Coronavirus Spread in India- With and without the Tablighi Jamaat incident: A quantitative estimation

We are now witnessing the spread of COVID-19 pandemic arising from the novel Coronavirus. Several countries are battling this disease adopting a multi-pronged approach. The primary focus in all the countries has been to flatten the curve so that their medical infrastructure can handle the number of infected people. Discovery of a vaccine against this virus, newer and faster ways of detecting this virus, and curbing the spread of this infection are being taken up in war footing manner in our country too. In this direction, the government of India have been taking several diverse yet focussed measures and declaring a countrywide lockdown for duration of 14 hours Janata curfew on March 22, 2020 by when 396 cases were detected positive for the novel coronavirus in India.  This was followed by a countrywide lock-down from 24/03/2020 initially announced till 14/04/2020. Furthermore, the government has extended this lock-down till 03/05/2020 with a review on 20/04/2020. This has been a very bold, well-planned and strategic step taken by our government with the sole aim of containing the spread of COVID-19 despite the possible deleterious effect of the lock-down on our economy.

Unfortunately, there have been few unprecedented activities that have severely affected the social distancing pattern anticipated during this lock-down period. The congregation of thousands of people at Markaz Nizamuddin Mosque in Delhi during March 13-15, 2020 followed by the attendees’, hereinafter referred to as the Jamaats, movement and clandestine activities have proved to be detrimental in containing the spread of this infection. This has been a major source of a disruptor in the social distancing pattern during the first phase of lock-down in our country. It must be noted that the news about Jamaats and they showing positive for the infection started emerging not before 01/04/2020.    

In this work our aim is to quantify the effect of jamaats in disrupting the social distancing pattern. We study the change in social contact structures throughout the timeline of the lock-down 1.0 (first phase of lock-down from 23^rd March to 14^th April).

Mathematics and the algorithm used

We used a modified version SIR (Susceptible-Infected-Recovered) epidemic model. Modification to this model was brought in by coupling it with a machine learning algorithm that estimates the value of the parameters through the previous data of the country and thereby not merely assuming the parameters a priori. This epidemic model predicts the spread of the coronavirus infection.

Without getting into the technicalities, it would suffice to state that the parameter of significance here is β. This parameter directly gives an estimation of the social contact structure of this pandemic. Naturally, the social contact structure is specific to the specific country, and so is β. The parameter obviously changes with the social distancing pattern and hence is expected to be different during and before the lock-down. Through this parameter, we quantify any disruptions in social distancing pattern, like the Tablighi jamaat incident.

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Using the above-mentioned method, besides taking cognizance of reality, we simulate a hypothetical situation by assuming that the jamaat incident did not happen at all. In the following paragraphs, we depict the results and the inferences drawn thereof. Please note that the congregation had happened in the middle of March and that the incubation period of this virus, that is the number of days between contracting the virus and showing symptoms, is around 6 days. But as mentioned above it is only after 1st April 2020 that news about the Jamaats started emerging and they were traced and tested causing a sudden spike in the number of infected cases in our country. This clearly shows that the Jamaats did not come forth for getting tested in the first week of the lock-down 1.0 lest the number would have spiked early on, between March 23 and 30. Hence in our analysis, which is aimed at quantifying the impact of the Jamaats, it is only the period from 01/04/2020 till 14/04/2020 that is of significance and hence we focus only on this period.

Scenario 1: Assuming No Tablighi Jamaat incident

Figure 1a shows the predictions of our model where the jamaat incident is taken into account.  The grey dots in the figure are the actual data (taken from the health ministry website) and the blue line is the outcome of our modelling. The same is magnified with an appropriate scale in the Y-axis in Figure 1b. The orange line in Figure 1a  is the projection of cases in the absence of any lock-down.

From the magnified figure (1b) it is clear that the coronavirus positive numbers predicted by our model vary significantly from the actual data. In fact, they are much lower than the actual data. This is because the parameter beta is obtained from the data between March 23 and 30. The actual data is indeed more because of the Jamaat incident. Actual data reveals that there are around 11,500 cases as of 14/04/2020 whereas our model predicts it to be around 7000 (without the Jamaat incident). Herein we show that around 40% of cases have been contributed directly by the Jamaat incident.

In a pandemic where one infected person has the potential to infect hundreds of people, a difference of 4500 cases will have a huge outcome over the results that hold for India.

The orange trend line in the above figure is the prediction of number of cases in the absence of both the Jamaat incident and lock-down. We would have touched an appalling figure of 1 lakh cases by 14/04/2020, a number which would have bled our medical infrastructure making some irreparable losses to the country.

Scenario 2: Reality: Taking the Tablighi Jamaat incident into account

Now we present the results of our predictions for the real situation by taking the Jamaat incident into account in figures 2a and 2b. These results are to demonstrate both the robustness of our model as well as to analyse the effect of the country-wide lock-down announced by our government as a measure of social distancing and thereby contain the spread of the disease. Like before, Figure 2b is the magnification of a portion of Figure 2a. The orange trend line in 2a indicates that in the absence of lockdown and given the Jamaat impact, the number of cases in our country would have been nearly 3,40,000 by April 14, 2020.

Surely this is very different from the actual number of 11,500 cases which is squarely attributable to the country-wide lock-down. It must be noted that this number of 3.4 lakhs cases is less than half of 8.2 lakh coronavirus cases predicted by ICMR. This difference is possibly arising due to the difference in the underlying models. The numbers have been quite different from our own predictions when we had employed a different model.  Figure 2b clearly shows that the model developed by us and used for the prediction is indeed robust as the predictions have an excellent agreement with the actual data. So, even if the lockdown didn’t completely halt the COVID 19 cases in India, it saved the health care system in India from breaking.

Though the number of cases today, owing to the Tablighi Jamaat incident, is high, lockdown still was effective in saving India from a community transfer.

Disruption in the social contact structure through the timeline

Finally, we would like to present the variation in the parameter beta for India. This reflects the change in the social contact patterns. Beta values presented here are learnt from a week-long duration of data. The lower value of beta directly corresponds to a lower number of positively infected cases and vice versa. We see that the beta value spiked up to 0.3031 in the first week of April, owing to the Jamaat incident. Subsequently, owing to the restricted social contacting pattern through lock-down the value of beta then dropped to 0.2526. This trend once again reinforces the deleterious impact of the Jamaat incident.

Summary

We summarise the quantification of the Jamaat incident in the matrix above where the numbers indicate the number of positive cases as for 14/04/2020.

Authors: Jay Naresh Dhanwant and V. Ramanathan, Department of Chemistry, IIT (BHU), Varanasi