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Photo: Reuters
Photo: Reuters

Coronavirus: Decoding covid-19’s growth rate

  • From doubling every three days in the middle of last week, the current growth rate implies doubling every 6.1 days
  • The number of cases is growing at a much slower rate than last week

BENGALURU : There’s a sliver of good news amid the spread of the coronavirus in India —the number of cases is growing at a much slower rate than last week. From doubling every three days in the middle of last week, the current growth rate implies doubling every 6.1 days.

By now, it is clear that covid-19 cases grew exponentially in the initial days. Every country has shown this trend, and it has become common to express a country’s viral growth rate in terms of the growth rate of another country a few days back.

Not all exponential growth is the same, however, and the rate of growth has a huge bearing on how bad the problem is. For example, if the number of cases were to grow at 1% a day (a hypothetical situation, but exponential nevertheless), it would appear that the growth is benign. On the other hand, something that would double every day could represent an alarming situation.

growth rate of cases
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growth rate of cases

For this purpose, quantifying and understanding the rate of exponential growth is important. One way to do this would be to plot the total (cumulative) number of cases each day on a graph with a logarithmic Y-axis. The problem with this is two-fold. First, it takes supreme eye skills to learn the growth rate and any change in growth rate, from the logarithmic graph. Second, absolute growth rates are not easy to appreciate—what does a decrease in daily growth rate from 15% to 12% (for example) entail?

Instead, a prudent method to look at the growth rate of the epidemic is to look at it in terms of “days to double". Using the “rule of 72" that readers of the personal finance pages of this newspaper might be familiar with, a growth rate of 12% per day implies doubling in 6 days. A growth rate of 15% per day implies doubling every 4.8 days.

Before we turn daily growth numbers into doubling rates and plot them, we need to keep in mind that daily growth rates can be “noisy" and have high variability. One way to get around this is to take an average over a longer time period. A good trade-off between removing variability and keeping the data current is to use a three-day period to calculate the “cumulative daily growth rate" (it’s interesting that the quantities we normally look at on an annualized basis, we are now looking at on a daily basis), and then use that to calculate the doubling rate.

There has been a clear recovery in the growth rate of the novel coronavirus infections in India in the last one week. On April 2 and 3 (immediately after the Nizamuddin Markaz cluster was discovered) the total number of cases grew at a rate that would have meant doubling of infection rates every 3.2 days, which is dangerous territory.

While the number of cases has grown after that, the rate of growth has slowed, as the graph shows. Now, at the national level, cases are growing at a rate that results in doubling every 6.1 days, a more manageable number.

But, there is wide regional variation. In Kerala, where India’s first three covid-19 cases were registered, and which led the country in terms of total number of cases for a long time, growth has slowed to the extent that now we can expect the numbers to double only once in 22 days. Neighbouring Karnataka has controlled the disease to the extent that it doubles once in 11 days.

Tamil Nadu, which has a large number of cases related to the Markaz, also seems to have got the spread under control.

Of particular concern now are the northern states, especially Haryana and Punjab. While the absolute number of cases in these two states isn’t yet very high, cases have been doubling every 3.4 and 4.7 days, respectively. Madhya Pradesh is another state with concern, where apart from a low doubling period of 3.7 days, a number of government officials have also been affected.

It is still unclear what the national strategy will be following the end of the current lockdown on 14 April.

Looking at these trends, however, it seems a decentralized strategy might be prudent, where different states relax the restrictions at different points in time, and to different extents.

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