NedNotes (not blog): 07aug20 General COVID data

Introduction. Over the five weeks between the 3rd of July and the 7th of August, the U.S. death toll spiked by 29% from 125,980 to 161,476, implying a weekly growth rate of 5.1%. The news seems to be grim, since one could see 300,000 deaths by year's end per the projections of epidemiologists. 

Should present growth rates not abate, by the end of February 2021 (i.e., the first year of the American epidemic), death tolls could approach the 675,000 endured during the 1918 flu epidemic. The separate analysis of the family clusters also addresses these issues.

Analysis of normailised death tolls. In the table below, the death tolls of each state and the territories is normalised by taking the state's particular level of mortality relative to the population (i.e., the deaths divided by the population) and then multiplying that percentage to the U.S. population of 333 million. 

This normalisation is similar to scaling the various death tolls of the several states to deaths per 100,000 or one million people. The full calculation is illustrated immediately below.

The restated death tolls can be compared directly to the national death total of 161,476; these revised figures can then be compared to each other to see how states are doing relative to their peers. 

Each state receives a severity rating based on a scale anchored in my one-year projections of four months ago; any rating in red-font indicates that the state in question has deteriorated, thus migrating from a lower / better rating to one notch worse / above it.

Unfortunately, Idaho and Arizona have graduated to more severe levels this week. In this chart, the revised death tolls for over two thirds of the states fall below the baseline. 

The average normalised death toll for the thirty-three states and six territories comes close to the baselinee at 160,000. The median (i.e., the value at which half of the death rates are higher and half lower), however, remains substantially below the average at 104,771 deaths.

The reason for this upward drift lies with the outliers in normalised death rates in New Jersey (re-stated death toll of 631,952), New York (557,810), Massachusetts (419,930), and Connecticut (413,933). These states were hit first and hardest when the coronavirus migrated from Europe to New York and Boston in January and February of 2020.

The severity of the initial death rates in much of Western Europe and these Northeastern states during the early part of the pandemic suggests that the virus itself may have mutated for the worse as it migrated west from China. 

This tentative theory does not hold China responsible for the out-break, but it does lend itself to scepticism toward the numbers currently being reported by Peking. Additionally, there is evidence that China obscured the severity of the pandemic. Alleging this cover-up may well overlook the lag times involved in recognising a contagion and its transmissibility. 

Thankfully, the marginal rates have declined over the past month to the 1-5% range for the family clusters concentrated in the East and Michigan. The marginal monthly rates average 2.1%, with half being below 2%. The New York and Boston metropolitan areas are facing a possible second wave.

The good and necessary news. The five states of the South and Southwest reviewed in detail below (i.e., Arizona, California, Florida, Texas, and Oklahoma) displayed notable signs of slowing down as Governors in Arizona, Texas, and California began to slow or reverse re-opening their states. 

The tables -- above and below -- present the following:

• the normalised mortality rates of thirty-three states and six territories, representing 85-90% of the population and 90-95% of the national mortality; as well as,
• the study of five states in the South and Southwest comprising 55-60% of the population, confirmed cases, and number of deaths for the reagion.

The key implication of this table remains the possibility of a death toll in the S/SW region of 300-325,000 during the next three months should weekly growth rates fail to slow down across the region.

The “long grim fairy tail” of loss rates sensitive to initial conditions. Leadership by Texas, Arizona, and California should avert this disaster. These guesstimates are likely to be quite high since I am applying the 'rule of 70'.

This rule-of-thumb states that dividing the periodic growth rate into seventy will calculate the number of periods required to double the base number. Below are the calculations in detail assuming thirteen weeks for three months.

1. Applying the compound growth rate: 70 / 12.5 = 5.6 weeks; 13 / 5.6 = 2.32; (55,968 x 4) + (.32 x 223,872) = 295,511 deaths.
2. Applying the time-weighted average growth rate: 70 / 13.5 = 5.2 weeks; 13 / 5.2 = 2.51; (55,968 x 4) + (.51 x 223,872) = 338,047 deaths.

Geometric growth calculation. The compound weekly growth rate from the 16th of May through the 7th of August is 12.5%. The product of 70 / 12.5 is 5.6 weeks. That means the base number will double twice and will be a third of the way to doubling a third time.

Thus 55,968 deaths doubles to 111,936 in 5½ weeks; the 111,936 deaths doubles again to 223,872 in another 5½ weeks. The death toll goes a third of the way toward doubling yet again, or 71,639 deaths before the thirteen-week interval runs out. This quarterly total comes to 295,511 deaths.

Time-weighted or trend-weighted average growth rate explained. The trend-weighted average growth rate is 13.5%. This growth rate takes the most recent periodic growth rate and multiplies it by the number of periods to date (e.g., from the table, 12.4% x 12). 

Then it takes the second most recent growth rate and multiplies by the number of periods applicable to it (i.e., the number to date minus one period, or 21.1% x 11). 

This calculation repeats for the preceding ten periods with the coefficients trending from ten down to one for the declining number of periods. The doubling with a 13.5% weekly growth rate is 5.2 weeks. 

The calculation proceeds in the same manner as the one laid out above, except that the death toll is 51% of its way toward doubling a third time. Thus, 223,872 plus 114,175 generates a total forecast quarterly death toll of 338,047.