India crossing 1 Lakh leads to Fresh Prediction

India crossing 1 Lakh leads to Fresh Prediction

Dr Himanshu Shekhar

Introduction: As per prediction done on the basis of data of confirmed cases from 15 March 2020 to 30 April 2020, and assuming an exponential rise in daily cases, India was supposed to reach 1 lakh total confirmed cases on 17.05.2020. The prediction on 30.04.2020, about India is reproduced from earlier post of the blog. The current article takes into account the progress in total number of daily confirmed cases from 15.05.2020 to 19.05.2020, when India crossed the 1 lakh number of total confirmed cases.

Current Status: When India failed to achieve on 17.05.2020, the predicted value of 1 lakh for the total number of confirmed cases, as per prediction, and daily addition of confirmed cases, were of the order of 4000 till 16.05.2020, it was presumed that India is moving towards controlling the pandemic. Then attempts were made to think about turnaround in the Pandemic and analysis was diverted towards such calculations. It is also presumed that with this rate India will reach 1 lakh total confirmed cases by 21.05.2020. However, from 17.05.2020, sudden jump in number of confirmed cases, were observed and India added more than 5000 confirmed cases daily to reach 1 lakh mark on 19.05.2020, itself. So, the prediction was off by only 2 days in predicting the total number of confirmed cases to reach 1 Lakh. Instead of 17.05.2020, it is achieved on 19.05.2020.

Analysis of Data: The comparison of prediction and actual data reveals that rate of rise for total number of confirmed cases has been slower and numerical values of actual cumulative number of confirmed cases, at any point of time is also less than prediction. For the last 6 days, data is shown in histogram. It reveals that both prediction and actuals are rising, but actual numbers are lower all the time.

The data for difference between actual and predicted number of total confirmed cases, also reveal that the difference is also rising with time and probably, the rate of rise is slower in India, than predicted by extrapolation from 45 days data (15 March to 30 April 2020).

This analysis revealed that the number of cases in India is still moving but a slower pace than predicted, based on certain assumptions on 30.04.2020.

Fresh Prediction: In fact, one of the avid readers of the blog, and my friend Shri Suman Kumar, on 10.05.2020 suggested to review the model and prediction in light of development and deviations in last 10 days, as assumptions taken on 30 April 2020, might have changed by 10 May 2020. In light of variation of actual number of total confirmed cases for India from prediction on 30.04.2020, it is thought mandatory to reconsider the variation and make a fresh prediction of India.

The way cases are rising in India, it is looking premature to think about the turnaround, now. So, predictions are made up to 10 June 2020, based on available actual data from 15 March 2020 to 20 May 2020 (56 days data).

Similar exponential curve, as used for prediction on 30 April 2020, is used here, also. However, the pre-exponential factor is made 9 times bigger and activation term is made half of earlier used values. The resulting curve has lower rate of rise, due to lower numerical value of exponential term. The pre-exponential term is not predominant for lower values of independent variable. However, for larger value of independent variable, the exponential term matters and the resulting effect is lower value of prediction than earlier prediction with larger activation term. For the Goodness of fit, Pearson coefficient for the 56 days is found to be 0.99917, which is a fairly good match for the situation. In fact, when default exponential curve is fitted to the data, the R² value was obtained as 0.9248. Definitely, the prediction has better goodness of fit than in-built exponential function. For the prediction on 30 april 2020, the Pearson coefficient is obtained as 0.964168, which is not considered that accurate, as more deviations are found in recent past.

The exponential variation is applied to daily number of confirmed cases and then from that data cumulative number of confirmed cases are predicted. Indirectly, fallacy lies with such prediction that continuous rise in daily confirmed cases is indirectly presumed. However, the response is somehow matching to actual values. The current method of prediction predicts around 5000 daily confirmed cases on 20.05.2020. It is supposed to become 6000 per day by 24.05.2020, 7000 by 27.05.2020, 8000 by 30.05.2020 and 18000 by 15 Jun 2020.

Such rise in daily number of confirmed cases is alarming and this need not be correct. I hope that such rise is not seen in India, even for next 10 days, but let’s wait and watch for the real figures.

Conclusion: On 30.04.2020, predictions were based on data of 45 days for the non-rise period and it was found to be matching till (45/3 =) 15 days, after which the predictions were over-estimates. On similar lines, current prediction made on 20 May 2020 has taken input for 56 days and it is justified to see that data will be valid for (56/3 =) 19 days. If the prediction is true even up to 30 May or 10 June 2020, the exercise is worth and assumptions made are validated. Let’s again pray for failure of this prediction and realization of less number of confirmed cases in India than the prediction. Comments and suggestions are always welcome from readers.

Dr Himanshu Shekhar