It is my intent to update the above graph for India from 22 Mar 2020 to 22 Apr 2020. The graph above will be replaced on a daily basis. In the above graph t=1 is Day-1 which is set at 22 Mar 2020. Like wise t=2 and so on will increment from the set point date of 22 Mar 2020. For those who don’t like math, they just have to look at the graph and see the trends.
The data for India from 22 Mar 2020 to 05 Apr 2020 is spurious. It is far removed from the truth. It is because of insufficient testing in the country. This gives an artificially low number for inFections. The graph, with MF=0.04, is the Italian trend for inFections. The India data is 56% lower than Italy, for the same time period of exponential growth. But, the Indian population is 22.56 times that of the Italian population.
The model has close likeness for MF = 0.02, which means that it is following a curve trend that has values lower than that for Italy. Further, we should be expecting an MF = 1, since India should scale to Italy based on the Population Ratio (PR). So, an MF = 0.02 is unreliable and should not be used as a possible model.
The real time data for the exponential growth phase for infections had started on 22 Mar 2020. However, as seen from the graph, the real data does not fit the model, for any value of practical MF. As such, it is very likely that the Real Data published for India by JHU is not of practical use and also does not represent a good sample of the population.
I’m pulling the real data for India from the data set publicly available from John Hopkins University & Medicine (JHU), Center for Systems Science and Engineering (CSSE). It’s not clear where they are getting the day-to-day data from for India, but it is surely from the list of data sources listed on their data archival portal. The Indian Government has a website page (https://www.mygov.in/covid-19 page) for COVID-19, but there is no “day-to-day” data history.
A key conclusion that can be made as on 05 Apr 2020 is that the reported data for inFections in India is totally wrong, in its entirety.
In my previous article, I had established the equation for the exponential growth model for Italy. The population ratio (PR) is 22.56673 for India. Multiplying the exponential growth model with PR should take into account the population differences. I’ve further multiplied it with a Model Factor (MF), which is a number greater than 0, but more likely about 1 for India. This factor fine tunes the scaling and at some value it will have a good match to the real world infection data. When MF is 1/PR, the curve is an identical match to the exponential best fit for Italy.
As such, for India, the modified exponential equation is:
y(t) = MF * PR * 631.06 * exp (0.1852*t)
y(t) = MF * 22.56673 * 631.06 * exp (0.1852*t)
To predict the Infection Cases in India, select an MF between 0 and 1, plug in a value of “t”, where “t” is the day count starting from 22 Mar 2020 (t=1) for India. The computed value of y(t) is the predicted Infection Cases on day “t”.