COVID-19 India: 2.4 Million Infections by 25 Apr 2020 (Mathematical Prediction)

Summary – Predicted Infections in India …

22 Mar 2020
= Day-1
Start of rapid InFection growth -exponential curve.
Based on Italian growth model for InFections.
20 Apr 2020
= Day-30
InfLection point
Slope of growth curve begins to decrease.
Slowdown in InFection
04 May 2020
= Day-45
Start of assymptote (based on trends)
InFection new cases begin to rapidly decline.
20 May 2020
= Day-60
Expect a true asymptote. Rapid decline in new InFections.
Rate of new InFections tending to zero.
Very small number of new cases each day.
DayDateInfections (Predicted)
Day-122 Mar 2020
Day-1031 Mar 2020 100,196
Day-1505 Apr 2020 272,945
Day-2010 Apr 2020 635,209
Day-2515 Apr 20201,180,269
Day-3020 Apr 20201,824,431
Day-3525 Apr 20202,407,025

The above are Predictions are based on the Italian infection raw data model. For their validity the standards of Lockdown and Social Distancing in India should be at par with that in Italy. The above Predictions would reveal in the testing data for India, provided India does a minimum 1500+ Tests/Million of population. There are also people with infections who never get tested and as such the true infection could be higher than predicted values by a factor of 5 to 10. For example, in Italy the true infections are projected to be 10 times higher than the published tested data.

A previous article has discussed the modeling methodology based on the Population Ratio (PR), Model Factor (MF) and taking Italy as the bench mark reference point. It is also shown there that the model works for almost all the countries evaluated, but not for India. In my first article on COVID-19, I had described a model based on simple scaling with PR. In this article, this idea is further refined to make a prediction of infections from 22 Mar 2020 to 25 Apr 2020.

Published India Infection Data – Paints a Faulty Picture

The published India infection data from the John Hopkins University (JHU) data set is faulty. JHU sources its data from the Government of India portals. The problem with this data is that it is based on 32 Tests/Million people in India. Comparing with other developed countries, the quantum of these tests are so low, that it does not reflect a representative sample of the population. So, the existing data for India, at least from 22 Mar 2020 to 31 Mar 2020, is useless to start building a model for prediction.

South Korea7,940

Italian Infection Model is a Good Benchmark

The infection raw data for Italy, based on my analysis in previous articles, is a good benchmark for predicting the infection trends in other countries. I have found that once the infections reach a value of 400, the trajectory follows an exponential curve. The corresponding date is taken as Day-1 and all countries can start at the same point on a common graph. The analysis has also shown that the exponential curve for Italy can be scaled with PR and MF to model the infection grown curves for other countries.

This graph contains the real day-to-day data of COVID-19 infections for several countries. The PR ratio is shown in the legend. The idea is that if PR is more than 1 the curve should fall below Italy (blue line) and if it is less than 1 it should fall below Italy. US and Germany show this trend (PR > 1). Canada and South Korea are way below (PR < 1). England and France are close to Italy (PR close to 1). China is an anomaly, since it is hovering close to Italy, though its PR is 23.68! Thats because China’s data is tainted. India’s data is also tainted, since it is falling way below the curve for Italy. In conclusion the Italian curve is a good bench mark.

It must be noted that to bank on this model, the remedial measures such as lockdown and quarantine norms must be similar in all the countries. Otherwise there will be variations. For this reason, Spain is higher than it should be for its PR value. It is likely that Spain’s lockdown was not as effective as that of Italy.

Predicting the Infections based on Italian Model

Based on the above reasoning, using the Italian curve, other countries can be modeled by multiplying the Italian infection raw data with the PR.

First, a polynomial was established to fit the Italian infection raw data.

Y(x) = -0.2274 x^4 + 15.521 x^3 – 217.81 x^2 + 1451.4 x – 1540

Here, Y(x) is the Predicted Infection on day ‘x’, where ‘x’ is the same as time ‘t’ in days, with x = 1 and incrementing by 1 for each day.

Multiplying this by PR the individual curves for other countries are obtained.

The graph is not detailed for most of the countries, since the scale is enlarged because of China and India. Removing these, we get a much clearer graph for the other countries.

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