Can the US bend it like Italy or Spain?

Offering a glimmer of hope through analysis

The coronavirus pandemic is current raging throughout the world. At the time of writing, April 9th, coronavirus trackers are noting ~1.6 M cases, 95K deaths (~6%) and 352K recoveries (22%) worldwide. According to worldometer.info, about ~28% of the cases (447K) end up with an outcome (like hospitalization or death) with ~80% chance of recovery (352K) and ~20% chance of death (95K). These are some general global trends noted as the pandemic has raged.

(Note: M and K are used to denote million and thousand respectively.)

Italy has been terribly devastated by the pandemic with 143K cases of infection and nearly 18K deaths (representing a very high mortality rate of ~13%). Spain has followed in Italy's painful path with 152K cases of infection and 15K deaths (a mortality rate of ~10%). Both Italy and Spain represent an infection rate of 2800+ cases per million and a death rate of 300+ per million.

The situation in the US is alarming with 457K cases and ~16K deaths (as of April 8th), which represents a mortality rate of 3.5%. After initially labeling the outbreak a hoax, the White House now paints an extremely grim picture of 100-200K deaths in the US. The shock of the coronavirus on the economy has been devastating and the nation faces the specter of a growing unemployment crisis with total of 16M unemployment claims filed already (about 10% of the US workforce faces unemployment).

Just contrasting WH mortality predictions (say 150K deaths) with the world numbers (1.6M cases --> 95K deaths), we can see that the US is potentially facing 2.5M/4.3M cases depending on whether we assume a 6%/3.5% mortality rate for the US. [That is: 3.5% of 4.3M --> potential 150K deaths]

This is an extremely grim picture! Is there a better way to assess the future of the outbreak in the US?

Actually there is! By taking a look at the curve of daily new deaths in worst-hit Italy or Spain, we can form conclusions that give us a ray of hope. There are three important factors that stand out as predictors: the flattening of the curve of daily new deaths, the number days for that to happens (25-30 days), and the governing mortality rate for the population.

Let us look at the following excellent graphic from the Financial Times analyst John Burn-Murdoch. The FT Coronavirus Tracker has been an excellent source of data and visualization of the coronavirus impact.

What we see, as the graphic highlights, is the daily death tolls (the 7-day rolling averages) in Italy and Spain plateaued and are now dipping. Spain has been able to flatten the curve in 25 days or so. Italy took around 35 days to reach the plateau and reverse the death march. We can note that it took China also roughly 25 days to find the plateau and start to reverse the trend. Roughly it takes a nation 25-30 days to bend the curve of deaths. And the lockdown in Wuhan has been lifted.

The glimmer of hope is seeing the death curve in the US start to flatten in the above graphic.

Let us model the flattening with the logistics growth model for the 7-day rolling average of daily new deaths using data from worldometer.info:

As we can see from the graph, the logistics curve (details below) is a pretty decent fit for the 7-day rolling average of daily new deaths in the US.

Modeling the curve of deaths with the logistic curve:


X(t) = K/[1 + A*exp(-??*t)] --> logistic curve

Here K is the peak or limiting value and A and ?? are parameters. A is roughly the ratio of peak to initial value. ?? is the rate parameter. 

Properties of the logistics curve:

At t = 0, the initial value X(0) = K/[1 + A] --> A = [K/X(0)] - 1 

At t = log(A)/??, X(t) = K/2

We can construct a model using the US data:

We assume K = 1750

Assume initial value X(0) ~ 470 (March 31st 7-day rolling average)

A = K/X(0)-1 = 2.72

Assume at t ~ 4 days, X(t) ~ K/2 (875) (April 4th average: 890)


--> 4 = log(A)/?? --> ?? = log(2.72)/4 ~ 0.25  (the value used: 0.28)

The desired logistic curve is: X(t) = 1750/[1 + 14*exp(-0.28*t)]

We can see from the above grapic that this simple model fits the observed data quite well.

The projections are shown in the plot above.

So it may take roughly another 10 days to reach the assumed peak of 1750. This represents an additional death toll of ~16K.

The current death toll (April 9th): ~16K plus the additional death toll over the next 10 days: ~16K give us 32K as the death toll at the peak.

PS: One can get pretty fancy with techniques to fit the data. The simple logistic curve is quite useful for fitting this type of data.

Using this curve, we can estimate a death toll of 32K at the peak reached by the US after ~35 days. Assuming that the draw down curve has roughly the same shape, we can see from the FT graphic above that to reach a base level of say 50 deaths per day will take about 25 days.

The draw down death toll will be approximately ~14K, from the curve of daily deaths.

With this analysis, the overall death toll in the US comes out to be approximately 46K before stabilization. At a average mortality rate of 3% (note lower earlier around 2.5%, now at 3.5%), this represents around 1.5M cases in the US.

To calibrate the result, if we observe the global picture we see 1.6M cases of coronavirus with a death toll of ~95K representing a mortality rate of 6%. Adjusted for a 3% mortality rate and (1.5/1.6), this comes out to be 45K, almost the 46K deaths estimated. So a simple base rate analysis of actual deaths supports the prediction.

This is a far cry from 150K death toll initially presented by the authorities in the US!

We are clearly off by an order of magnitude in the national figures presented. I will leave it to other experts to determine why. I am pretty sure there will be corrections offered soon to the official national figures.

Just to be very clear, 1.5M cases/46K deaths are very high numbers but we can see that this correlates better with the experience seen across the world. It is a very important indicator for capacity planning: 1.5M cases present 375K cases (25%) for hospitalization and 150K cases (~10%) will need ICU care and 46K (3%) will not survive that ordeal. It makes a big difference to know the realistic pattern. These numbers are also important for shaping public confidence and providing hope.

The FT tracker shows how visualization can be powerful to convey information and detect important trends. The logistics growth model used here to parametrize the curve shows how we can use simple models to elicit patterns from data.

To sum up the analysis:

• For tracking the pandemic, three important factors stand out a key predictors: the curve of daily new deaths, the time period for flattening this curve (when it peaks), and the governing mortality rate for the region (e.g. 3% for the US).
• The daily new deaths curve provides some important information for assessing the progress of the coronavirus pandemic. The 30-day peak of this curve, where the curve flattens, seems to be a real indicator of stabilization.
• Current (16K) on April 9th + Time to Peak ~ 10 days (16K) + Draw Down period ~ 25 days (14K) --> Total (~60 days): 46K . [*Prediction*]
• The overall numbers for the US seem to be around 1.5M cases overall and 46K deaths, representing an average mortality rate of 3% [*Prediction*]
• The period of significant economic interruption can be 2 months. This type of picture will help with the economic modeling of the impact of a pandemic. [*Prediction*]

Look forward to your questions, comments and feedback. I want to stress again that this is a forecast based on the trends seen in the currently available data. How accurate it is, only time will tell. But it does give us a glimmer of hope that the tide is turning.

―Suresh Babu, April 09, 2020

Please also see my earlier article: "Pandemic: Assessing The Supply Side". The article discusses how we can use simple models to assess the impact of the pandemic and how technology can bridge the gap between the explosive growth of the disease and the limits of the care supply chain.