A "User-Friendly" Approach to Assess the Coronavirus' Spread and the Success of Containment Efforts
There is a great deal of confusion and disagreement about the current severity and future course of the coronavirus. The speed at which this crisis is evolving, the economic and social cost of the countermeasures, the risks of being wrong, and the lack of data have created a perfect storm of uncertainty.
We don't have agreement on critical information like the current extent of the virus, its communicability, or its fatality rate. So, experienced analysts have created sophisticated models, filling in the blanks with ranges of assumptions to determine the probability of various outcomes. These models are essential to help us all to make the best of what is a difficult situation.
But no model solves all problems. The purpose of these models is not diagnostic. They don't assess the recent course of the virus in a particular country. These models take time to run and communicate the results. So, many people in leadership positions will only occasionally get an update. The models are opaque. So, they aren't directly accessible to the general public.
This creates room for data visualizations that quickly communicate the recent course of the virus as well as its near-term trajectory. Perhaps, you've seen the chart immediately below the Financial Times puts together periodically.
It's an interesting chart that clearly tells the story that China, South Korea, and Japan have been much more successful in fighting the virus than Western countries and Iran. It also communicates these latter countries don't appear to be making significant progress.
These are important things to know, but subsequent updates of the chart often don't provide any additional insight. I should add that most people don't naturally think in terms of logarithms. So, it's probably a hard chart for many to interpret.
In an attempt to assist with our collective efforts to understand the threat this virus poses as well as to assess the success of our efforts to fight it, I designed a simple data visualization that can quickly communicate three essential pieces of information at the state, province, country, and/or regional/global level. These are:
The severity of the problem
The rate at which a state/country/region is making progress or falling behind.
How far the state/country/region has to go before the virus is neutralized.
Additionally, the visualization facilitates comparisons between countries, allows data for states/countries/regions to be combined, and can serve as a foundation upon which additional analyses can be built.
Before diving in, it's important to provide some background on the mathematics of contagion. Contagions work exponentially. Let's say a country starts out with 1,000 infected people and each week an infected person passes it on to an average of 1.3 other people. (1.3 happens to be the rate of infection associated with influenza). At the end of 12 weeks a total of 23,300 people will have been infected at some point. If the infection rate were instead 2.6 (as may be the case with the coronavirus), then after 12 weeks 95 million people will have been infected.
So, what may seem like a small difference in the contagion rate, has a huge impact on the outcome. As I tell my clients, if something is important to know, then it should be a metric you look at frequently. But we don't appear to have landed on a way to quantify how quickly the virus is spreading within each country in a way that allows one to compare it to the recent past, project the virus' near-term course, and facilitates cross-country comparisons.
I'll explain how the visualization works by comparing confirmed case and mortality data from South Korea and Italy. From there, I'll expand the analysis to Spain, Germany, Switzerland, The United Kingdom, and the United States.
Charting South Korea and Italy
South Korea is one of the countries that successfully fought the virus early on. The chart below portrays the total cumulative confirmed cases in South Korea from February 20 - March 21. The blue line in the chart demonstrates that around February 25 it looked like the coronavirus may have been on the verge of exponential growth.
But that didn't happen. Instead, confirmed cases just started growing at a faster linear pace. Then around March 4 the pace of growth slowed considerably, adopting a similar linear trend to one that started on Feb 20.
Italy's experience has been completely different. Confirmed cases there have been growing at an exponential rate since early March. But there's something important that is not obvious from the chart. The rate of increase is decreasing.
Now, that's a hard concept. I confess I had difficulty when it came to discussions of decelerating acceleration in Physics class. But I think I can make the point by first referencing the data from South Korea and then returning to Italy.
On February 20 South Korea counted 104 confirmed cases of the coronavirus. Seven days later on February 27 they had 1,766. After another 7 days, on March 5, they had 6,055.
Now let's determine how quickly the confirmed cases increased from week-to-week. On March 5, South Korea had 6,055 cases. That 's 3.4 times greater than the 1,766 cases they had on February 27. In turn, 1,766 cases is 17 times the 104 cases they had 7 days prior to that. I call these factors the "Confirmed Case Multipliers."
That Multipliers through yesterday are charted below.
South Korea's Confirmed Case Multiplier peaked at 41 on February 26. It's quite common for the early multipliers to be quite large because later numbers are being compared to the small number of cases early on. Within a matter of weeks the multiplier dropped to 1.1, where it has remained since. A contagion rate of 1 is the goal. It indicates the number of total cases today is the same as it was 7 days ago, or in other words the virus has stopped spreading.
It's really quite remarkable how quickly South Korea was able to minimize the coronavirus' threat. (Although I must report that as I write this, South Korea has attributed 7 deaths to the virus so far today (March 23). Hopefully, this does not mark the beginning of a resurgence).
As you might expect, Italy's Confirmed Case Multiplier looks very different. Due primarily to the fact Italy's Multiplier peaked at over 200 on February 27, I began the chart with data starting on March 1.
Italy's Confirmed Case Multiplier declined from 11.0 on March 1 to 2.4 yesterday. While that represents significant progress, it means that confirmed cases are continuing to increase by over a factor of 2 on a weekly basis. Italy's current case count is approximately 60,000. Putting these to facts together means that unless the measures Italy has taken continue to slow the virus' spread it very likely could have over 120,000 confirmed cases in the next week. Fortunately, as of this writing, I don't believe that will be the case.
This chart makes a number of things clear at a single glance:
Italy's pace of contagion has significantly decreased over the course of the past three weeks.
The rate is still dangerously high.
The pace of improvement may be linear at this point.
I mentioned earlier that this method allows one to quickly compare the progress of two countries. The chart below plots South Korea and Italy's Confirmed Case Multipliers as measured from the peak of that metric in each country (Feb 26 in South Korea and Feb 27 in Italy).
From the chart one is very quickly able to make meaningful assessments
South Korea's Confirmed Case Multiplier started out much lower than did Italy's
One can compare in meaningful terms the rate at which confirmed cases were increasing. For example, eight days after the peak, confirmed cases were quintupling in Italy, while they were growing by less than a factor of four in South Korea
South Korea's success relative to that of Italy accelerated after Day 8
The natural follow-up question is how does the count of the number of deaths compare with the Confirmed Cases Multiplier? To answer that, I created a measure called the Lives Lost Multiplier using the same method as I did with confirmed cases, but calculating the multiples based on total deaths.
You'll notice that in Italy's chart below that the Lives Lost Multiplier (in orange) is consistently higher than the Confirmed Case Multiplier. I have found this is generally true across all countries.
Italy's lives lost multiplier was 3.0 as of yesterday. Let's be clear about what that means. If that rate stayed constant over the next 7 days, Italy would lose another 10,900 lives above and beyond the 5,500 lost to-date.
Fortunately, like the confirmed cases multiplier, the lives lost multiplier is falling. The risk of an outcome that severe is lessening.
How well are the other countries of Europe and the United States doing? It's early, but, in general, not well. Below you can find the charts for Spain, Germany, The United Kingdom, Switzerland, and the United States.
The virus hasn't taken hold in these countries as quickly as it has in Italy. So, the curves haven't had as much time to stabilize. To compensate I've charted the three-day moving average in order to smooth out the lines. Even so, the results require explanation, which I've included below each chart.
Data for Spain's Lives Lost Multiplier starts on March 9 because it didn't have three days of fatality data until March 2.
The rate at which the virus has taken lives in Spain is similar to, if not worse than that of Italy.
The Lives Lost Multiplier is currently well over six, which means that the number of lives lost in Spain was over six times greater on March 22 (1,756) than it was on March 15 (289)
The Lives Lost Multiplier is falling fast, but it's still unacceptably high. If it doesn't continue to fall, Spain may ultimately rival Italy in terms of the number of fatalities
Germany has been credited with doing a great deal of testing, and the number of fatalities in the country is fairly low (94 as of March 22).
Presently, both Multipliers are at alarming levels, but that is typical for a country at this stage of the crisis. Both Multipliers should fall in the next few days, but, to me, their height underscores the importance of early and sustained action.
From the data at my disposal it's not possible to land on a reason for Germany's relatively low number of fatalities relative to its confirmed cases. Among likely explanations are that it could be on account of the quality of the country's health care system, the health/age of the German people, or their employing different method for classifying deaths.
The United Kingdom
As of March 22, The UK had 5,863 confirmed cases and had lost 281 people to the coronavirus
The case count has more than quintupled each of the past two weeks.
I'm going to repeat the same observation I had for Germany. Presently, both Multipliers are at alarming levels, but that is typical for a country at this stage of the crisis. Both Multipliers should fall in the next few days, but, to me, their height underscores the importance of early and sustained action.
It may surprise many, but, after Italy, Switzerland has the second highest number of confirmed case per capita (892 per million).
As of today, the coronavirus has taken 118 residents of the country, which is a significant number considering it's population of 8.7 million
Given the high fatalities for a country of its size, Switzerland has less margin for error than may be generally be appreciated
The United States
Both Multipliers are increasing, which is, of course, concerning, and suggests follow-up work is necessary to understand whether that reflects the true course of the virus or the state of our data testing.
Given the size of the country and 419 lives lost as of March 22, it is conceivable the Lives Lost Multiple could remain elevated for days, if not weeks.
Of the 419 lives lost so far, nearly 28% (117) were lost yesterday (Mar 22)
The escalation in confirmed cases is very likely due to a backlog in fulfilling demand for testing. It will take some time for that to work itself out to get a truer picture of how quickly the virus is spreading
I hope you've benefited from this perspective on charting the path of the coronavirus. I intend to update the charts at least weekly. If you have any suggestions or ideas, then please send them to me at firstname.lastname@example.org.