File:2020.03.08coronaBels17t.png

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Daily cases of Coronavirus excluding mainland China, data to 2020.03.08 by worldometers [1], and their approximation (forecasts).

Experimental data used for the approximations are marked with green bars. Data, added lated, are shown with pink bars, in order to qualify the precision of the forecast.

Description

Let \(n=n(t)\) be number of daily new cases or coronavirus registered outside of China mainland. This set of data is chosen because the communist ideology of the China administration not only allow misinformation, but proscribe to use it for the propagandistic goals (to show advantages of China and, in general, that of the communistic regime).

Assuming the independent (Poisson) statistics of cases, the statistical deviation of data \(n\) from some trend is supposed to be of order of \(\sqrt{n}\).

I plot \(y=\sqrt{n}\) instead of \(n\); then, the random errors of characterization of spread of the coronavirus are of order of unity for all the experimental dots.

The discrete parameter \(t\) is just number of day since the beginning of alarm and observation. For the analysis, I assume, that 9 cases are registered at the first day of observations, id est, 2020.01.22.

Each datum is represented with green bar; its size corresponds to the typical statistical deviation of the measured number from the general trend. The goal is to choose this trend and use it as forecast, prediction.

The three approximating curves are:

\( \mathrm{Gaussian}(x)=4.29889 + 79.5733 \exp(-0.0034987 (x-55.3674)^2) \)

\( \mathrm{Lorentz}(x)=0.589212 + 60.7287/(1 + 0.0134769 (x-46.6375)^2) \)

\( \mathrm{Secan}(x)=3.46783 + 60.4588/\cosh(0.141236 (x-47.9474)) \)

For each od the three approximations above, values of parameters above are chosen in order to minimize the mean square deviation from the original data. The primary experimental data by worldometers [1] are copipasted below; they refer to year 2020:

Data

1.22 9
1.23 6
1.24 15
1.25 10
1.26 16
1.27 10
1.28 18
1.29 18
1.30 29
1.31 28
2.01 14
2.02 13
2.03 4
2.04 31
2.05 27
2.06 30
2.07 52
2.08 24
2.09 28
2.10 79
2.11 20
2.12 45
2.13 61
2.14 21
2.15 89
2.16 84
2.17 115
2.18 103
2.19 125
2.20 88
2.21 173
2.22 330
2.23 340
2.24 374
2.25 335
2.26 568
2.27 956
2.28 1085
2.29 1416
3.01 1775
3.02 1733
3.03 2454
3.04 2159
3.05 2966
3.06 3526
3.07 4005
3.08 3847
3.09 4371

C++ generator of curves



#include<math.h>
#include<stdio.h>
#include<stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)

int ado(FILE *O, int X, int Y)
{ fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%');
        fprintf(O,"%c%cBoundingBox: 0 0 %d %d\n",'%','%',X,Y);
        fprintf(O,"/M {moveto} bind def\n");
        fprintf(O,"/L {lineto} bind def\n");
        fprintf(O,"/S {stroke} bind def\n");
        fprintf(O,"/s {show newpath} bind def\n");
        fprintf(O,"/C {closepath} bind def\n");
        fprintf(O,"/F {fill} bind def\n");
        fprintf(O,"/o {1 0 360 arc C F} bind def\n");
// fprintf(O,"/times-Roman-Bold findfont 20 scalefont setfont\n");
        fprintf(O,"/Helvetica-Bold findfont 2 scalefont setfont\n");
        fprintf(O,"/W {setlinewidth} bind def\n");
        fprintf(O,"/RGB {setrgbcolor} bind def\n");
return 0;
}

double f35(double x){return 3.233596555073794 + 0.25278295790658345*exp(0.1204105367697047*x);}
double f40(double x){return 3.774610005387354 + 0.09749051738788238*exp(0.1496313645313525*x);}
double f41(double x){return 3.415452123434854 + 0.16386947166609223*exp(0.1352858211607943*x);}

DB e61(DB x){ x-=54.4402; x*=x; return 4.33655+75.3824/exp(0.00369723*x);}
DB s61(DB x){ x-=46.7652; return 3.64316+55.5322/cosh(0.148507*x);}
DB fr(DB x) { x-=44.3107; return 107.665-51.6531*erfc(0.0693204*x);}
DB ft(DB x) { x-=41.3478; return 4.10171+40.5279*(1.+tanh(0.094987*x));}

DB fG(DB x){ x-=55.3674; return 4.29889 + 79.5733*exp(-0.0034987*x*x);}
DB fB(DB x){ x-=46.6375; return .589212 + 60.7287/(1.+ 0.0134769*x*x);}
DB fC(DB x){ x-=47.9474; return 3.46783 + 60.4588/cosh(0.141236*x);}

int main(){ DB d,x,y,f,F,G,H; int j,m,n,K,S; FILE *i,*o;
o=fopen("17.eps","w");
ado(o,608,846);
#define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);
#define o(x,y) fprintf(o,"%6.2f %6.2f o\n",0.+x,0.+y);
fprintf(o,"2 2 translate 10 10 scale 1 setlinejoin\n");
DO(m,12){M(5*m,0)L(5*m,80)}
DO(n,9){M(0,10*n)L(55,10*n)}
fprintf(o,"0 0 0 RGB 2 setlinecap .1 W S\n");
i=fopen("daily.txt","r");
S=0;
for(n=1;n<199;n++){j=fscanf(i,"%lf%d",&d,&K); if(j<2) break;
        S+=K;
        F=f35(n);
        G=f40(n);
        H=f41(n);
        printf("%2d %4.2lf %4d %6d %7.1lf %7.1lf %7.1lf\n",m,d,K,S,F*F,G*G,H*H);
        M(n,sqrt(.01+K)-1.5)
        L(n,sqrt(.01+K)+1.5)
        fprintf(o,"0 1 0 RGB 1 setlinecap .7 W S\n");
       
        if(n/5*5==n) { if(n<40) fprintf(o,"gsave %4.2f 35.5 translate 90 rotate 0 -6 M 0 0 0 RGB (2020.0%4.02f) show grestore\n",n-5.3,d);
                        else fprintf(o,"gsave %4.2f 5.5 translate 90 rotate 0 -6 M 0 0 0 RGB (2020.0%4.02f) show grestore\n",n-5.3,d);
                        }
          }
n=50; fprintf(o,"gsave %4.2f 5.5 translate 90 rotate 0 -6 M 0 0 0 RGB (2020.03.11) show grestore\n",n-5.3);
n=55; fprintf(o,"gsave %4.2f 5.5 translate 90 rotate 0 -6 M 0 0 0 RGB (2020.03.16) show grestore\n",n-5.3);
fclose(i);



        for(m=0;m<61;m++){y=fG(m); if(m==0)M(m,y) else L(m,y); if(y>84) break ;}fprintf(o,"1 0 0 RGB 1 setlinecap .3 W S\n");
        for(m=0;m<61;m++){y=fC(m); if(m==0)M(m,y) else L(m,y); if(y>84) break ;}fprintf(o,"0 .5 0 RGB 1 setlinecap .3 W S\n");
        for(m=0;m<61;m++){y=fB(m); if(m==0)M(m,y)

Latex generator of labels


\documentclass[12pt]{article}
\usepackage{geometry}
\usepackage{graphicx}
\usepackage{rotating}
\usepackage{color}
%\definecolor{pink}{RGB}{255,127,255}
\paperwidth 620pt
\paperheight 870pt
\textwidth 800pt
\textheight 1200pt
\topmargin -108pt
\oddsidemargin -72pt
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\pagestyle{empty}
\begin{document}
\parindent 0pt
%\sx{1}[.9]{\begin{picture}(530,830)
{\begin{picture}(530,854)
\put(30,10){\ing{17.pdf}}
%\put( 0,815){\sx{1.7}{$\sqrt{n}$}} \put(60,817){\sx{1.7}{$n$, number of new cases}}
\put(8,815){\sx{2.1}{$y$}} \put(56,820){\sx{1.7}{$n\!=\!y^2$, number of new cases}}
\put(4,707){\sx{2}{70}} \put(33,707){\sx{1.7}{4900}}
\put(4,607){\sx{2}{60}} \put(33,607){\sx{1.7}{3600}}
\put(4,507){\sx{2}{50}} \put(33,507){\sx{1.7}{2500}}
\put(4,407){\sx{2}{40}} \put(33,407){\sx{1.7}{1600}}
\put(4,307){\sx{2}{30}} \put(33,307){\sx{1.7}{~900}}
\put(4,207){\sx{2}{20}} \put(33,207){\sx{1.7}{~400}}
\put(4,107){\sx{2}{10}} \put(33,107){\sx{1.7}{~100}}
\put(4,07){\sx{2}{~0}}
\put(26,-7){\sx{2}{0}}
\put(120,-7){\sx{2}{10}}
\put(221,-7){\sx{2}{20}}
\put(321,-7){\sx{2}{30}}
\put(421,-7){\sx{2}{40}}
\put(521,-7){\sx{2}{50}}
%\put(575,-7){\sx{2}{$t$,days}}
\put(555,-7){\sx{2}{$t$,days}}
\put(522,670){\rot{65}\sx{3}{$y\!=\!\mathrm{Gauss}(t)$}\ero}
\put(540,646){\rot{-74}\sx{3}{$y\!=\!\mathrm{Lorentz}(t)$}\ero}
\put(510,540){\rot{-79}\sx{3}{$y\!=\!\mathrm{Secan}(t)$}\ero}
\end{picture}}
\end{document}

References

  1. ↑ 1.0 1.1 https://www.worldometers.info/coronavirus/coronavirus-cases/ Outside of China 2020.03.08

File history

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Date/TimeThumbnailDimensionsUserComment
current17:49, 10 March 2020Thumbnail for version as of 17:49, 10 March 2020857 × 1,203 (159 KB)T (talk | contribs)update
13:32, 9 March 2020Thumbnail for version as of 13:32, 9 March 2020857 × 1,203 (159 KB)T (talk | contribs)add link bar
23:04, 8 March 2020Thumbnail for version as of 23:04, 8 March 2020857 × 1,203 (158 KB)T (talk | contribs)

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