I explained yesterday that I have devised a more sophisticated method of projecting the numbers of COVID-19 cases and deaths in the U.S. I had earlier projected 250,000 cases and 10,000 deaths. My new method yields higher numbers than those, but far fewer deaths than the official estimate issued by the White House: 100,000 to 240,000. My guess is that the official estimate has been inflated to scare people into staying at home, which will reduce the rate at which new cases arise and prevent the number of deaths from reaching 100,000 or more.
In any event, a day makes a difference. Yesterday, relying on data collected through April 1, I projected 870,000 cases and 40,000 deaths by the end of June. Today, with an additional day’s worth of date, the situation actually looks a bit better: 830,000 cases and 39,000 deaths. The difference isn’t significant, but the good news is that today’s estimate isn’t worse than yesterday’s. On the current projection, the fatality rate will be close to 5 percent of cases.
Figure 1 shows the projected numbers of cases and deaths by date. The curve for cases resembles a Gompertz function, which is a classic descriptor of the growth of pandemics.
Notes about data: I use official statistics reported by States and the District of Columbia and compiled in Template:2019–20 coronavirus pandemic data/United States medical cases at Wikipedia. The statistics exclude cases and deaths occurring among repatriated persons (i.e., Americans returned from other countries or cruise ships). The source tables include the U.S. territories of Guam, the Northern Mariana Islands, Puerto Rico, and the Virgin Islands, but I have excluded them from my analysis. I would also exclude Alaska and Hawaii, given their distance from the coterminous U.S., but it would be cumbersome to do so. Further, both States have low numbers of cases and (thus far) only 3 deaths (in Alaska and 2 in Hawaii, so leaving them in has almost no effect on my analysis.
RELATED CHARTS AND ANALYSIS
As indicated by Figure 2, the number of cases is 7/100th of 1 percent of the population of the U.S.; the number of deaths, 17/1,000th of 1 percent. Only 2.4 percent of cases have thus far resulted in deaths, but the final fatality rate will be higher (as mentioned above) because new deaths lag new cases (as discussed later). Note the logarithmic scale on the vertical axis; every major division (e.g., 0.01%) is 10 times the preceding major division (e.g., 0.001%).
Figure 3 shows how the coronavirus outbreak compares with earlier pandemics when the numbers for those pandemics are adjusted upward to account for population growth since their occurrence. (Again, note that the vertical axis is logarithmic.) Thus far, the number of COVID-19 cases is only 4/10th of 1 percent of the number of swine-flu cases, but the number of COVID-19 deaths has reached 45 percent of the number of swine-flu deaths. In the end, the U.S. fatality rate for the swine-flu pandemic was 2/100 of 1 percent; for the Spanish flu pandemic, 2 percent.
As shown in Figure 4, the daily percentage change in new cases is declining, as is the daily percentage change in new deaths.
However, new deaths necessarily lag new cases. As of yesterday, the best fit between new cases and new deaths is a 5-day lag (Figure 5).
Figure 6 shows the tighter relationship between new cases and new deaths (especially in the past two weeks) when Figure 4 is adjusted to introduce the 5-day lag.
Figure 7 shows the similarly tight relationship that results from the removal of the 6 “hot spots” — Connecticut, Louisiana, Massachusetts, Michigan, New Jersey, and New York — which have the highest incidence of cases per capita.
The good news here is the the declining rate of increase in the incidence of new cases, both nationwide (Figure 6) and in the States that have been less hard-hit by COVID-19 (Figure 7). The rest of the good news is that if the rate of new cases continues to decline, so will the rate of new deaths (though with a lag). Thus the prediction at the top of this post, which is derived by applying the lagged relationship between new deaths and new cases to the declining rate at which new cases develop, which is described by a mathematical function known as a decaying exponential.