Covid19 in India — The Breaking Point
I wrote about the R0 effect nearly 10 days ago, on the 26th of March (a few days after the national lockdown was announced) — India then had 681 confirmed infections with 12 deaths.
Since then, the number of confirmed infections has exploded to 4298 with 118 deaths in just 10 additional days. This translates to a multiple of 6.3x for infections and 9.8x for deaths. The sheer number of confirmed deaths compared to the reported number of infections in such short duration has thrown up a number of interesting insights. For example:
a) Although the number of tests delivering a positive confirmation have been around 3–3.5% for India, have we indeed tested enough?
b) We expected that the number of new daily cases would have reduced over time, at least 10 days after the announcement of the lockdown. Why has this not happened?
c) With this rate of explosive growth, does India have the necessary medical infrastructure to take care of its citizens?
d) Which states would be under the most amount of pressure from this point onward?
This brings me to the first point of discussion.
1. Estimating under-reporting via Delay-Adjusted CFR
An easy way to estimate under-reporting that has been used in multiple reports has been to evaluate the total number of active cases via the total deaths that have occurred due to Covid19.
The model evaluates under-reporting based on the following
i) Dividing deaths-to-date by cases-to-date leads to a biased estimate of the case fatality ratio (CFR)
ii) Deaths today would mean that the infected person(s) had caught the infection at least 18 days prior to death. In this duration, the person would have likely infected a few more people.
iii) Using the distribution of the delay from hospitalization-to-death for cases that are fatal, we can estimate how many cases so far are expected to have known outcomes (i.e. death or recovery), and hence adjust the naive estimates of CFR (total deaths/total cases) to account for these delays
The fundamental reasons why this methodology is effective is because:
a) Nearly 20% of all Covid19 infections are asymptomatic. This means that many people continue to live their lives without displaying any symptoms like fever, cough etc and continue to infect an average of 2.4 more people.
b) It is easy to under-report the number of active cases, but extremely difficult to under-report deaths due to Covid19.
We can use the infections and death data for the states in India to evaluate the accurate CFR via the following:
The best estimates of CFR (post-adjustment) are in the 1%-1.5% range taken from a detailed study in China which is around 1.38% (95% CI: 1.23–1.53%). This means that if the adjusted CFR is around 8.5%, which is the case for India, then the actual under-reporting is 1.38%/8.5% = 16.2%.
This is how the situation looks like for India at the moment, with the reported cases:
However, if we now apply the adjusted CFR for the Indian states and determine under-reporting, this is what shows up:
Note how states like Maharashtra, Madhya Pradesh, Gujarat and Telangana now have a massive number of under-reported cases — this is primarily since the number of deaths in these states are extraordinarily high compared to the number of reported infections.
Maharashtra seems to skew this graph a lot, so lets look at it without MH:
Summary: With a little bit of math, we are able to estimate the number of unreported cases of Covid19 in India. It seems like we have ~26606 actual infections in the country — instead of the currently reported number of 4298 (as on 06th Apr 2020).
The Silver Lining: So far, we’ve all heard stories of the excellent contact-tracing conducted in India, opening up of Covid testing to private players and the aggressive approaches taken up by the government to tackle the situation both at the national level and at the state level. We can hope that the number stated above is an over-estimation.
The next part evaluates how well prepared India’s medical infrastructure is to tackle this crisis.
2. Healthcare Capacity — The Breaking Point
We’ve just seen that there are massive disparities between different states in terms of the number of Covid19 cases — both reported and potentially, the under-reported ones. There are some additional complications:
a) The medical infrastructure available in each of these states are also unevenly distributed.
b) Populations of the vulnerable, especially the 65+ population in each of these states, are also varied.
c) With an exponential rise in cases, we could expect many of these systems being stressed to potentially a breaking point.
To start, lets assess the number of hospital beds available in each of these states. A lot of this data is available in the public domain, multiple reports like this one by the National Health Profile 2018, carry decent information on the state-wise infrastructure available. I have made a few estimates to supplement this data with additional information on private hospitals and augmented capacities in current ones.
Here’s the number of beds available in India state-wise:
India has 0.07% beds/person — this translates to ~930,000 beds for the population of 1.33b or 0.7 beds per 1000 people (or 1 bed/1419 people). This compares poorly with international standards, especially in countries which have shown a high number of Covid19 cases.
For example, the United States has ~2.9 beds per 1000 people (this is roughly the same for the United Kingdom as well). In addition, Germany boasts of ~8.3 beds per 1000 people.
Why is this important? Even with superior numbers, we’re hearing reports of hospitals running short of beds in many places in the US, especially in New York, calling in hospital ships to supplement resources.
Even in India, the number of beds/person is not evenly distributed — the southern states of TN, Karnataka and Kerala do have above-normal capacity.
Let’s look at another stat: Beds/Population of 65+
This is important since the population that is at the most risk to this virus are the elderly.
Here we see a few states have slightly better capacity to tide over the crisis — like West Bengal, TN, Karnataka, Delhi etc.
Where are we going with this?
The virus has an exponential spread — the number of cases have been doubling every 4–5 days in India for the last few days. Assuming that hospitalizations also increase similarly (exponentially), we could be seeing a breaking point very soon in many states. Keep in mind that I’m only counting the “official” cases for now — the situation could be much worse if we counted all the cases.
The next graph estimates the breaking-point using the following:
a) Exponential spread of cases (similar to what we’re seeing right now)
b) Assuming that 25% of the beds can be utilized for these patients — others would continue to be utilized for regular patients.
c) Mapping the current number of official cases with the beds available at a state level (not even at a city level — which could be much more accurate, and unfortunately, much more worse)
d) Beds would be unoccupied once a patient recovers after ~20 days
So, in how many days would our medical capacities hit the “breaking point”?
Summary: We are soon reaching a breaking-point in terms of the number of active Covid-19 cases that we can effectively treat primarily due to the shortage in medical infrastructure. States like Maharashtra, AP, TG and Delhi would be in trouble within the next 3 weeks, unless things improve dramatically.
This is why “flattening-the-curve” is important. Even a large scale expansion in capacity, say 30%, would only give us only 3–4 additional days, primarily due to the exponential growth.
So that’s that — stay at home, eliminate contact, practice strong social distancing and protect the elderly. Staying at home won’t just save your life — it’ll save a lot more. It’s the least we can do.
