Last week (25 March), we had presented a heuristic predictive model for Covid-19, which has allowed us to provide a detailed state-wise projection map for India.
Our prediction horizon was limited to four weeks; one week of meticulously tracked data by others has poured in since we released our model. Here, we will critique our model and predictions.
Like many a modeller, who has gazed into his mathematical crystal ball, we have mixed news to deliver.
So, first the good news – by and large the lockdown seems to have helped ‘flatten-the curve’. Global trends had suggested an increment between 5x-10x for the first week; however, an in-depth analysis of the divergence between our predictions and recorded infections suggests that the lower-bound multiplicative factor is closer to 2-3.
In simpler terms, the growth rate seems to have noticeably reduced in India last week (between 24 March-31 March) in contrast to the predicted scenario.
However, we must be rather restrained in interpreting these early trends. As per our understanding, the nation-wide lockdown helped us flatten the curve by an extra week; this time must be utilised in resource-planning and execution of disaster management protocols.
Another good news comes from two of the Himalayan states – Ladakh and Himachal, which seem to have successfully contained the contagion.
A study of measures taken by these states is likely to be very informative and gainful study.
When we had proposed the model, we had strongly hoped that we will over-predict for all states. Contrary to our wishes, our predictions are closer to reality for states such as Andaman & Nicobar, Bihar, Goa, Madhya Pradesh and Tamilnadu.
Readers, who wish to compare data should remember that our ‘infected persons’ count must be divided by the appropriate ‘inflation parameter’ (n) value to get the correct “reported infections” count.
This is necessary as our model assumes that due to asymptomatics and low testing, the reported infection count is lower than the actual number of infected patients.
This match between our predictions and reported infections suggests that some of the states have started following global trends despite the current lockdown scenario.
However, these are still early trends so, we still have hope that our model will over-predict the evolving scenario.
Another key prediction of our model was that different states will see different parts of the pandemic wave at any given time – data reveals that this is clearly unfurling.
However, the truly worrying trend in the data is the divergence between the fatality rates (ratio of reported deaths and reported infections) amongst different states.
West Bengal, Madhya Pradesh and Gujrat have reported fatality rates of 15 per cent, 6 per cent and 8 per cent respectively. We know from South Korea’s data that when large-scale testing is performed, fatality rates of approximately 1 per cent are seen.
Even in India, states such as Kerala, which have aggressively performed large-scale testing seem to have fatality rates close to South Korea’s.
We feel that states which are registering greater than 4 per cent fatality rate should invest in more testing.
The exercise of matching our predictions with the available data of the last one week has been a very enriching exercise, allowing us to fine-tune our model.
As more data has arrived, we can see that in general, testing has improved.
Interestingly, reported fatalities (ratio of reported deaths to reported infections) continues to hover in the range of 2 per cent to 3 per cent, which is not very far from the Korean benchmark of approximately 1 death per 100 infections.
Despite this improvement, the fatality rate still shows a strong state-wise heterogeneity in its distribution. This implies that ‘n’ or the inflation factor is now a strong function of the state.
The current top 3 Covid-19 hit states are Maharashtra, Kerala and Gujrat. Refer to tables 1 and 2 for further details.
Finally, with the availability of district-wise data, we have now expanded our initial prediction footprint to include districts.
Here, we provide a three-week prediction for top ten different districts (Table 3).
Large population density clusters like Hyderabad, Gurugram, Pune and Bangalore are predicted to be some of most severely hit regions.
Moreover, we can see that lockdown has led to the fragmentation of Covid-19 hit regions into various hot-spots.
The district-level information is expected to be critical to disaster management planning in the coming days.
Once again, we have made our calculator available to the general public and it is available at https://mesoscalelab.github.io/covid19/index.html .
For our future outlook, we can see that along with current hot-spots such as Maharashtra, Kerala and Gujarat, we have emerging hot-spots such as West Bengal and Madhya Pradesh.
The next few weeks are critical to India’s battle against Covid-19, and like the rest of the nation, we also await with bated breath to observe the course of this disease.
Finally, we would like to repeat something we have clarified before: we hope our model over-predicts and we are very happy to be proven wrong as far as estimated infections are concerned.
Disclaimer: The article expresses the personal opinion of the authors.
Acknowledgement: The authors would like to acknowledge the contribution of Dr. Soumyadeep Bhattacharya in developing the website and the models. The authors would also like to acknowledge the help of Mr. Shreyas Kallapur for help with model validation.
Shaurya Kaushal is a PhD student at Jawaharlal Nehru Centre for Advanced Scientific Research. Prof. Santosh Ansumali an Associate Professor at Jawaharlal Nehru Centre for Advanced Scientific Research. He is currently also the CTO of Sankhya Sutra Labs. He tweets at @SAnsumali. Dr. Aloke Kumar is currently an Assistant Professor at the Indian Institute of Science, Bangalore. He tweets at @aalokelab
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