Is India Winning the Covid War?

“We have gone quite ahead towards winning this war against Covid-19”, claimed Mr. Harsh Vardhan the health minister of India on 30th April.

Is he right? And does India’s death rate of 3.2% indeed support the minister as he claims?

The observed death rate or Case Fatality Rate is simple to understand and easy to calculate. It is determined by simply taking the number of reported Covid-19 deaths and dividing it by the number of confirmed Covid-19 cases.

Observed Death Rate (Case Fatality Rate) for Selected Countries. (Data Source: accessed on May 3, 2020)

Each of the curves in the above figure has a story to tell.

Look first at the topmost curve. Why were Italy’s death rates so high? One obvious reason is Italy’s aging population since the fatality rates are much higher for the elderly. Yet that is clearly not the only reason — quite possibly not even the main reason. After all Italy’s median age is 45.4 to Japan’s 47.3 years; about 23% of Italy’s population is over 65 to Japan’s 26%; yet Japan’s death rate was far, far lower than Italy’s.

As we all know Italy’s death rate is so high because the virus spread quickly overwhelming its healthcare system. There were simply too many patients for each to receive adequate care.

Paradoxically, Italy’s rising death rate is a good sign. It is happening because both new case and death counts are decreasing suggesting that the epidemic has peaked. However new cases are decreasing faster than deaths, since the dying patients were those admitted to hospital a few weeks ago.

Suspected and Confirmed Covid-19 Cases in Indonesia (Data Source: Straits Times, Apr 30, 2020)

Indonesia’s high death rates are due to the country’s inability to test all suspect cases. There are more than twice as many “patients under surveillance” awaiting testing as there are confirmed cases. Remember that the death rate calculation uses the number of confirmed cases in the denominator. Indonesia has disputed WHO’s method of counting the country’s fatality rate. They would like the rate to based on number of confirmed plus suspect cases. Their death rates would be about the same as India’s if this method is adopted.

India’s Death Rate Puzzle

India’s fairly low death rates have puzzled many commentators and experts.

Could the reason be under-reporting of Covid-19 deaths?

Under-reporting of Covid-19 deaths has been a major issue worldwide. A recent Financial Times article which compares baseline mortality at multiple locations during past years with that during the pandemic concludes that Covid-19 deaths have been under-reported by as much as 60% worldwide. Another study concludes that in Italy at least twice as many people died from the virus as reported. In Ecuador, where sufficient coffins could not be found to bury the dead the actual toll is believed to have been 15 times that reported.

The funeral of a person thought to have died of Covid-19 and who was buried in a cardboard coffin in Ecuador. (Photo Credit: New York Times, April 23, 2020)

Reporting standards have been inconsistent across the world and even across India. According to a news item published on 30th April in the most widely circulated in Bengali daily, in the Indian state of West Bengal, 33 deaths have been attributed to Covid-19 whereas deaths of 72 other Covid positive patients have been attributed to co-morbidities. There is some credible evidence that the West Bengal government has pressurized doctors to under-report the number of Covid-19 deaths. Some other states might have done the same.

Also, and especially during the nation-wide lockdown, all deaths may not have been registered. Even when the death was registered the cause of death could have been misdiagnosed for some Covid-19 patients. Still there is no firm evidence of massive under-reporting of Covid-19 deaths in India. In fact preliminary reports from certain locations suggest that death rates during the pandemic were lower than normal, possibly because of reduction of deaths from traffic accidents, air pollution and murder.

Indian doctors protest against the lack of adequate PPE and N95 masks. (Photo credit: Economic Times, Apr 6, 2020)

India was clearly unprepared for the coronavirus crisis in the early days. There were insufficient PPEs (Personal Protective Equipment) and test kits leading to infection of many healthcare staff and shutting down of several hospital wards. However, India’s indigenous production capacity and ingenuity has helped and production is being ramped up. Certainly hospitals and morgues have not been overflowing as in New York, Italy, Spain, Iran and Ecuador.

What then accounts for the low death rate?

Some ascribe it to India’s youthful demography. But that doesn’t seem to be the whole answer. After all India’s median age is 26.8 years to Ecuador’s 27.9 and Iran’s 32.0 years. Both Ecuador and Iran suffered greatly. Hot weather is probably not the answer either. Ecuador is situated on the equator and its climate is hot and humid too. Others ascribe India’s low death rate to the prevalence of early BCG vaccination. The jury is still out on that one.

In any case, India’s death rate does not suggest an out-of-control epidemic. In fact, going by this metric most the developed world has done worse than India.

The Wrong Puzzle

We might however be asking the wrong question.

Perhaps instead of “Why is India’s death rate so low?” we should be asking “Why is it so high?”.

Estimation of Unreported Cases in India

We have so far been talking about the observed death rate or Case Fatality Rate. However the confirmed cases make up a biased sample as we have seen in my previous blogs. People who are more at risk — either because they already show the disease symptoms, are close contacts of confirmed cases or frontline workers at hospitals — are more likely to be tested and therefore confirmed as Covid-19 cases. However there are plenty of people — many with mild or no symptoms — who do have the virus but are not tested and so not identified. The risk of death is therefore higher among confirmed cases.

The true death rate or Infected Death Rate is the number of deaths divided by the total number of cases including both confirmed and unconfirmed/unreported number of cases. This is likely to be much less than the 3.4% estimated by WHO on March 3. A widely cited (and much criticized) Santa Clara study implies that the true death rate is not much higher than that for ordinary flu i.e. ~0.1%. But most experts think it’s a good bit higher, somewhere in the range 0.5–1%.

Of course we do not know the true death rate in India, but if we assume some rate we can back calculate the number of unreported cases. The figure above illustrates the calculation. From the chart it seems likely that India has anywhere between 80,000 and 200,000 unreported cases.

There is also some circumstantial evidence supporting the possibility of a large volume of unreported cases.

Foreign Workers as Percentage of Singapore’s Confirmed Cases (Data Source: accessed on May 3, 2020)

Over 16,000 of approximately 300,000 foreign workers living in dormitories in Singapore are infected by the virus. These constitute ~ 90% of Singapore’s confirmed Covid-19 cases (16,422 out of 18,205). Most live in dormitories where cramped and unhygienic living conditions provided a perfect opportunity for the epidemic to rage like wildfire.

Dharavi Slum in Mumabi (Photo Credit: accessed on May 3, 2020)

It is unlikely that Indian city slums are much better in terms of hygiene and living space than worker dormitories in Singapore. In Dharavi, a large slum in the megacity of Mumbai, approximately 700,000 people crowd into a 2.1 sq Km area. Yet the total number of cases reported in the entire city of Mumbai is about 8,000 or half of that in Singapore’s dorms. It is quite likely that Singapore is finding these cases because it is looking while India is not. Singapore’s testing rate is 24,600 per million while India’s — though rising — is still only 758 per million.

Unreported cases do not in themselves constitute a problem. Part of the reason that foreign workers in Singapore slipped under the radar was that most of them showed mild or no symptoms and therefore passed temperature screening which is required at all worksites. The good part is that most of them — being healthy and young — do not require hospitalization and are unlikely to add to Singapore’s toll of death or critical cases. It may be hoped that most of India’s unreported cases will be mild as well.

Unreported cases only matter if they spread infection in the community. The major worry for India at this point is that a large number of undetected cases point to community wide transmission of the disease.

So is the Lockdown Working?

India, after testing the waters with a single day curfew, imposed a lockdown at 4 hours notice on Tuesday 24 Mar. The government has been criticised widely for the short notice and the “unplanned” nature of the lockdown. However, the short notice was probably actually part of the plan and intended to stop migrant workers from moving back to their villages, though we can’t be sure, since India’s decision making process seems more opaque than those of other democracies.

Sample Oxford Government Response Tracker (Source: accessed on May 3, 2020)

The lockdown was harsh. The stringency of government responses to the coronavirus crisis is tracked on an ongoing basis by an Oxford University study group. A rather self-congratulatory article by Amitabh Kant — CEO of Niti Ayog the Indian government think tank- and a colleague from the same organization, notes with evident approval that this response tracker gave India the maximum stringency score of 100 shortly after initiation of the lockdown.

However the lockdown must not be judged on the basis of its stringency, any more than an employee should be judged by the number of hours she spends at her desk. What matters is the effectiveness of the lockdown in halting transmission.

It is now time to talk about the other metric that matters during an epidemic.

Most of us have in recent weeks heard about R₀ (pronounced R nought). R₀, the basic reproduction number for a disease, is the average number of people an infected person will infect during his/her infectious period. In epidemiological jargon, it is the average number of secondary cases per primary case. This is generally reported as somewhere between 2 and 3 for Covid-19 as against about 1.2 for flu.

R₀ is really a mathematical abstraction like the frictionless pulleys and dimensionless masses of high school physics. During an epidemic the more important number to look at is Rₜ the effective reproduction number, the actual average number of secondary cases per primary case people being infected at calendar time t; for the policy maker and the common citizen it is important to know what Rₜ is when t stands for today. Rₜ depends on both the intrinsic contagiousness of the disease and the intervention measures in place.

In the not very distant future, all news media will probably routinely provide the Covid-19 Rₜ every day along with air quality indices and high and low temperature forecasts. In fact Hong Kong has been doing that for quite some time!

The coronavirus will die away if Rₜ continues to be less than 1 (as is the case for New Zealand for example) and grow if Rₜ continues to be greater than 1. If Rₜ is exactly 1 the disease will persist at a steady level with recoveries balancing new cases.

Of course any single statistic is bound to tell an incomplete story. Still Rₜ probably represents better than any other single number how a country (or state, district or town) is doing in the war against Covid-19.

Epidemiologists at Institute of Mathematical Sciences at Chennai estimate that Rₜ fell from 1.83 on 6 April to 1.55 on 11 April. It continued to fall to 1.36 on 21 April.

This is good news of course but with the reproduction number still significantly higher than 1 it is still too early to conclude that India is winning.

It is of course much higher at several hotspots. These are so far restricted mainly to large urban clusters. That suggests that India has been largely succeeded in its aim of containing the disease in a number of zones.

Success has come at a tremendous cost. The poor — especially migrant workers- have borne a disproportionate part of that cost. The collateral damage is impossible to assess with any degree of accuracy. But undoubtedly hundreds of thousands or possibly even millions suffered. Quite possibly dozens — or even hundreds — may have died as a result of the lockdown.

How many lives did the lockdown save?

This is an impossible question to answer with confidence since we can’t know how many would have died from the disease if the lockdown had not been implemented. Quick back of the envelope calculations that I reported in a previous blog suggest that there might have been 1.6 million cases by mid May. A more rigorous study by an University of Michigan study group reported that 2.2 million could have become infected by that date.

If the current fatality rate of ~3% continued to apply, that would have led to about 70,000 deaths. However it is likely that the death toll would have been considerably higher as the Indian healthcare system might have been overwhelmed well before that point was reached.

India is far from winning the Covid war but it hasn’t been lost yet either. India now approaches its Stalingrad, the turning point of the Covid war. It must now resolve a seemingly impossible dilemma. The lockdown continues to remain essential from the standpoint of public health and increasingly untenable from an economic point of view. It needs to find the way out.


Disclosure: I am the Director of Smart Consulting Solutions Pte Ltd, incorporated in Singapore and its subsidiary Radix Analytics Pvt Ltd, incorporated in India. I am also a Visiting Faculty Member at the Indian Institute of Management, Udaipur. However, the opinions expressed in this post are solely mine and not necessarily shared by any company or institution with which I am affiliated.

The following article published in the Lancet estimates an infected fatality rate of ~0.66% for Covid-19.

This recent Washington Post article based on data from New York antibody tests suggests an infected fatality rate between 0.5–0.8%.

I have used the following sources for estimates of the excess mortality due to Covid-19.

An excellent introduction to mathematics of Rₜ calculations is given in “The Effective Reproduction Number as a Prelude to Statistical Estimation of Time-Dependent Epidemic Trends” by Hiroshi Nishiura and Gerardo Chowell published in G. Chowell et al. (eds.), Mathematical and Statistical Estimation Approaches in Epidemiology, DOI 10.1007/978–90–481–2313–1 5, C Springer Science+Business Media B.V. 2009.

Statisticians can use the R package Ro ( which provides an array of sophisticated statistical methods to calculate Rₜ.

The following paper by Aguilar et al. suggests that Covid-19 may be even more infectious than currently believed. This is what he has to say.

The currently accepted estimates of the basic reproduction number (Ro) of the virus are inaccurate. It is unlikely that a pathogen can blanket the planet in three months with an Ro in the vicinity of 3, as reported in the literature. In this manuscript, we present a mathematical model taking into account asymptomatic carriers. Our results indicate that an initial value of the effective reproduction number could range from 5.5 to 25.4, with a point estimate of 15.4, assuming mean parameters.”

This paper is a pre-print that has not yet been peer-reviewed. If the paper is right in its conclusions then it would go a long way towards explaining how Covid-19 wreaked so much havoc around the world in just 3 months.

Covid-19: Part 1

Covid-19: Part 2

Covid-19: Part 3

I am, as always, grateful to my friend Dr. Ashish Kumar Dawn for many insightful comments and sharing some documents.

I thank my colleague Ms Seema Vaidya for drawing my attention to an article on the possible role of BCG vaccine in developing immunity to Covid-19.

Do please share the post if you think it may inform or interest others. I invite comments on the post. Please feel free to write to me at

I have spent over 30 years in academia and industry exploring how to use mathematical methods to solve real world problems