Post originally written February 16, 2020.
As someone who likes statistics and doesn't like disease, I've been following numbers each day on the new coronavirus. Unfortunately, I don't have medical expertise, and like everyone else away from the front lines, I'm limited to what data we have. So take anything here with a bag of salt: it's just some guy on the internet messing around with the numbers and seeing what he can see.
Fortunately, although the medical details are often murky, we are getting daily updates on some key figures. The principal figures I've been interested in are
- confirmed cases: the total number of confirmed cases so far
- suspected cases: the total number of people identified by their governments as being suspected of carrying the virus
- recovered cases: the total number of people who have recovered so far
- deaths
These are the numbers most often reported in the news: especially confirmed cases. The news was also, until February 12th, beginning to fill with headlines about whether coronavirus might be peaking. As to whether it really is peaking, I have no way to know, but at the very least I can check if the data was consistent with peaking, and it did seem to be tending in that direction.
I have found these numbers in the WHO Situation Reports, as well as on a nifty site called outbreak.cc, on Wikipedia, and, finally, from the Chinese government. That last site is in Chinese, but it all auto-translates easily enough. We have the technology. They all seem broadly in agreement with each other, once allowances are made for occasional retroactive updates to data, the different times of day that sites are updated, and two big definitional issues.
The first has to do with what "China" is, and for my purposes I am including mainland China, Hong Kong, and Taiwan as a single nation. Although various sensitive political issues are involved, the mainland, Hong Kong, and Taiwanese governments all agree that they constitute a single nation, and so I will follow their lead for the purposes of this exercise and wish them the best as they continue to work out their differences.
The second definitional issue has to do with what a "confirmed case" is. Until February 12th, this was not a problem. Talk of the virus peaking was common in my Google News feed, and the WHO and China were on the same page about how many confirmed cases there were.
Then, on February 12th, the government of China suddenly added about 15,000 "confirmed cases" in a single day, and announced that these numbers were due to a change in the definition of "confirmed". Prior to February 12th, only lab tests were acceptable as confirmation; starting February 12th, CT scans were also admissible. The World Health Organization, however, continued reporting lab cases most prominently in its situation reports.
At the same time, two other trends were becoming increasingly important. Tragically, a larger number of people were beginning to die of the disease; somewhere on the range of 100 to 150 per day. On the other hand, great numbers of people were beginning to recover from the disease; something like 1000 to 1500 per day.
The WHO spoke positively about China's recording of CT scan cases, while still choosing to keep its own data consistent with pre-February 12th norms. The Chinese government continued to report lab data as well, as a subset of its total cases. Since both the WHO and China appear to see some value in the other's approach, I have also chosen to track both the broader and narrower senses of "confirmed".
In the case of the Chinese data, which has been subject to redefinitions, I find myself unconvinced that we can meaningfully speak of long-term trends in terms of the "confirmed" versus "suspected" distinction. It seems, especially since February 8th, that there has been a lot of movement from "suspected" to "confirmed" in a way that causes apparent shifts in numbers but does not have a clear relevance (so far) for understanding the full situation. So for my broader measure, I have added both together. This is my "broader test" number.
For both the WHO and Chinese approaches, I think it is useful to think in terms of "active" cases. If we want to get a handle on how big the disease is right now, and how many people are known or suspected to be capable of spreading it, we need to avoid including the recovered and the dead.
The math is simple, but tedious. Python can handle this. First, I keep a running tab on six numbers, which takes all of a minute or two a day and a couple website visits to update. Right now, that looks like this (all lists begin January 20th):
{% highlight ruby %} # Number of lab-confirmed cases (WHO approach). lab_tested = [295, 445, 580, 845, 1317, 2015, 2800, 4581, 6058, 7813, 9821, 11948, 14551, 17389, 20628, 24553, 28276, 31439, 34876, 37552, 40553, 43103, 45171, 46997, 49053, 50580, 51857]
Number of cases reported by governments as "confirmed" (mostly Chinese)....
broad_tested = [295, 445, 580, 845, 1317, 2015, 2800, 4581, 6058, 7813, 9821, 11948, 14551, 17389, 20628, 24553, 28276, 31439, 34876, 37552, 40553, 43099, 44919, 60326, 64442, 67100, 69104, 71330]
Cases reported as suspected by governments....
suspected = [54, 436, 393, 1072, 1965, 2684, 5794, 6973, 9239, 12167, 15238, 17988, 19544, 21558, 23214, 23260, 24702, 26539, 27657, 28942, 23598, 21675, 16067, 13435, 10109, 8969, 8228, 7264]
Cases reported as recovered by governments....
recovered = [25, 28, 28, 34, 38, 49, 51, 60, 104, 125, 175, 255, 341, 489, 648, 912, 1175, 1563, 2075, 2675, 3324, 4039, 4783, 5988, 6955, 8192, 9434, 10984]
Total deaths reported....
dead = [6, 9, 17, 25, 41, 56, 80, 106, 132, 170, 213, 259, 304, 362, 426, 492, 565, 638, 724, 813, 910, 1018, 1115, 1369, 1383, 1526, 1666, 1775]
People outside China reported to have the coronavirus....
outsiders = [4, 4, 7, 10, 11, 23, 29, 37, 56, 68, 82, 106, 132, 146, 153, 159, 191, 216, 270, 288, 307, 319, 395, 441, 447, 505, 526, 683] {% endhighlight %}
Then, it's a matter of just a little math to work up our lists for the broadest and narrowest measures of total active cases.
{% highlight ruby %}
active_narrow = []
for x in range(len(lab_tested)):
active_narrow.append(lab_tested[x] - dead[x] - recovered[x])
{% endhighlight %}
Since viewing a trend works best with a graphic, we can import
matplotlib.pyplot and whip up a function to draw a quick, dirty graph:
{% highlight ruby %} import matplotlib.pyplot as plt
def quick_dirty_graph(y, caption): """Make a quick, dirty graph from some list with a caption.""" x = [] for i in range(len(y)): x.append(i) plt.bar(x, y, label=caption) plt.legend() plt.show() {% endhighlight %}
And then all we need to do is call it, like so:
{% highlight ruby %} quick_dirty_graph(active_narrow, "Global Active Cases (Lab-Tested Measure).") quick_dirty_graph(active_broad, "Global Active Cases (Broadest Measure).") {% endhighlight %}
And it gives these graphs:
Certainly, we could do more to make the graphs pretty and informative, but if the goal is just to quickly visualize all sorts of data, we've got a framework here where we can quickly whip up code to do different kinds of math and take a look.
For example, both measures seem to show what looks like a recent peak in active cases. I say that as someone just eyeballing the numbers, of course. Consult your national health service for any kind of data you'd actually use, etc.
Perhaps we'd like to see the day to day changes more clearly. We could draw up a function that takes, essentially, the derivative of some list:
{% highlight ruby %} def delta_list(data): x = [] for i in range(1, len(data)): x.append(data[i] - data[i-1]) return x {% endhighlight %}
And then we can use that to call up the daily changes:
{% highlight ruby %} narrow_deltas = delta_list(active_narrow) caption = "Daily Changes, Global Active Cases, Lab-Tested" quick_dirty_graph(narrow_deltas, caption)
broad_deltas = delta_list(active_broad) caption = "Daily Changes, Global Active Cases, Broadest Measure." quick_dirty_graph(broad_deltas, caption) {% endhighlight %}
And we get the following two graphs:
The lab-tested measure shows about two weeks of escalating increases in active cases, following by smaller and smaller increases. The broadest measure, which includes all sorts of nebulous "suspected" and "clinical cases", is more chaotic, and shows the disconcerting spike at February 12th, but outside of the spike it does seem to show a peak in growth, even followed by a number of days where cases have declined.
Now, with any outbreak like this, the big concern is exponential growth. If the number of active cases were to grow at some steady percentage rate each day, be it 10% or 50% or even 1%, that trend would, if not stopped, eventually lead to everyone getting the disease. And with a mortality rate that is in the neighborhood of perhaps 2%, that would be disturbing. So we might be curious about what is happening to the percentage rate of growth, to see just how closely this outbreak matches an exponential curve.
And so we can draw up another function that draws up the percentage changes we want, and then call it appropriately.
{% highlight ruby %} def percent_changes(data): """Show how a list changes from index to index, as a percentage.""" x = [] for i in range(1, len(data)): x.append((100 * (data[i] - data[i-1]) / data[i-1])) return x
percentages_narrow = percent_changes(active_narrow) caption = "Daily Percent Changes, Lab-Tested Active Cases" quick_dirty_graph(percentages_narrow, caption)
percentages_broad = percent_changes(active_broad) caption = "Daily Percent Measure, Broadest Measure of Active Cases" quick_dirty_graph(percentages_broad, caption) {% endhighlight %}
This gives us the following:
And so, on both measures, we see that the daily growth rate is anything but stable, and in fact has been steadily dropping from early in the outbreak. Now, it's garbage in, garbage out if the data doesn't accurately reflect the real situation, and an amateur like me isn't at all in a position to say that the trends will hold.
But I hope the trends are real, and I hope they hold up, and I'll be keying in my various data and building these and other graphs daily for at least the next few days.
And because I am not aware of anyone else online who is running these six graphs on a regular basis, I plan to post updated graphs day by day as new data comes up.
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