9. Weekly Update: Europe Improves, U.S. Doesn’t

(4/8/20) A recovery is in sight for most of the world but the U.S. continues to lag. False hope for NY. We are probably at near maximum active cases nearly everywhere and must exercise strictest social isolation.

Remember to check my post called “Daily Rumblings” for late breaking updates.

This is not intended to be a technical discussion, but I do need to present the underlying model for you nerds out there. It really is not complicated, but you can get to the main conclusions by just looking at the Figures and reading the bullet points.

We present our weekly update and introduce an extension of our Gaussian model, which was previously shown (Post 8. A Simple Model for Forecasting Final Fatalities) to be a useful working model for forecasting total deaths following recovery and is now extended here to forecast present and future active cases (prevalence) and new cases (incidence). First, we show below the latest death rate plots for hot-bed countries and U.S. states.

The qualitative red, yellow, and green rankings reflect accelerated, rolling over to a peak, and well on the decrease death rates, respectively.

Internationally, the good news is that Italy and Spain are now joining Iran as showing strong evidence for reaching a peak in the death rate. Our previous model showed that at the peak of the death rate curve a population has reached half of its terminal death count (assuming a symmetric path down). Iran, oddly, seems stuck at its peak and we hope to see a decrease in death rate soon. The U.S., France and U.K. continue on an accelerated death rate and it is hard to tell if it has transitioned from exponential to linear, but certainly no evidence of rolling over on its way to a peak.

Domestically there is not much to be hopeful about. At best Washington and Louisiana may be showing a rolling over in death rate and hopefully will reach a peak soon. New York is horrific; after Mayor Cuomo hesitantly stated that the situation was improving with two consecutive days of lower death rate, yesterday the death rate spiked again to a new high. New Jersey and Michigan are growing fast (though NJ may be slowing). California still has a steep death rate, but the total number of deaths are significantly less than other states ranked red in severity.

Based on these reported death rate data we can apply our Gaussian model (Post #8) to update our forecast for terminal (total) deaths and present-day active cases and new cases. The general premise as described previously is to use death rate data and an assumed rise and fall curve (Gaussian distribution) to forecast total deaths by estimating where on the Gaussian curve the actual death rate curve lies. The remainder of the curve can then be integrated (area under the curve) relative to the current date/position and the current death count. We make a couple of other assumptions to compute the number of current active cases and rate of new cases. We assume COVID-18 lasts about 2.5 weeks resulting in either recovery or death (ample reported studies show this). We also assume that the Gaussian rise and fall has a width at half its maximum of 4 weeks, which is consistent with the results for China (plot above) and for the 1918 Spanish Flu. So, then the current number of deaths on a given day would reflect the number of new cases 2.5 weeks earlier divided by the mortality factor.

Left: Plots of new events below (rate, e.g., per day) and total events above for deaths and COVID-19 active cases. Right: The Table shows how to calculate terminal fatality, prevalence, and incidence by determining where the real death rate data lies on the rate curve relative to the peak. Then one multiplies the current total deaths by the factors shown to get the other values.

The lower plot below shows the model curves for daily deaths and new cases. The Gaussians are plotted on a logarithmic intensity scale. In the plots below we assume a mortality factor of 1.0%, but this can be varied easily as we show soon. The units for the axis are relative, but we have chosen conditions so that the Relative time is in units of weeks and the Relative counts scale with the number of deaths per unit time (e.g., daily).

The upper plot is an integration (area under the curve) of the lower plots. For total deaths the integration reaches a plateau after death rate approaches zero. For total cases, the recovery of patients means that this count goes to zero as the rate of new cases approaches zero. The plot of total cases with time is very important for forecasting when the prevalence of cases decreases to a safe enough level to allow the full or partial relaxation of social restrictions.

Some key observations regarding the above plots:

  • The peak for prevalence (current active cases) peaks about half-way between the peaks for death rate and incidence (new cases).
  • At the peak of death rates, the prevalence is only down about 20% from its peak, so when the death rate is rolling over and reaching a peak, the prevalence is still near its maximum and the population needs to be exercising its greatest social restraint!
  • We recommend strict adherence to social distancing beyond 2 weeks after a population reaches its peak death rate. At that time the prevalence is at about 22% of its peak value. This value goes down to about 7%, 2%, and 0.3% at weeks 3, 4, and 5, respectively. Relaxing of social distancing may be acceptable in less severe states, e.g., CA at week 3 after the peak, but for severe states, e.g., NY, week 5 would be more prudent.

Now we look at the forecasted values for terminal deaths, current active cases (prevalence) and current new cases (incidence). The method for computing these values is described in the caption to the Plots above.

Assumptions: Mortality factor is estimated as 1.0% for most favorable populations (not yet strained health care system) and up to 2.0% for least favorable populations (strained healthcare system). The uncertainty in these values is greatest the furthest from the peak is the death rate. For example, the U.S. uncertainty range is about 30,000 – 120,000 (factor of 2x), whereas Italy and Iran are about ± 25-50%.

Key international observations from the above Table are:

  • The total (terminal) fatalities are consistent with last weeks forecast, however, for the most part on the lower limits as evidence of approaching or reaching a peak became evident.
  • The U.S. is forecasted to exceed all other nations in total deaths.
  • France is forecasted to exceed all other nations in total deaths per capita.
  • According to the model the current number of active cases in the U.S. is about 1% of the population in the U.S. (10,833 per million), in France about 3%, and in Italy surprisingly <1% as they have progressed past the death rate peak. The peak prevalence for Italy is computed to have been about 2-4% of the population.

Key domestic and general observations from the above Table are:

  • New York is projected to lead any nation in total deaths per capita. Its current prevalence is about 5% of the population.
  • California, which appears in news report as a hot-bed state appears not to be so relative to the other five states highlighted. CA is forecasted to have significantly the lowest per capita total death than the other states.
  • The current number of active cases in CA is about 0.3% of the population or about 1 in 330 as contrasted with 1 in 18 in NY.

Current prevalence (active cases) are calculated in the above Table to be typically about a factor of 10x greater than confirmed cases. Again, as I’ve explained many times before, confirmed cases are a poor indicator of progress as it strongly depends on the rate of testing, which has been insufficient at best. If one is surprised or dubious about these high prevalence numbers, please consider the following facts:

“More than a quarter of the people tested for coronavirus at a Hayward site that opened this week turned up positive, city officials said Thursday, as confirmed cases climbed in the Bay Area, topping 1,400, with at least 32 deaths.”
(https://www.sfchronicle.com/health/article/Bay-Area-coronavirus-cases-climb-as-testing-15160182.php)

The following results come from a Gallup poll survey:

“Has had fever in past 30 days, saw health professional, received COVID test:    344,053
Has had fever in past 30 days, saw health professional, received COVID test, tested positive: 106,092″
(https://news.gallup.com/opinion/gallup/306458/estimating-covid-prevalence-symptomatic-americans.aspx)

Once we are well on our way to recovery, new antibody tests will enable a determination of the percentage of the population who had COVID-19 by detecting immunizing antibodies in COVID-19 recovered individuals.

We now compare our total deaths and time respective to the peak death rate to that from the highly regarded University of Washington (UW) model (http://www.healthdata.org/covid/).

The comparison is reassuringly more in relative agreement than disagreement (within a factor of 2x in all but two cases). Noticeable differences include:

  • We believe that France has not reached its death rate peak. Referring to the plots at the top of this post we believe that the spike a couple of days ago and the subsequent lowering in the death rate was an aberration. A couple of more days will tell. We therefore forecast about 3.5x as many total deaths as UW. [Update: We learned that the spike to 2,000 deaths/day for France was due to a lump addition for deaths unaccounted for in nursing homes. This would mean this should be redistributed to early days thereby giving a curve that may be rolling over closer to the peak. We expect to revise our estimate downward on our next reporting.]
  • We also believe for the same reason that NY experienced a false peak and we therefore forecast about 2x more total deaths.
  • Interestingly a week ago when we did our first comparison to UW they forecasted 5,068 total deaths for CA well above our range of 1,122 – 3,829. They have since considerably lowered that forecast to 1,611, which is now more in-line and even below our latest forecast of 2,209.

Finally, I show the interesting log-log plot first shown at the end of Post #7 (Weekly Update: Grim News). This is now showing some deviation from the line for Italy and Spain as also evident in the death rate plots at the top of this posting. Hopefully these two most serious nations are on their way to recovery.