Deriving the COVID-19 Formula from any Graph

Most of the graphics published about the COVID-19 have exponential behavior. A lot of them have been driven with only the data given by government institutions. In this paper, the authors attempt to describe a general procedure to convert any group of data into a graph, where the application of the Least Square Method can provide a mathematical formula that can be used for different situations and purposes including improving the current graphs of the disease. *Corresponding Author: Dr Jose Mujica, Escuela Superior de Audio y Acústica, Caracas, Venezuela; E-mail: jmujica@escuelasuperiordeaudio.com.ve Citation: Mujica J, Mata-Toledo RA (2020) Deriving the COVID-19 Formula from any Graph. Int J Comput Softw Eng 5: 157. doi: https://doi.org/10.15344/24564451/2020/157 Copyright: © 2020 Mujica et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published on March 13, 2020. The objective is to obtain a graph to which we can apply the LSM to derive a mathematical formula that we can use, as indicated later, for several other purposes including the study of any variable of this or any other disease. As a caveat to the reader, the figures used in this paper are not at a true scale although the values shown are actual measurements; all figures are only used to convey shapes and procedures. Figure 1 illustrates a typical COVID-19 curve profile and its values. Identifying the coordinates The coordinates of the graph were found by measuring the height of the curve at seven different horizontal intervals, as shown in Figure 2. International Journal of Computer & Software Engineering Jose Mujica1,* and Ramon A. Mata-Toledo2 1Escuela Superior de Audio y Acústica, Caracas, Venezuela 2James Madison University, Harrisonburg, Virginia, USA Int J Comput Softw Eng IJCSE, an open access journal ISSN: 2456-4451 Volume 5. 2020. 157 Mujica et al,. Int J Comput Softw Eng 2020, 5: 157 https://doi.org/10.15344/2456-4451/2020/157 Introduction In this article, the authors propose the use of the Least Square Method (LSM) as a procedure that can help us obtain a mathematical formula that can be used to complement, and if possible, better any of the models used so far, particularly, on the area of medicine. The LSM will be used to fit the curve of a graph from which we can generate a mathematical formula. The procedure is a simple three-step process: first, collect the field data. Second, make a graph from the data obtained, and, as the third and last step, use the LSM to generate a mathematical formula. From the plot of this graph, after applying the LSM, we can generate a formula that can be easily taught and used worldwide without the need of having specialized workshops to teach the use and application of the formula. Using the Least Square Method to Find the Equation of Covid-19 Curve Sample To illustrate the proposed methodology in a step-by-step fashion, we will use a real-life example to find the equation of the curve of COVID-19 behavior. The data was obtained from a New York Time Article, The Exponential Power of Now by Siobhan Roberts [1] with the graphic of Britta Jewell [2], of the Institute for Diseasing Model. Figure 1: Advert cases curve (Britta Jewell.).

Published on March 13, 2020. The objective is to obtain a graph to which we can apply the LSM to derive a mathematical formula that we can use, as indicated later, for several other purposes including the study of any variable of this or any other disease. As a caveat to the reader, the figures used in this paper are not at a true scale although the values shown are actual measurements; all figures are only used to convey shapes and procedures. Figure 1 illustrates a typical COVID-19 curve profile and its values.

Identifying the coordinates
The coordinates of the graph were found by measuring the height of the curve at seven different horizontal intervals, as shown in Figure 2.

Introduction
In this article, the authors propose the use of the Least Square Method (LSM) as a procedure that can help us obtain a mathematical formula that can be used to complement, and if possible, better any of the models used so far, particularly, on the area of medicine. The LSM will be used to fit the curve of a graph from which we can generate a mathematical formula.
The procedure is a simple three-step process: first, collect the field data. Second, make a graph from the data obtained, and, as the third and last step, use the LSM to generate a mathematical formula. From the plot of this graph, after applying the LSM, we can generate a formula that can be easily taught and used worldwide without the need of having specialized workshops to teach the use and application of the formula.

Using the Least Square Method to Find the Equation of Covid-19 Curve Sample
To illustrate the proposed methodology in a step-by-step fashion, we will use a real-life example to find the equation of the curve of COVID-19 behavior. The data was obtained from a New York Time Article, The Exponential Power of Now by Siobhan Roberts [1] with the graphic of Britta Jewell [2], of the Institute for Diseasing Model.

Choosing the curve's form
After determining the coordinates, it was necessary to choose a curve that approximates the shape of the COVID-19 sample curve. Figure 3 shows the graphs of some of the most commonly used functions for fitting curves using the LSM [3].
For this case, we chose the graph of the exponential function y = ae bx (F1) because its mirror-image, about the horizontal axis of the graph. We will use the LSM to fit the exponential graph to the profile of the curve.

System of equations
To obtain the coefficients a and b of the exponential function, LSM requires solving the system of equations F1 shown below. Table 1 explains the meaning of the different terms depending on the type of curve selected [4].   Where "n" is the number of coordinates previously obtained and whose values are shown in Table 2.

Solving the System of Equations
Calculating the individual terms [4] In this example, n = 7 (the number of coordinates) The summation of all Xs values is: The summation of all the squares of the Xs coordinates is: The summation of the logarithms of the Ys coordinates of Table 2 is: The summation of all Xs coordinates multiplied by its corresponding Y logarithm is:

Substituting all terms in the System of equation F2
Performing the corresponding arithmetic operations, we obtain the following results:

Calculating the b coefficient
Solving the top equation of (F3) for Ln(a) give us Replacing this value in the second equation of F3 we obtain:

Calculating the a coefficient
To find the coefficient a, we replace the value of b in the second equation of the system F3 and solve for Ln(a). That is, Raising e to value just obtained results in:

Equation of Covid-19's Curve
Following the procedure outlined we can rewrite the equation 1 using the coefficients a and b just calculated Using the exponential equation previously selected (F1) and substituting the coefficients, a and b we get the following function [5] When we plot the latter equation into the Maple software the values of x initially obtained in Table 2, the graphic (Figure 4) obtained is very close to shape of the Figure 1. So, equation 1 approximates indeed the profile of the graphic.

Excel Workbook Test
To improve the work we made a Microsoft Exce™ calculation spreadsheet with the LMS parameters. In the first column we placed    This EXCEL Workbook can be downloaded at the following link: http://www.escuelasuperiordeaudio.com.ve/covid19formula.html the Xs coordinates. In the second one we can find Ys coordinates. The third column is the summation of all the Xs. The fourth column has the summation of all the squares Xs. The fifth, the summation of the logarithms of the Ys. And the sixth one, the product of each Xs by the logarithms of all the Ys.

Conclusion [7]
With the LMS method and the EXCEL Workbook propose, any person related to the study of the COVID-19 phenomenon can have a tool to predict the behavior of the disease in the time.
The authors can provide EXCEL formula translation to all who may be interested. Just email any of the authors at the email addresses indicated along the author's names.
In addition, the Workbook can be extended to any number of samples. This obviously will help improving the accuracy of the formula.