Transforming the Exponential Curve

A lot of the information that we have been consuming off late about the Coronavirus has revolved around the exponential graphs that it is associated with- what these graphs tell us is that as time passes, there are more and more cases of the virus that are detected per unit of time. In our Indian scenario what that essentially means is that the first week of March, accounted for only 30 of the total cases that had been detected, the second week, accounted for 60, and the third accounted for 270. And these trends have been terrifying to say the least. This exponential graph, as plotted using the data-set made available by Our World In Data, looks something like this:

But, the issue here is that for the layman, this graph is not very easy to read, and even harder to study. It is also difficult to figure out whether the policies that are currently in action have had an effect. The aim, as we know it, is to ‘flatten the curve’, for which the nationwide lock-down had been announced on the 25th of March. But, as the graph tells us, the numbers that were detected positive have only exponentially increased since.

In an interesting article published in the New York Times, Kenneth Chang wrote about a different way to chart the spread of the virus (You can read the piece here) He talks about how the data actually looks very different when plotted on what is called a logarithmic scale- in this, instead of plotting numbers linearly on the Y-axis, we plot them as a power of one unit, say 10, 100, 1000…

This same curve, when plotted logarithmic-ally, makes the deviations from the exponential spread easier to discern- showing us what policy is working, and the extent to which it is working. That same graph, transformed with a logarithmic scale, looks something like this:

Showing that in actuality, up till now, the cases have not slowed in their increase, but it may as well be too soon to tell, since the nationwide lock down was announced on the 25th of March. To compare with other countries, some that are beginning to overcome the virus may be helpful.

From these charts, it's evident that the rate of infection seems to be slowing, in China and South Korea, faster than in countries like the United Kingdom and United States.

1. 2. 3.

4. 5. 6.

1- South Korea; 2-Italy; 3-United States; 4-United Kingdom; 5-China; 6-Iran

While studying these charts, one must keep in mind that the countries are on different timelines, in terms of the start of the spread, and as a result, also the day that the nationwide lock-downs were announced as a means to curtail the spread.