Coronavirus can take over India in 30 days

Photo by Mika Baumeister on Unsplash

On the night of March 24th, millions of Indians sat in front of their television to see Prime Minister Narendra Modi address the nation to announce a 21 day long, nation-wide lockdown. In an unprecedented move to contain the spread of the novel Coronavirus, residents of India are to stay in their homes and practice social distancing.

Once a dynamic and bustling country of 1.3 billion, India has quickly become silent.

The lockdown, albeit ambitious, is necessary after the sheer growth of the virus. In just 10 days after March 14th, the number of confirmed cases in India has increased by about 570%. The virus has taken the lives of 29 people with a mortality rate of ~2.5%. India must use this narrow window of opportunity to contain the virus and prevent further inhibition of national activity. With the correct measures in place to minimize human interaction and increase healthcare capacity, we may come out bruised, but we will emerge intact.

In this post, I want to explore how India’s healthcare system will react to a crisis like this, and what India’s curve would look like.

You may have heard the term “flatten the curve” being thrown around a lot. This “curve” refers to the growth of COVID-19 over time; it follows a trend called “normal distribution”, more commonly known as a “bell curve”.

At a given time, there will be a threshold for what a country’s healthcare system can handle.

This point exists below the peak of the number infected, meaning that the country’s healthcare system will not be able to treat and care for all patients, leading to mortalities.

Theoretical curve from start to end

By flattening the curve, the distribution of cases is wider, therefore fewer individuals are infected at a given time. If the curve can be flattened below the threshold, the healthcare system will be able to handle the crisis throughout its duration.

For now, I want to look at the left side of the curve: the growth until the peak.

Here’s some information: according to India’s 2019 National Health Profile, there are 713,986 public hospital beds. The amount of beds that are being used at a given time is very high, about 80%, before the pandemic. That means that the available number of hospital beds at any time is going to be 142,797 exclusively for the virus. I’m going to set this number as “the healthcare capacity threshold”. Furthermore, I’m going to be using an updated compound daily growth rate using the data from March 1st to March 29th.

Formula for Compounded Daily Growth Rate (CDGR)
CDGR from March 1st to March 29th

This means that the number of people infected grows by about 22.2% every day. The virus lasts between 16–28 days including incubation and the symptomatic period. To estimate the number infected, let’s take the average, 22 days. With this, we can approximate the number who still have the virus at a given time by taking a predicted exponential growth and subtracting the number of people who recovered, which is the number of people who contracted the virus 22 days earlier. The Center for Disease Control highlighted that in the United States, 19% of Coronavirus carriers were hospitalized, so we will only take 19% of the number infected at a given time to find out the number of people in India who need to be hospitalized because of Coronavirus. Let’s use this information to find out how long it will take to reach the aforementioned threshold from the date of writing this, March 29th.

Here’s the equation I used to estimate the number infected at a given time from March 29th:

We can substitute the threshold, 142,797, for I(t) to find when we will overload the available healthcare capacity.

Graphical interpretation of I(t)

The data from March shows that on May 1st, assuming nothing is done to prevent the growth of the Coronavirus, the number infected will be too high for hospitals to handle. The beds will be taken, lengthy queues will build up, patients will sit on floors in the corridor, and those who can’t receive the care they need will die. Even during the time of the national lockdown, the virus has not slowed down significantly enough. The virus continues to grow by 14% compounded daily. This only delays the crossing of the threshold to mid-May.

With such a limited capacity, we are unlikely to be able to prevent the crossing of the threshold. However, proactive changes that can increase the healthcare capacity accompanied by acts that will flatten the curve can minimize and potentially even reduce the peak number of patients to below 142797, and therefore deliver sufficient care to patients. Over the 21 day lockdown implemented by PM Modi, exponential growth is likely to continue, but at a lower rate. The spread of the disease is directly caused by social proximity and interaction, and since Indians are minimizing their social interaction, they’re also minimizing the spread of Coronavirus.

With the lockdown in place, we will delay the growth of the Coronavirus, and we won’t reach the threshold until 19th May. But delaying the growth is just a part of a much bigger problem. Even if India was able to adapt to the situation and prevent deaths caused by a lack of care, there is still a 2.5% mortality rate, even with the spare capacity of the healthcare system. For a country as large as India, this absolutely cannot be ignored. With that number, about tens of millions will die, regardless of the availability of hospital beds. Preparing hospitals for a large inflow of patients is important, but the stakes are far too high to be overly focused on flattening the curve. Leaders and those at the forefront of the pandemic must work together to develop proper preventative measures and potential cures because a mortality rate this high will be catastrophic in the long-run.

In my next post, I will discuss the mortality rate and how India is going to deal with it.


Student in Delhi NCR. Using math to better understand the events of the large blue marble we stand on.

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