Coronavirus: How each country is riding the bell curve

Objective of this article:

• To make it easier to draw comparisons of coronavirus growth rates across countries
• To assess how each country is doing … are they ahead or behind the curve?

As we all try and make sense of the current situation we’re all wondering if our own country will follow the growth rates observed in Italy and Spain, or if perhaps, all of this social distancing will help us be more like Taiwan and Singapore.

We’re all wondering how long will this last, and how long will it take for this to go through our system.

It’s hard to compare the growth rates when they start at different times in different regions. We also need to think about how do we compare regions with +100 million residents to smaller regions like Canadian provinces and US states.

Sneak peak of the findings

• It generally takes about 1 to 2 weeks for a country, state or province to go from having 10 confirmed cases to 100 confirmed cases
• It generally takes another week to go from 100 to 1,000 and generally another week to go from 1,000 to 10,000 confirmed cases
• Countries like Canada, Australia and the UK have now already missed their chance to manage the coronavirus as well as Taiwan and Singapore, but they are are currently faring reasonably well
• The US, and in particular, New York and New Jersey are on track to fare as poorly as Spain, Italy, and Germany unless they do something quick

Chart: Growth rate in confirmed coronavirus cases, lining up the start of the clock to the day of the 100th confirmed case

How I figured it out

Much of the data that we need is publicly available on github. The following link includes daily data of confirmed cases for each country in the past several weeks:

https://github.com/datasets/covid-19/blob/master/data/time-series-19-covid-combined.csv

We have to keep in mind that each day it shows the numbers that were reported across the world as of the previous day.

If we want to be better able to line up each region with the growth rates of other regions, we will need to do a few things:

Step 1: Look at some countries that are further along in their patterns

Step 2: Normalize the starting time so that it’s comparable

Step 3: Separate the countries that have slow growth rates (our best case scenario) from the countries that have fast growth rates (our worse case scenario)

Step 1: Learning from countries that have been at this a while

Chances are that you’ve already seen the China Hubei charts that show the cumulative confirmed cases and the new confirmed cases:

Chart 1: Cumulative confirmed cases for China Hubei

Chart 2: New confirmed cases for China Hubei

Even though this is could be considered a “worst case scenario” pattern, the most positive aspect of it is that the pattern has stabilized, and it happened in approximately 7 weeks. The shape of the cumulative curve is an “S” shape, meaning it has an exponentially increasing pattern in the beginning, an inflection point in the middle in mid-February, and an exponentially decreasing pattern at the end.

It is widely reported that the growth rates in other China provinces were substantially improved based on the learnings from the Hubei region. As an example, the same curves are shown for the Chongqing province.

Chart 3: Cumulative confirmed cases for China Chongqing

Chart 4: New confirmed cases for China Chongqing

Visually we can see the S curve last with the first week showing exponentially increasing growth rate, an inflection point in the second week, and the third week already showing an exponentially decreasing growth rate. So, we could consider curves like the to be our “best case scenario”. You can also see from Chart 4 that the inflection point happens when the number of new confirmed cases per day starts to decrease from one day to the next. It actually happened twice … once in early February (in week 2) and again on the second week of February (in week 3).

For another “worst case scenario” we look to Spain.

Chart 5: Cumulative confirmed cases for Spain

Chart 6: New confirmed cases for Spain

We can see that we have not hit our inflection point yet and that the number of new confirmed cases is still zigzagging upwards.

Now we need a way of lining things up, so we can see if this is better or worse than expected.

Step 2: Normalize the starting time so that it’s comparable

A simple and easy way of normalizing the starting time is to take note of the first day where there were 10 confirmed coronavirus cases in a given region. This is the first toehold in the region. We know that if there are 10 confirmed cases then chances are there are a lot more cases that are in the community that have no symptoms or have not yet been tested and reported.

Chart 7: Cumulative confirmed cases for Spain and Chongqing

Now that the confirmed cases are on the same scale, and the time axes are the same scale we can see that the Spain situation on day 14 (March 10, 2020) is remarkably worse than observed in Chongqing on day 14 (February 6, 2020). The Chongqing province was already showings signs of slowing down at that point, whereas the country of Spain was still in the period of exponentially increasing growth. Spain has 39,885 confirmed cases as of March 24, 2020.

Similarly, we can normalize the starting time is to take note of the first day where there were 100 confirmed coronavirus cases in a given region, and again for the first day there were 1,000 confirmed cases, and the first day there were 10,000 confirmed cases.

We can use these numerical milestones to measure and compare the growth rates. We can look at how long does it take for a region to increase from 10 confirmed cases to 100 confirmed cases, and then how long does it take to go from 100 to 1,000 and from 1,000 to 10,000.

Because not all regions have stabilized and matured, we only have so many counts for each. The following table shows us the range of time it takes to go from 10 confirmed cases to 100 confirmed cases

Table 1: Number of days between 10 confirmed cases in a region and 100 confirmed cases in a region

There are clearly some regions that showed a faster initial growth rate of less than 7 days including Italy, Spain and Iran. Interestingly, the Chongqing province had a fast initial growth rate, but we know that they stabilized the growth so rapidly that they never hit the next milestone of 1,000 confirmed cases.

There are several regions that had a very slow initial growth rate including Japan, Singapore, Hong Kong, Australia and Taiwan. We also know that some of the regions with slow initial growth rates lost their gains later.

Chart 8: How long it takes to go from 10 confirmed cases to 100 confirmed cases in a region:

The chart shows that, in general, this first part of the growth curve typically takes 1 week with some regions able to stretch it past 3 weeks.

If we go through the same exercise for the transition from 100 confirmed cases to 1,000 we observe that it takes about a week for that to happen too. Iran and the Hubei province of China had the fastest growth rates, whereas Canada, Australia and Japan were able to slow their growth rate down during this period to 11, 12, and 30 days respectively.

There are fewer countries that have transitioned from 1,000 to 10,000 confirmed cases, but the pattern is about the same again … it takes about a 1 week for this transition to happen.

Step 3: Separate the countries that have slow growth rates (our best case scenario) from the countries that have fast growth rates (our worse case scenario)

As shown previously, we are able to use these milestones to identify the countries that represent our “best case scenario” and our “worst case scenario”.

Chart 9: Best case scenario growth curves for cumulative confirmed cases

The best case scenario would be to follow the same slow initial growth in cases observed in Hong Kong, Singapore, Taiwan and Australia. Note that the scale of the y axis is 300 cases.

Chart 10: Worst case scenario growth curves for cumulative confirmed cases

The worst case scenario would be to follow the rapid initial growth observed in Italy, Spain and Iran. Note that the scale of the Y axis is 30,000 cases, a 1,000 times larger than shown in Chart 9.

So, now that we’ve done that, how are we doing?

Many regions are just in the starting phase of their growth pattern, and now we can use the above curves to see if we’re on the trajectory of Spain or if we’ve got this managed like in Taiwan.

I’m from Canada so, in a very un-Canadian way, I’m going to show our country first.

Chart 11: New confirmed cases for Canada

We’re increasing our cases every day, so it looks like we’re still in the exponentially increasing part of the curve. Our first day of 10 confirmed cases was on Feb 24, 2020 and you can see we’ve done a good job of stretching out this initial period.

Chart 12: Cumulative confirmed cases for Canada, plus best and worse case scenarios

If we compare ourselves against the best and worse cases, we’ve done very well since 10 confirmed cases. If we recalibrate the worst case scenario based on the start date of 100 confirmed cases we can see that Canada is reasonably in the middle of the best and worst case scenarios. Clearly we don’t have a shot at achieving the low case counts observed in Taiwan and Singapore, but things could be worse.

Turning our attention to our neighbors to the south we can see a much more concerning picture.

Chart 11: New confirmed cases for the US

The numbers are bigger, as would be expected for a larger country and it looks like they are still in the exponentially increasing part of their curve too.

Chart 14: Cumulative confirmed cases for the US, plus best and worse case scenarios

The more concerning pattern is the growth rate relative to the worst case scenario. The US is increasing at a much faster rate than expected.

Obviously we’re treating each region as if they were comparable, which they are not. The population and the population densities are different. But to put it in perspective, if we filter on just the state of New York which has a smaller population than Canada, and apply the same growth curves we get the following chart.

Chart 15: Cumulative confirmed cases for the State of New York, plus best and worse case scenarios

New York state has approximately one third the population of Hubei, but they already have 39% of the confirmed cases reported in Hubei (26k versus 69k). On a positive note, the new cases reported on March 24, 2020 were the first ones to decrease in more than 10 days.

Looking back to Canada we can see that there are regional differences here too.

Chart 16: Cumulative confirmed cases by Canadian province

The province of Quebec is following the “worst case scenario” pattern, whereas many provinces have such small counts that they are not even registering in this analysis. Most provinces are well between the best and worst case scenarios.

The best and worst case scenarios provide us with a relative guidepost. They don’t tell us where we’re necessarily going to be next, but more so they give us an idea of where we are now.

Main take away messages

In summary, these are the things that I did not know until I did this analysis:

• All of the regional growth patterns of confirmed cases generally follow the same “S curve”
• The regions that are doing well are the ones who have been able to nip the problem in the bud … they get to the inflection part of the “S curve” and never get to 1,000 confirmed cases
• Some regions like France and Germany did well at reducing the growth at the beginning but then lost their gains later … this may indicate the importance of not getting over-confident
• Many regions have reached the slowing of the growth curve by 3 to 4 weeks … the worst may be yet to be seen, but it looks like the upper end has been 6 to 7 weeks for those regions that have been dealing this for a while