Applying Levitt’s Equation for Prediction of Pandemic Control

Applying Levitt’s Equation for Prediction of Pandemic Control

 

Dr Himanshu Shekhar

 

Shri Vinay Pandey, one of my friends forwarded details of Levitt’s Equation and its applicability for the prediction of time for the Control of Pandemic. This post is based on his input.

 

Introduction: Shri Vinay Pandey sent me details of a study related to prediction of control of Pandemic. This was based on Levitt’s equation, which is generating a parameter, similar to growth factor, but for the total confirmed cases, followed by fitting a straight line to extrapolate it a value unity. The date on which unity value is realized is taken as date of Pandemic control. The same exercise is undertaken for data up to 20.07.2020 for India and its various states in this post, to understand the date of turnaround or Pandemic control.

 

Calculation for India: The ratio of total number of confirmed cases for India for two consecutive days is taken and the values are plotted against days lapsed since 14.03.2020. The values are slightly unstable in the beginning, but it stabilized after 26.04.2020 (day 40) and the plot is curtailed from 40^th day since 14.03.2020 till 20.07.2020. Both uncensored and curtailed curves are given below for completeness. For the curtailed curve, the unity value of Levitt’s number is calculated on day 122, which is 14.07.2020. The date has already crossed and it is incorrect way of calculation.

 

 

The plot is curtailed from beginning till 26.04.2020 (day 40). A linear variation is fitted and the time to reach unity is calculated as 206, which is predicting a control on 06 October 2020.

 

 

Indian States: Similar analysis is repeated for some of the major contributing states of India. The major contributor is Maharashtra and the data assuming 09.03.2020 as day zero is plotted. Again there are certain oscillations and the data from day 40 (18.04.2020) is considered for calculation. The linear fit is applied and the unity value of Levitt’s number is predicted to be achieved on 07 August 2020.

Tamil Nadu has peculiar variation and it has a very high value in between as shown below. The data is curtailed before 65 days (10.05.2020) and the linear fit gave unit value of Levitt’s number on 27 September 2020.

The calculation for further states are carried out on similar lines and unit value of Levitt’s number is calculated. The nature of curves is given below, along with the value of control date, based on unity value of Levitt’s number.

 

Conclusion: The linear variation is criticised for Levitt’s number, as the variation slows down at the later stage. However, this method is considered the easier, handy, faster and quicker way to predict control of Pandemic. It is also obvious that linear fit has very poor R-square values and the curve fitting may not be a good and optimized. In addition to this extracting data from the entire set is also a concern and data is very stable in the beginning. The values are found to be very sensitive to extraction of data. For some states, specially, Karnataka and Bihar, the curve is found to be slopping upward, as these states are moving towards burst of cases and data is extracted to get a negative slope of the curve. The summary of entire calculation is tabulated below.

 

Region	R-Square	Trunaround
India	0.7581	06-Oct-20
Maharashtra	0.6201	07-Aug-20
Tamil Nadu	0.6145	27-Sep-20
Delhi	0.5122	31-Aug-20
Gujarat	0.6539	29-Sep-20
Karnataka	0.1153	11-Aug-20
Uttar Pradesh	0.353	07-Aug-20
Bihar	0.1083	23-Sep-20

  

Regards.

Dr Himanshu Shekhar