Estimation of Covid 19 Diffusion in the United States

April 7th, 2020, 11:30 PM

I published the following essay in Medium early morning of the 7th (2 AM, April 7th.) 

https://medium.com/@GurumurthyKalyanaram/estimation-of-spread-of-covid-19-in-the-us-c160ba1e6576

The executive summary of the essay: The initial estimates of potentially 1-2 million death in the US were simply speculative, and not seriously model-based or evidence based. The current estimates of about 82,000 deaths by August 4th may be right -- but even that is on the high end. It is likely to be less than 80,000 in the next four months.

After I published the following hopeful essay, we got terrible data today -- Tuesday, April 7th. New York state experienced a huge spike in the number of deaths. From about 600 to about 731 -- the highest one-day increase and one-day total. So did the nation. From about 1,200 deaths to over 1,900 deaths -- against highest one-day increase, and one-day total.

So where do we stand now? The next 2-3 days of data would clarify. Deaths are usually lagging indicators. When deaths peak, they are clearing the backlog. The lag may be 2-4 weeks. Usually, the number of infections and hospitalization show a decrease after the number of deaths peak. That's what happened in Lombardy, Italy.

For instance, even as registered highest number of deaths today (April 7th), there were many encouraging signs. For instance, New York recorded lowest number of admits to ICU (89) in the last two weeks. Fewer newer cases today than yesterday, ( April 7th: 8147; April 6th: 8658; April 5th: 8327; April 4th: 10841; April 3rd: 10482; April 2nd: 8669; April 1st: 7917.)

So, we will have to wait and see.

And now the essay in the Medium. See below.

Coronavirus (Covid 19) has proved to be very infectious, transmitted via contact and air-borne. By various estimates there are about 30 percent of patients who are asymptomatic. And they can transmit the infection too.

Covid 19 has been spreading across the globe with speed and ferocity. Here, in the US too, the infection is inflicting a lot of hurt.

The question is: what is a reasonable estimate of mortality? Estimates have ranged from 2 million to 100,000 by end of July. One of the widely cited models is the University of Washington Model.

March 31st:

At the end of March, the model projected about 93,000 deaths by about August 4, 2020. See here: https://covid19.healthdata.org/

I wrote then: “While this is plausible, even 93,000 appears to be on higher end. Here is why.” See here: https://gkpolicybriefs.com/briefs/covid-19-estimates-of-mortality-in-the-us

My arithmetic was straightforward. The aggregate numbers of infections and mortality for the US (on March 30th) were thus. Total number of infections was 139,773. Total number of deaths was 2,429. So, the percentage of mortality was about 1.7. For 100,000 deaths, assuming mortality rate of 2 percent, the number of total infections must be about 5 million. Based on the evidence thus far, those numbers appeared to be very high. On March 20th/31st, there were about 150,000 infections or so in about two weeks. The data from all of US, and from the State of New York which was most afflicted, appeared to already show a leveling off. https://twitter.com/Kalyanaram_G/status/1244810297669554183?s=20

April 7th:

The current data increasingly suggests that the initial estimates certainly appear to be on the higher end. I have been arguing this for sometime. See here and here and here. )

On April 6th, the University of Washington lowered the mortality numbers to about 82,000 (from about 93,000). Even that is likely to be revised because the said model projected 1967 deaths for April 6th, and the actual numbers are 1255.

The raw data for the USA and New York for the last one week is as follows.

Mon 4/6–1182 (USA); 599 (NY); 583 (Rest of USA)

Sun 4/5–1184 (USA); 594 (NY); 590 (Rest of USA)

Sat 4/4–1352 (USA); 630 (NY); 722 (Rest of USA)

Fri 4/3–1178 (USA); 562 (NY); 616 (Rest of USA)

Thu 4/2–1084 (USA); 432 (NY); 652 (Rest of USA)

Wed 4/1–954 (USA); 391 (NY); 563 (Rest of USA)

Tue 3/31–807 (USA); 332 (NY); 475 (Rest of USA)

New York is certainly showing a leveling off, so does the rest of US.

In light of this, it is reasonable to hope that there may be fewer than 82,000 deaths (by August 4th). Here is the simple arithmetic.

The current total number of infections is 363,220, and the number of deaths is 10,847. So, the rate of mortality is about 3 percent. Using this peak rate and projecting it in the future — even though we can observe the leveling off — the total number of infections must be 2.1 million to cause additional 70,000 deaths. That is over 500,000 infections a month, when we have reached the peak and will begin taper off.

All of this assumes social distancing till end of May. The US government has mandated social distancing only till of April. So, there are many questions:

What would happen if the US government does not extend social distancing beyond April 30th?

What would happen after end of May when social distancing ends (as assumed in the model)?

We do not yet know the answers. There is much uncertainty, and it is imperative on all of us to be thoughtful and careful.

An observation. Leveling off occurs because the epidemiological phenomenon is a S-shaped curve. The phenomenon increases at increasing rate and then levels off (asymptotically.) But this leveling is not obvious in the charts of the number of infections and deaths presented by many publications. The reason is this: almost all of them are using logarithmic metric and when logarithmic metric is employed the inflection points are lost.

Here are useful sources of data: Covid Tracking; University of Washington; John Hopkins; and New York City Tracker.

Footnote: Please note the University of Washington model updates its estimates and projections periodically. About March 27th or so, the estimate of mortality was about 81,000 (by end of July), then the estimate increased to about 93,000, and now (April 6th) it is back to about 82,000.