Jay Naresh Dhanwant and V. Ramanathan
This is a refutation of the article titled, “Data show India’s coronavirus lockdown may not be working” written by RupaSubramanya which appeared on April 14, 2020, in the Quartz magazine (https://qz.com/india/1837337/data-show-indias-coronavirus-lockdown-may-not-be-working/). We had earlier approached the Quartz by email asking whether they will be interested to know the rebuttal to this article. With no response, we approached them through Twitter on April 18, 2020, which too did not avail any response from them. Having waited for more than a week we hereby present our refutation in this platform.
The article mainly decries the country-wide lockdown imposed in India from March 22, 2020, till April 14, 2020 (later lockdown extended to May 03, 2020). The article may be sectioned in two, the first dealing with opinions on economic losses that the country is facing and will face due to this lockdown and the second section deals with data on COVID-19 cases in India. In this refutation presented here, we mainly focus on the second section.
This article buttresses on another article that appeared in Scroll which had raised several objections on the ICMR figure of 8.2 lakh number of corona cases. Just for a quick recap, on Aril 11, 2020 ICMR in one of its press briefings announced that had there not been any lockdown India would have witnessed around 8.2 lakh corona cases by April 15, 2020. There have been several objections, questions and opinions on this figure of 8.2 lakh. Several questions have been raised on the underlying rationale for this figure.
Be that as it may, it is interesting to note that though the article’s title begins with the word ‘data’ but it is entirely bereft of it. The article merely reproduces the ICMR’s graph and another from the Worldometerwebsite which is a database that updates the total number of cases on a daily basis. Amidst all the aspersions, there is indeed an element of comic relief for those with minimum numeracy. We request the attention of the readers to the caption of the figure. For a quick reference, the ‘data’ of the article is reproduced below:
Before explicitly revealing the comic portion, a small lesson in basic logarithm is in place. In math, we write the equation a^b=c also as log_ac=b. In this, the term ‘a’ is called the base. If the base is 10, it is referred to as the base 10 logarithm or simply log. If the base is the irrational number ‘e’; approximately equal to 2.71828, then the logarithm is referred to as natural logarithm. Whereas the Worldometer site reports the data in base 10 logarithm the same when ‘copy and pasted’ in the article becomes mysteriously “natural logarithm.”
Now the fun part comes. The author has titled the figure (erroneously) as “Natural logarithm” and the sub-title says, “..infections are growing at a constant proportional rate” (emphasis added). Furthermore while describing the text, the author repeats the same thing, “……and if the curve looks like a straight line, then infections are growing at a constant proportional rate.”(emphasis added). Sheer lack of basic numeracy is in display here as the fundamental difference between exponential growth and linear growth is thoroughly mixed up! We sincerely sympathise with the readers of the article who may believe the author’s expert opinions on the economic impact of lockdown appearing in the first section.
Furthermore, the article has yet another absurd statement and this time from basic calculus. The author writes, “If the lockdown had any effect, you would expect the slope of this line to flatten or bend toward the horizontal axis.”(emphasis added). The slope is obtained by taking the first derivative which is the measure of an extent to which a quantity (in this case the number of COVID-19 cases) changes with another quantity (in this case this other quantity is time). If the number of COVID-19 cases is growing exponentially, its derivative will also be an exponential. The author seems to be unaware of this fundamental truth! Further down, the article is merely verbiage, naysaying the Government of India’s decision of lockdown and highly opinionated. The article says,
The article harps on the usual question on whether the number of tests have been adequate or not and asks whether a small state like Goa needs a complete lockdown. The author seems to have forgotten that even India once had only 2 COVID-19 cases and we still see over 28 thousand cases today. The problem lies in understanding the nature of pandemic altogether. But we can’t expect this from an author who sees constant proportional growth in exponential growth! The numbers today is far less than the total undetected infections, so by all means, the lockdown has been extremely necessary.
Let us now look at the actual data and see the result of mathematically modelling the reality using a well-known epidemiological model called Susceptible-Infected-Recovered (SIR). In simpler terms, this model involves three differential equations and associated parameters. In our approach of modelling, we use machine learning methods to optimise these parameters and predict the course of the COVID-19 spread.
The following figure demonstrates the robustness of the model that we have been developing. In this figure, the blue trend line is our prediction and the small grey circles are the real data(taken from https://www.mohfw.gov.in/ ). The close agreement between our prediction and the real data is highly encouraging. As said before, in this model there are few parameters and one of them is beta which signifies the of a social contact structure in domain where this model is applied. So the following prediction is obtained by taking the data from the lockdown period, ie., from March 24 till April 14, 2020.
Figure 1: Comparison of prediction for the lockdown condition using the SIR model and real data
In India, the lockdown started from March 24. By looking at the data prior to the lockdown period we get a different value for the beta (parameter for social contact structure) and the blue line in the following figure is the prediction for the number of COVID-19 cases in the absence of any lockdown. Our prediction (considering the lockdown) and real data are repeated in this figure for offering a direct comparison. We must highlight here that this is a very conservative estimate of the figure for the COVID-19 cases in the absence of lockdown. From this figure we see that had there been no lockdown, there would have been around 3.4 lakh COVID-19 cases as on 14/04/2020.
Figure 2: Comparison of prediction for the lockdown Vs no lockdown condition using the SIR model and real data.
This number is quite different from the one that we had previously reported (https://epaper.organiser.org/index.php?edition=Mpage&date=2020-04-11&page=20
) as the underlying model was different compared to what we present here wherein we used had regression-based model and in the following figure the updated figures using this regression model is presented for the sake of comparison:
Figure 3: Comparison of prediction for the lockdown Vs no lockdown condition using a Regression model.
Now we know that in reality, we had around 11,000 COVID-19 cases as on April 14, 2020. And without the lockdown, the SIR model predicts this number to be around 3.5 lakhs and the regression model predicts it to be above 6 lakhs of COVID-19 cases.
In conclusion, we wish to reiterate that the lockdown 1.0 has been effective in checking the COVID-19 spread in India despite the fact that we had a disruption in the social contact structure in the first week of April by members who attended the Markaz congregation that happened in New Delhi in the middle of March. Flaws in the article from the Quartz magazine have been highlighted and we have shown through our mathematical model that data indeed shows that lockdown has been a success. While the lockdown has not stopped the COVID-19 spread by 100%, it has indeed solicited wild imaginations that are busy fabricating fables of failure.
(Jay NareshDhanwant and V. Ramanathan, Department of Chemistry, IIT(BHU) Varanasi)