changes to fit the new data.  So without any further ado...

Data:

I am still using the same data sources for cases and deaths as I did last week.  I just can't find anything that even remotely seems better.  I now have enough CDC death numbers that I'm showing those as well.

Results:

There are four plots below that graphically show the fits.  I am satisfied that while they are some what ad hoc, they agree to a more than adequate extent.

A                                                                              B

Figures 1A and B. Two plots of the Worldometer and CDC Data and the Model results (the one on right, B, being a blow up of the y-axis to show the quality of the agreement at large numbers).

Figure 2. Plots of the Day-to-Day cases numbers.  Note that the data are extremely noisy over the last 10 or so days.

Figure 3. Data for the number of deaths.

It is clear that the model is doing a good job of capturing the dynamics of the CoViD-19 outbreak.since last week.

The conclusions I would draw have changed only somewhat taking into account that last week the model was predicting far fewer cases, because I was completely taken in by the wiggle you can see in the day-to-day case data from around 3/27-3/31.  Beyond that the comparison to last weeks "suggestions" are:

1. The stay-at-home orders and the social distancing being practiced across the country are having a clear and downward pressure on the cases and will also show a reduction in the deaths as well.  This still holds.
2. There is some indication that there is some small positive influence on disease outcome (people not dying!) from whatever treatments are being provided. This still holds.
3. The number of infectious cases is still very high and these practices must be maintained for the foreseeable future if we are to clear the virus from our population. This still holds.
4. The maximum number of new cases (i.e., the number of people who get infected on a specific day, and hence are now infectious) is likely behind us (model says it occurred on or about March 28). The conclusion holds, but the date at which it occurred was April 2.
5. The maximum number of infectious people on any given day is also likely to be behind us (model says this happened on or about April 2 or 3). The conclusion holds, but the date at which it occurred was April 7.
6. The maximum number of newly Confirmed Cases on any given day is likely to have happened, be happening, or about to happen (model shows it somewhere in the span April 5, 6, or 7).  The conclusion holds, but the date at which it occurred was April 10.
7. The maximum number of new deaths is likely to still be in the future (somewhere around April 8 - 11).  The conclusion holds, but the date at which it will occur is on or about April 16.

The other major change is that the length of time to fully clear the infection is MUCH longer.  I won't even say how far out the model predicts them, other than to say, some of them extend into 2021.  I should also mention that the predicted number of deaths has jumped to about 63,000.  Also the number of people actually infected (and almost entirely recovered) ends up being just under 150 million of the total population of 330 million.

I should also mention that two of the primary factors that influence the model are the number of total cases versus the number of confirmed cases.  These results are based on the same numbers I used last week.  Recently KT has pointed me to two rather interesting reports (Thanks!).  The first is a report that claims the mortality for CoViD-19 is around 0.06% (see the second bullet under the New Studies under the April 12, 2020 heading here).  That is in quite good agreement with the parameter I have been using (7.6%/137. ~ 0.056%) The second is a rather interesting report (even though somewhat anecdotal) from Chicago that 30 - 50% of the people tested shows signs of having had CoViD-19.  If the higher figure holds that suggests that the number of hidden cases might be significantly higher than the assumed parameter of 137 (perhaps as high as 190, but also as low as 110).  A few runs using the high end parameter resulted in a nearly identical looking fit, with essentially the same dates for the peak, but with slightly shorter time to fully clear the cases (but still out to December), around (but below) 60,000 deaths, and something like 190 million total cases.  .The lower value will push the numbers the other way.