The data analysis of IFR vs Age of the population shows a significant correlation ( r ) of Sigmoid model ( 3-5 ) . Then this mean dataset ( Figure – 1) is analysed by best -fit software like of which Logistic regression shows a significant correlation coefficient ( r ) [ 0 < r < 1.0 ] with tolerable std.error ( s ) , Cov ( Matrix ) and residual table of the Parametric statistics . A part from regression analysis a PIE chart of the dataset is also shown as bellow. The sigmoid function results from the analysis can be represented as follows ( Figure – 4 ) .
Y ( IFR ) = Sigmoid f [ X ( Age ) ] = [ a / ( 1 + b* exp ( -cx ) ] --------eqn( 1 )
a , b , c are the coefficients obtained from best fit analysis [ 5 ]
By expanding [ e^ ( -x ) ] series we can get the modified equation as follows :
exp ( - cx ) = 1- cx + c^2 / 2! + c ^ 3 / 3! - ..................... approx = ( 1- bcx ) ----------------eqn ( 2 )
So eqn ( 1 ) can be simplified as Y = a( 1- bcx ) ^( -1 ) = a ( 1 + bcx – b c^2x^2 + b c^3 x ^ 3 +............)
approx = a ( 1 + bcx – bc^2x^2 ) ----------------------( eqn 3 )
From eqn ( 3 ) one can simplify the Y ( IFR ) is a second order quadratic polynomial fit of X ( Age ) .
The eqn ( 1-3 ) represents the desired model equation and the measure of a sigmoid probability ( 3,5) of fatality rate of Covid -infection with age of the patients . A simplified Excell representation ie Pie chart ( Figure -5 ) also supports the sigmoid distribution . eqn ( 3 ) also represents the sigmoid probability can be also approximately represented as quadratic fit .
A further statistical analysis on fatality frequency ( X ) as a result of co morbidity vs fatality percentage ( Y ) can be expressed as a linear variation( Y= a + bX ) of of the above two parameters like scattered data , bar chart ,PIE and contour distribution showing the following results Figure -6 , Figure -7 , Figure -8 by standard Statistical checkpoint of ChiSq , Covariance matrix , Correlation table .
Figure – 6 ,7, 8 an user defined linear model with the following testing of goodness of fit pearson coefficiant ( r ) of 0.9999 with standard error ( s ) of 0.0390 , ChiSq Convergence = 1e-006 tolerance limit , 2x 2 variance matrix correlation , a,b , c are coefficiant of variations ( Figure 10 ,11 ,12 ).