The Omicron Surge In Numbers: Reproduction Number Up, Doubling Time Down

The high value of R, a key indicator of Covid-19 spread, suggests a surge of infections in most major states, including Bihar and Jharkhand, which have the lowest vaccination rates among larger states

The Omicron Surge In Numbers: Reproduction Number Up, Doubling Time Down

A health worker collecting a swab sample for Covid-19 testing at Chandni Chowk, Old Delhi, on 6th January, 2022

Kolkata and Mumbai: For the first time in seven months, India recorded over 100,000 cases on January 6, 2022. As several parts of the country witness a surge due to the Omicron variant of SARS-CoV-2, the virus that causes Covid-19, two indicators–effective reproduction number (R) and doubling time–suggest a further increase in cases in the coming days.

The reproduction number is a measure of transmission–the average number of people infected by one infected person. The government announced on January 5 that the R is 2.69 and this is higher than the R during the second wave. That is, each Covid-19 patient is infecting 2.69 others, on average.

If the R of a disease is greater than one, it means that the number of cases is growing fast and can cause an epidemic. If the R is equal to one, the disease is growing slower but is still dangerous and many could contract it. If the R is lower than one, that is, one person infects fewer than one other person, on average, then the disease will slowly die out.

Doubling time is the number of days taken for cases to double. India's doubling time fell from 3,684.4 days on December 27, 2021 to 454.9 days on January 6, 2022. During this period, there was a corresponding eighteen-fold increase in daily new cases.

We analyse the trends for these indicators in states which are reporting over 500 new cases daily, and highlight the exponential growth in states with very high R-values.

Reproduction number

Based on the estimates for the period of December 29 to January 2, Sitabhra Sinha, professor of computational biology and theoretical physics at the Institute of Mathematical Sciences, Chennai, calculated an R value of 1.96 for India. "This is certainly larger than what I have estimated during the height of the second wave,'' he said, adding, "the highest R was during March 9 to April 21, 2021. At that point, it was 1.37".

The difference between the R announced by the government and the one calculated by Sinha is because of the higher errors in estimation due to fluctuations in data which are likely to occur when cases have just started rising, Sinha explained. "In reality, people don't immediately figure out that they are infected; there is a lag between actual occurrence of infection and time of reporting, which leads to data fluctuation." In addition, when you only consider a short time period, such as a week, there are larger estimation errors, he said. "We are focusing on a very very small part of the curve at present, and we might not be looking at the true trend, but overestimating or underestimating."

The R would be revised after considering cases over two weeks, he said. "Even though they are approximate, quick estimations are very important for deciding what actions need to be taken, like issuing fresh guidelines for localised quarantine, travel and so on."

Several states like Bihar, Jharkhand and Delhi have a high R, Sinha's calculations show. Some of these states also have low vaccination coverage (see chart 2).

Doubling time

Maharashtra had the highest number of daily cases as of January 6, at 36,265, followed by West Bengal at 15,421, and Delhi at 15,097 respectively. These three states account for 57% of all new cases in India.

The doubling time in Delhi has been decreasing gradually since November 27, whereas in West Bengal, the drop has been sudden, since December 27, 2021.

In Maharashtra, doubling time has been fluctuating since November 2021 until December 16, 2021 when it started falling. Since then, daily cases have risen from 877 to 36,265.

Kerala is an exception to the national trend: It has seen a gradual decline in the number of daily cases through November and December. Daily cases by the end of December were a third of those recorded in early November (see chart below). Cases have seen an uptick from January 04, 2022.

Tamil Nadu, Karnataka and Gujarat also reported over 4,000 cases on January 6, 2022.

Bihar & Jharkhand among states which have high R-values, are likely to see a surge

Bihar's doubling time started to drop from December 21, while Jharkhand's started falling on December 15. These states, as we said, also have a high R and a relatively lower vaccination coverage, indicating a potential surge.

Punjab, Uttar Pradesh, Haryana, Rajasthan and Chhattisgarh have also seen an uptick in cases beginning December 28, 2021.

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