Jaipur: Between May 16 and May 25, the number of people infected by one COVID-19 patient on average (known as the effective reproduction rate or R of the disease) was 1.23, down from 1.29 between April 13 and May 4 and from 1.83 between March 4 and April 11, according to calculations by Sitabhra Sinha, a professor at the Institute of Mathematical Sciences in Chennai.

This means that between March 4 and April 11, at an R0 of 1.83, if 25 people had had COVID-19, they would have transmitted it to about 45 people while they were infectious. At the current R of 1.23, 25 people would infect 30, on average.

R is one measure to know whether India is controlling COVID-19. It explains how infectious the disease is by telling us how many people are infected by one COVID-19 patient over the course of their infection.

The decrease in R is “very likely the effect of the lockdown”, said Gautam Menon, professor of physics and biology at Ashoka University in Haryana. The Indian government had declared a strict nationwide lockdown from March 24, 2020.

When everyone in the population is equally susceptible, that is, when no one has developed immunity against the disease either because they recovered from the disease or because of a vaccine, and there is regular contact between people without any quarantining or containment measures, researchers calculate the basic reproduction rate (R0 or naught) to understand the infectivity and rate of spread of the disease, said Menon. As time passes and some people recover from the infection and become immune, and there are measures for containment through isolation, using masks and physical distancing, researchers calculate the effective reproduction rate (R), he said.

If the R0 or 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 R0 or R is equal to one, the disease is growing slower but is still dangerous and many could contract it. If the R0 or R is lower than one, that is, one person infects fewer than one other person, on average, then the disease will slowly die out.

India’s current R is 1.23, which means the disease is still growing fast. “If one had expected to see the epidemic go away with the lockdown alone, that of course hasn't happened,” Sinha said. “However, it has certainly helped in ensuring that our health infrastructure has not been overwhelmed so far.”

Easing of the lockdown

As the lockdown restrictions are eased, cases of COVID-19 could go up faster with more people coming in contact with one another.

“If you would have asked me two weeks back, I would have said the R would increase as the lockdown is eased but I am puzzled that the R has come down after May 3,” Sinha said. On May 3, 2020, the central government had eased some of the rules around the lockdown, allowing green zones to open up and permitting some activities in orange and red zones. “I have no idea why it [the R] has come down, but perhaps people are adhering to the distancing norms more strictly now,” Sinha said.

Will the R be lower in the future as the lockdown is further eased? “Probably not,” said Sinha. “We have not allowed the epidemic to take its natural course with containment measures,” because otherwise the number of cases and people dying would have skyrocketed, Sinha said, explaining that the pattern in most countries has been for the disease to peak and then decline. India is still away from the peak, but the rate of growth of the disease can be reduced with containment measures, he said.

“That also means that it would just take another spark to start the epidemic all over again because we still have a large number of susceptible people in our population,” Sinha added.

How Is The Reproduction Rate Of A Disease Calculated?

There are multiple ways to estimate R0 or R. One is by calculating it from the doubling time of the number of active cases. The other, used by Sinha for the R estimations in this story, is to use the estimated exponential growth rate of active cases, and then factor in the mean generation interval in the calculation. The mean generation interval is the average duration between an individual getting infected and the people that he/she passed on the disease to getting infected, Sinha explained.

For COVID-19, this time duration is estimated at 5.2 days based on research from Singapore. Statistical techniques are used to increase the accuracy of the R estimation.

The growth rate of the disease has to fit an exponential trend for the R to be accurately calculated. If there is too much fluctuation in the data, the accuracy of the R becomes lower. Sinha does not use data if the threshold of accuracy falls below 99%, he said. 

The R is dependent on the number of new cases every day, so better the testing and better the publicly available data, the higher the ability to calculate the R accurately, said Menon.

State-level COVID-19 effective reproduction rate

For the R to be accurate, Sinha uses the longest possible contiguous period to calculate the R and does not provide data if it is not 99% accurate. Because of this, the R of different states cannot be compared as it is for different time periods. The table below provides the R for some states. 

Estimated R Value For States
State Period of Estimation Estimated R
India March 4 - April 11 1.83
April 13-May 14 1.29
May 16 - May 25 1.23
Maharashtra April 13-April 26 1.49
April 23-May 15 1.34
May 4-May 25 1.27
Gujarat April 30-May 9 1.23
May 7-May 10 1.26
Tamil Nadu April 29-May 4 1.83
April 30-May 7 2.01
May 7-May 10 1.31
Delhi May 7-May 10 1.31
May 20-May 25 1.2
Punjab April 28-May 4 1.48
May 5-May 8 1.32
Rajasthan April 19-April 22 1.34
May 10-May 25 1.27
Madhya Pradesh April 16-May 1 1.23
May 10-May 23 1.23
Uttar Pradesh May 1-May 4 1.28
May 19-May24 1.33
West Bengal April 15-April 28 1.51
April 28-May 1 1.14
May 4-May 10 1.34
May 15-May 25 1.22
Andhra Pradesh April 6-May 1 1.27
Karnataka May 16-May 24 1.62

Source: Data shared by Sitabhra Sinha, Institute of Mathematical Sciences, Chennai
Note: 1. Because of fluctuations in data and accuracy for R below 99%, R estimations are not available for all states for all time periods. The author has tried to take the longest time period possible for these estimations. 2. The R for Tamil Nadu and Gujarat could not be calculated with the same degree of accuracy as other states for May because of fluctuations in the data.

R estimates based on testing

The R is calculated based on the active cases each day in the population as reported by the government.

As the number of cases detected depends on the testing regime, they may not be an accurate representation of the number of cases in the population. Many with the disease will be asymptomatic or have mild symptoms and hence not get tested, said Menon.

The difference in the R over time would still be an accurate way to measure the growth rate of the disease, provided that the testing criteria remains unchanged over time, said Sinha.

(Khaitan is a writer/editor with IndiaSpend.)

We welcome feedback. Please write to respond@indiaspend.org. We reserve the right to edit responses for language and grammar.

Jaipur: Between May 16 and May 25, the number of people infected by one COVID-19 patient on average (known as the effective reproduction rate or R of the disease) was 1.23, down from 1.29 between April 13 and May 4 and from 1.83 between March 4 and April 11, according to calculations by Sitabhra Sinha, a professor at the Institute of Mathematical Sciences in Chennai.

This means that between March 4 and April 11, at an R0 of 1.83, if 25 people had had COVID-19, they would have transmitted it to about 45 people while they were infectious. At the current R of 1.23, 25 people would infect 30, on average.

R is one measure to know whether India is controlling COVID-19. It explains how infectious the disease is by telling us how many people are infected by one COVID-19 patient over the course of their infection.

The decrease in R is “very likely the effect of the lockdown”, said Gautam Menon, professor of physics and biology at Ashoka University in Haryana. The Indian government had declared a strict nationwide lockdown from March 24, 2020.

When everyone in the population is equally susceptible, that is, when no one has developed immunity against the disease either because they recovered from the disease or because of a vaccine, and there is regular contact between people without any quarantining or containment measures, researchers calculate the basic reproduction rate (R0 or naught) to understand the infectivity and rate of spread of the disease, said Menon. As time passes and some people recover from the infection and become immune, and there are measures for containment through isolation, using masks and physical distancing, researchers calculate the effective reproduction rate (R), he said.

If the R0 or 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 R0 or R is equal to one, the disease is growing slower but is still dangerous and many could contract it. If the R0 or R is lower than one, that is, one person infects fewer than one other person, on average, then the disease will slowly die out.

India’s current R is 1.23, which means the disease is still growing fast. “If one had expected to see the epidemic go away with the lockdown alone, that of course hasn't happened,” Sinha said. “However, it has certainly helped in ensuring that our health infrastructure has not been overwhelmed so far.”

Easing of the lockdown

As the lockdown restrictions are eased, cases of COVID-19 could go up faster with more people coming in contact with one another.

“If you would have asked me two weeks back, I would have said the R would increase as the lockdown is eased but I am puzzled that the R has come down after May 3,” Sinha said. On May 3, 2020, the central government had eased some of the rules around the lockdown, allowing green zones to open up and permitting some activities in orange and red zones. “I have no idea why it [the R] has come down, but perhaps people are adhering to the distancing norms more strictly now,” Sinha said.

Will the R be lower in the future as the lockdown is further eased? “Probably not,” said Sinha. “We have not allowed the epidemic to take its natural course with containment measures,” because otherwise the number of cases and people dying would have skyrocketed, Sinha said, explaining that the pattern in most countries has been for the disease to peak and then decline. India is still away from the peak, but the rate of growth of the disease can be reduced with containment measures, he said.

“That also means that it would just take another spark to start the epidemic all over again because we still have a large number of susceptible people in our population,” Sinha added.

How Is The Reproduction Rate Of A Disease Calculated?

There are multiple ways to estimate R0 or R. One is by calculating it from the doubling time of the number of active cases. The other, used by Sinha for the R estimations in this story, is to use the estimated exponential growth rate of active cases, and then factor in the mean generation interval in the calculation. The mean generation interval is the average duration between an individual getting infected and the people that he/she passed on the disease to getting infected, Sinha explained.

For COVID-19, this time duration is estimated at 5.2 days based on research from Singapore. Statistical techniques are used to increase the accuracy of the R estimation.

The growth rate of the disease has to fit an exponential trend for the R to be accurately calculated. If there is too much fluctuation in the data, the accuracy of the R becomes lower. Sinha does not use data if the threshold of accuracy falls below 99%, he said. 

The R is dependent on the number of new cases every day, so better the testing and better the publicly available data, the higher the ability to calculate the R accurately, said Menon.

State-level COVID-19 effective reproduction rate

For the R to be accurate, Sinha uses the longest possible contiguous period to calculate the R and does not provide data if it is not 99% accurate. Because of this, the R of different states cannot be compared as it is for different time periods. The table below provides the R for some states. 

Estimated R Value For States
State Period of Estimation Estimated R
India March 4 - April 11 1.83
April 13-May 14 1.29
May 16 - May 25 1.23
Maharashtra April 13-April 26 1.49
April 23-May 15 1.34
May 4-May 25 1.27
Gujarat April 30-May 9 1.23
May 7-May 10 1.26
Tamil Nadu April 29-May 4 1.83
April 30-May 7 2.01
May 7-May 10 1.31
Delhi May 7-May 10 1.31
May 20-May 25 1.2
Punjab April 28-May 4 1.48
May 5-May 8 1.32
Rajasthan April 19-April 22 1.34
May 10-May 25 1.27
Madhya Pradesh April 16-May 1 1.23
May 10-May 23 1.23
Uttar Pradesh May 1-May 4 1.28
May 19-May24 1.33
West Bengal April 15-April 28 1.51
April 28-May 1 1.14
May 4-May 10 1.34
May 15-May 25 1.22
Andhra Pradesh April 6-May 1 1.27
Karnataka May 16-May 24 1.62

Source: Data shared by Sitabhra Sinha, Institute of Mathematical Sciences, Chennai
Note: 1. Because of fluctuations in data and accuracy for R below 99%, R estimations are not available for all states for all time periods. The author has tried to take the longest time period possible for these estimations. 2. The R for Tamil Nadu and Gujarat could not be calculated with the same degree of accuracy as other states for May because of fluctuations in the data.

R estimates based on testing

The R is calculated based on the active cases each day in the population as reported by the government.

As the number of cases detected depends on the testing regime, they may not be an accurate representation of the number of cases in the population. Many with the disease will be asymptomatic or have mild symptoms and hence not get tested, said Menon.

The difference in the R over time would still be an accurate way to measure the growth rate of the disease, provided that the testing criteria remains unchanged over time, said Sinha.

(Khaitan is a writer/editor with IndiaSpend.)

We welcome feedback. Please write to respond@indiaspend.org. We reserve the right to edit responses for language and grammar.



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