Are we heading to a catch-22 situation?

India's first COVID-19 case was detected on 30^th January 2020, then 2 more cases were reported by 3^rd February. There was no case reported from anywhere in the country during the month of February till 2nd March. There after, the COVID-19 infections started to slowly spread across the country. As on 14^th March, the total confirmed positive cases reached a figure of 107. This has further increased to 223 on 20th March, showing the number of confirmed cases doubled within less than 7 days. As per the latest data released by MoHFW at 8 AM on 20th April, the confirmed cases reached 18601.

FIRST PREDICTION

ICMR data on 21^st March shown that there are 315 confirmed cases, while the MoHFW release shown this as 283, this inconsistency of figures between the two entities of Union Government continues even today. However, I have taken MoHFW figures here for my analysis. The data on 21st March showed that the confirmed cases were doubling in every 5 days and we are on an exponential curve.

In the above context, I had done a regression analysis on 22^nd March based on a short series of data spanning from 1^st March to 21^st March, to examine that whether India is on an exponential trajectory or not. Further I had projected this data, based on the prevailing growth trajectory to see where we will reach in future, IF THE PREVAILING TREND CONTINUOUS! I published this analysis on twitter on 22^nd March as a long thread.

The above prediction indicated that India may hit 2167 cases by 31^st March and IF THE SAME GROWTH TRAJECTORY CONTINUES we may have 6 lakh infections by 1^st May. It is important to remember that these predictions were done based on a small set of data of 21 days and the trend available before the lock down. Then the lock down was announced from 24^th March for 21 days, so the entire dynamics of spreading the COVID-19 changed from that day onwards.

Asianet News, a prominent Malayalam TV news channel, approached me for an interview after seeing this twitter thread. They done an interview with me on 27^th March, three days after the lock down. To their specific question where we will be after the lock down (the first phase of lock down), my answer was as per the earlier projection trajectory there would be 36,000 confirmed cases as of 15^th April.

I made it clear then that the above numbers should be considered WITH A RIDER that at least another 21 days data is essential to understand the effect of the lock down on the growth trajectory, because the trajectory will definitely come down due to the iron type grip on the social mixing due to the lock down.

BAFFLING PREDICTION

Meantime, BJP’s social media head Amit Malviya tweeted on 10^th April that, if there was no lock down, India would have crossed 8.2 lakhs confirmed cases by 15^th April, citing a purported ICMR study quoting ABP News. When the journalists quizzed Luv Agarwal, Joint Secretary, MoHFW about this projection during the evening press conference on the same day, he denied that any such study was conducted by the ICMR and his Ministry was not aware of the same.

But Agarwal made a somersault on the very next day and endorsed the numbers tweeted by Amit Malviya. “If we hadn’t taken any action, the cumulative growth rate may have been 41% growth,” he said. “By April 15, we would have reported 8.2 lakh cases.” Agarwal then furnished a chart bearing these projections to the journalists, which is shown below. However, he clarified that this was not a projection done by the ICMR. The health ministry, he said, had done its own “statistical growth rate-based analysis”, a curious case of a task done by the officials of the Ministry, who has no experience in such esoteric subjects. It should be appreciated that it was so generous from the part of Agarwal to spare expert epidemiologists of ICMR from the responsibility of this cryptic study!

The above graph circulated by Agrawal, without any further supporting details, shown that the estimated growth rate of the virus was 28.9% in the pre-lock down, this is contrary to the factual growth rate observed. Based on the above rate of growth, a figure of 1.2 lakh infections projected up to 15th April, which is way beyond the trend prevailing that time, in my projection I got a figure of 36,000 cases instead. 

Of course, I did not use the complex mathematical models, which are being used by epidemiologists. Also I am not in possession of the data required as input into these complex models. But the statistical projection done by me was based on a fairly good series of 21 days, which will give fair idea where we are heading. More baffling fact is that there is no information on the rationale behind the 41% growth rate that yielded the contentious 8.20 lakh figure. Both the projected figures peddled by the Ministry is highly variance with the prevailing trend then and totally unreliable!

CREDIBILITY AT STAKE

The epidemiologists generally use SIR model to project the trajectory of the pandemic/epidemic. For the inquisitive readers to understand what is SIR Model, this link from Mathematical Association of America (MAA) is a good primer. 

When epidemiologists doing the projections, they heavily rely on a number called R naught (R0), basic reproduction number but the projection shared by Agarwal did not show that number instead it is only shows Compound Growth Rate (CGR)! Even after repeated queries from the media, MoHFW did not disclose the study report or not ready to disclose what was the reproduction number and transmission probabilities considered in the purported study.  

There is no doubt that the lock down had a substantial effect on the spread of the virus. As we had 12,380 confirmed cases detected as on 31st March, against my projection of 36,025 cases can be attributed to lock down, of course, with a rider. The rider is the detected positive case numbers of 12,380 on 31st March did not actually represent the existing cases on that day because India is not testing enough to detect all prevailing infections. Whether this lock down will help India to flatten the curve in the longer run or it will only postpone the inevitable for a couple of more weeks is a perplexing riddle. I will discuss this later.

The pertinent question is why the propaganda machinery of the BJP tried to shove into the throats of the public an unrealistically colossal projection? Is this an attempt to cover up the the sad commentary that when the Government had given the affluent NRIs four days’ lead time and did not spoil their travel plans, but gave the poor and disenfranchised people hardly four hours. May be it was their plight to be the sacrificial lambs whether it is demonetisation or a national lock down. Anyway, this propaganda subsequently endorsed by the Government, totally defying the logic and mathematics, will definitely put our scientists at ICMR in a tight spot before their peers in the international scientific community.

PRESENT TREND

India reached 2301 confirmed cases as on 2nd April. If this data is compared with my projection, it can be seen that it took 2 additional days more to reach 2000 plus infections. This is an initial indication that the lock down instead of flattening the curve significantly, only pushing the inevitable to a near future. If this is the case, how much infections will be there at the end of the present lock down 2.0?

To grapple whether or how the trend shifted, the graph was updated with the data available from 1st March to 19th April. As 50 datasets are at disposal, a fair set of data is available to establish the trend from the earlier 21 numbers. The corresponding analysis shown that the confirmed cases shifted from the trajectory of the exponential growth instead follows a third degree polynomial, FOR THE TIME BEING. This polynomial curve is a relatively flatter than the steep exponential curve. 

The blue shaded area represents the growth trajectory of the confirmed cases detected till 19th April, while the blue dotted line represents the third order polynomial projection, which is the best-fit curve with an R² value of 0.9991, representing a high accuracy projection, shows where we are heading.

The above graph shows that we will cross the 35,000 confirmed cases by this month end. What is it means? As the curve still grows without showing any significant flattening and India only postpones the inevitable to further two weeks more with a 40 days lock down exercise!

DOUBLING SCENARIOS

To further correlate the above trend, another exercise was done to examine at what interval the infection numbers are doubling. Hence the present graph of confirmed cases was plotted between various doubling scenarios, to check out where was India during the Prime Minister’s first national address on 19th March and lock down announcement on 23rd March. As on 22nd March, the infection curve doubled before reaching 6-days and inching closer to the 5-days doubling curve. 

To inquire where India heads with the present rate of confirmed cases, the entire series of 50 datasets up to 19th April, a graph is plotted as shown above and the confirmed cases curve perfectly fit between 5-days and 6- days doubling trend-lines.

As the present series of confirmed cases fits between doubling 5-days and 6-days and is closer to doubling in 6 days, analysis was done to see the future. If the current growth follows the trend of doubling in 6-days, India would reach 54784 cases as of 28^th April and if India is able to flatten the growth further and fall into the trend of doubling in 7-days, the confirmed cases would reach 54784 cases on 7^th May. 

Of course, these numbers are with a caveat that these are the possible scenarios assuming that if we would not reach the inflection point of the curve (The inflection point is the point at which it changes from “growing ever more rapidly” to “growing ever less rapidly,” and is therefore the point at which its growth rate is at its maximum) during the above mentioned period, which now seems the most plausible scenario.

PARADOXICAL CATCH-22

What is this means? The lock down 2.0 is also not helping India to reach the inflection point, but only pushing the peaking to a further distance. This really creates a daunting challenge for the policy makers to decide what new strategy to be adopted to contain the spread of virus! It is an undeniable fact that India miserably failed in its initial response to totally seal the import of the infected cases to India, thanks to the sieve like porous thermal screening followed by a rigid and limited testing strategy advocated by the ICMR. These issues were deliberated in detail in my article on the latest issue of FRONTLINE.

If the trend of emerging data is considered, that will lead to a logical conclusion with high confidence level that India is nowhere near the inflection point, as far as COVID-19 is concerned. The inflection point will normally attain when the community attains the herd immunity, and consequently shows a decrease in the growth of infections. Instead, the hard evidence pouring at present is that COVID-19 remains asymptomatic for quite longer, as long as 28 days in many cases. This phenomenon along with the present trend of getting increased percentage of positive cases as the testing expands are ominous signs. In my opinion, our policy makers are now in a catch-22 situation, as any vaccine or an effective anti-viral drug for COVID-19 are far away from the end of lock down 2.0.