THE TECHNICAL DETAILS

# Is there really no community transmission of coronavirus in India? Let’s do some math

India is beginning to ramp up testing for Covid-19. The central government and several states have begun to procure lakhs of RT-PCR test kits to screen for the virus. Scores of government workers have fanned out across the country to track contacts of people who have tested positive. Moreover, India is considering novel testing protocols in order to increase the population that can be covered with the tests it already has.

However, India still lags behind several countries, with a testing rate of just over 200 per million persons, though some states are significantly higher. In this context, the health ministry’s recent announcement that there is no community transmission in India needs to be investigated further.

Despite occasional stories of individuals who have reported going to a hospital with Covid-19 but had no travel history, two official studies conducted have found no positive cases from the community. Consistent with guidelines from the World Health Organization (WHO), the Ministry of Health announced after the second of these studies—which found only 40 positive cases among people with no relevant travel history, out of 5,911 patients with severe acute respiratory illness—that Covid-19 had not spread through the community.

While this is comforting news, it is prone to misinterpretation. The problem these studies face is that, with low rates of testing, there is a high chance of not finding Covid-19 in the community even if it is there. By our statistical calculations, even if nearly 0.01% of the community were infected, there would be a greater than even chance that these two studies of non-travellers would yield no confirmed cases.

Let’s understand why.

## Consider a simple game

Suppose that we gave 7,300 people in Madhya Pradesh a special gold coin, told them to hide it in their pocket and go to their homes. If we let you pick 9,050 homes to visit, what is the chance that you would not find even one of those people? (We’ll give you a moment to work it out with paper and pencil.)

There are roughly 73 million people in Madhya Pradesh, meaning we gave gold coins to about 0.01% of the people in that state. For every home you visit, there is a 99.99% chance you would not find someone with a gold coin. The chance that you would not find even one of the gold coins after 9,050 visits is roughly 40%. (This is approximately 99.99%^9050, if we ignore that you do not visit any one home twice.) We did not pick these numbers at random: Madhya Pradesh had conducted 18,099 tests as of April 21, the vast majority in hospitals. Our game asks what would happen if as much as one half (9,050) were conducted in the community.

This is a problem across India. The following chart gives the total number of tests conducted across a range of states, the vast majority of which are conducted in hospitals. The chart also gives the chance that we would not find even a single Covid-19 case if the actual infection rate in the community was 0.01% and half the tests were conducted in the community. Notice that the probability of detection rises with the number of tests one performs.

Even if there were thousands of people infected in these states, there is a high probability that testing to date would find zero confirmed cases.

Is 0.01% prevalence really any different than no infection? YES. First, 0.01% prevalence in a country of 1.353 billion people would imply that there are 1.35 lakh people infected. That is more than all the confirmed Covid-19 cases in Brazil and Russia combined. It is over 50% more than the number of cases in China.

Second, almost all the epidemiological models that have been used to model Covid-19 in India begin by assuming fewer than 50 people were infected to start with. Having 1.35 lakh infected in the community would lead to half the country becoming infected rather quickly.

Third, it would be nearly impossible to trace and isolate so many individuals.

We do not intend these numbers to alarm people. We are not saying there are1,35,000 infected individuals in India. Rather, current levels of testing would more likely than not fail to detect any of those individuals, if they were infected.

## Understand the technical details

When the government stated that there is no community transmission, it was (correctly) using a technical term defined by the WHO. Under the WHO’s definition, there is no community transmission until there are a “large number of cases” that cannot be linked to travellers. However, the public, and many political leaders, do not know these technical details. They may incorrectly think that the Indian government is saying there is no community prevalence at all, which will hurt its efforts to lead responsible efforts towards controlling Covid-19.

Despite our statistical skepticism, we are not so pessimistic about India’s trajectory. The Indian Council of Medical Research (ICMR) is leading the way in getting tests and labs approved, importing tests, getting labs to work 24×7, and allowing labs to pool test samples to increase how many people can be tested with the limited tests in labs now.

It is also carefully weighing the costs and benefits of testing the community in hospitals versus the field. We need to support the government as it pushes for more testing. Only with a higher test rate will we know whether we have 135 infected persons or 1,35,000. The answer is critical to India’s battle against Covid-19.

Anup Malani is the Lee and Brena Freeman Professor at the University of Chicago Law School and Professor at the Pritzker School of Medicine.

David Kaiser is the Germeshausen Professor of the History of Science, Professor of Physics, and Associate Dean for Social and Ethical Responsibilities of Computing at the Massachusetts Institute of Technology.

Rupam Bhattacharyya is a doctoral student in the Department of Biostatistics at the University of Michigan.

Bhramar Mukherjee is the John D. Kalbfleisch Collegiate Professor of Biostatistics, Professor of Epidemiology, and Professor of Global Public Health in the School of Public Health at the University of Michigan, where she chairs the Department of Biostatistics.