The short answer is that, in most countries, the cumulative case total doubles every two to three days. This assumes sustained local transmission where the local counter-measures have not slowed that transmission.
If we assume a doubling every three days, then 100 cases today will grow to around 13,000 in three weeks and 1.6 million in six weeks. If one to ten per cent of those with the virus need hospital treatment, uncontrolled growth in infections would be challenging for the health system.
Some countries (eg. China and Korea) have arrested growth. Others (eg. Singapore and Japan) have a slower growth rate.
For this analysis, I have taken the case numbers from Our World in Data (OWID). The latest records were dated 11 March 2020. [Update: I have updated the charts for the latest data to 12 March 2020; again for the latest data to 14 March 2020; again for the latest data to 16 March 2020; and 17 March 2020].
Update: From 16 March, I have added charts with data from the European Centre for Disease Prevention and Control (EU). While similar, the two data sources are not aligned in many cases.
I have focused on those countries with more than 100 cases in the most recent report, and those countries with at least four days of data with over 50 cases each. I wanted to focus on countries where local transmission had been established, and where I had enough data points to fit a regression.
For each country, I have fitted a regression equation for exponential growth in the form:
$$y=\alpha e^{\beta x}$$
where \(x\) is the number of days with 30 or more cases, and \(y\) is the total number of cases on that day (cumulative).
To calculate the doubling time, I have taken the \(\beta\) exponent from the above regression equation and applied the following:
$$Doubling\ in=\frac{ln(2)}{\beta}\ days$$
I have excluded China, as an exponential growth model no longer describes what is happening there, given the effectiveness of its containment measures.
The results follow. I have annotated the anomalies.
Of note: the doubling rate in Australia does not appear to be as fast as other counties.
The Iranian data does not look like exponential growth; I am not sure why, and I have no direct information about what Iran is doing, but it is possible that containment strategies in Iran are having an impact.
Japan has a slower doubling time than most other countries.
Singapore has a particularly slow growth rate. However, this may be changing with the most recent data.
This is not the best regression fit. We can see that South Korea is arresting the growth rate in cases. This is an example of when the exponential growth regression no longer applies.
Some further comparisons can be seen in the following charts (all based on data from OWID).
The code I used to generate the above plots is saved as a GitHub gist. [Note: To see the Jupyter notebook with the Python3 code, you will need to access the gist from a desktop or laptop computer. It often does not work from a mobile device].
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