SEPIR Modell  
Modellierung  Testverfahren,
 Verlässlichkeit (Sensibilität)η,  Spezifizität 100%,
 mit Testquote β  ab  ta =  Mitte Okt oder ...
2 Szenarien beide ohne social distancing
genannt  “PCR”: l=1, β=0.9
bzw.  “Antigen”: l=4,  β=0.7

07.06.2021

Vorbereitung: Laden/Aufbereitung  der Daten und Hilfsfunktionen

NotebookEvaluate["//home/erhard/Dropbox/Mathematica_notebooks/Corona/0-Standardmoduln/dat-Germany-2021-05-31.nb"]

Char1[x_,axx_ ,bxx_] := 2^-1 (Sign[x -axx] - Sign[x-bxx]); 
suppMult[x_,Axx_,Bxx_,cxx_ ]=( Char1[x,-10^6, Axx]+((1+cxx)/2+((1-cxx)/2)Cos[((x-Axx)Pi)/(Bxx-Axx)])Char1[x,Axx,Bxx]+cxx  Char1[x,Bxx,10^6]); (*multiplikative Absenkung bzw Anhebung von 1 auf cxx von A nach B f mit cosinus-Glättung*)
LinsuppMult[x_,Axx_,Bxx_,cxx_ ]=Char1[x,-10^6, Axx]+(1+  ((cxx-1)/((Bxx-Axx))) (x-Axx) )Char1[x,Axx,Bxx]+cxx  Char1[x,Bxx,10^6];(*multiplikative Absenkung bzw Anhebung von 1 auf cxx von A nach B linear*)
Char[x_,AAA_,BBB_]=Piecewise[{{1,AAA<=x<=BBB}},0];(*charakteristische Funktion des Intervalls [a,b])*)
hilf1ModMult[x_]= Piecewise[{{0,x≤0},{Exp[-(x^(-1))],0≤x}}];
hilf2ModMult[x_]=((hilf1ModMult[x])/(hilf1ModMult[x]+hilf1ModMult[1-x]));
ModMult[x_,AAA_,BBB_,ccc_]=1+(ccc-1) hilf2ModMult[((x-AAA)/(BBB-AAA))] (*glatte Anhebund oder Absenkunt um Faktor ccc im Intervall [AAA,BBB]*);

(i) Aktuelle Daten (lange Intervalle) und Modellierung

(*lange Intervalle im Sommer 2020*)
parT={t0->1,t1->t1JHU,t2->62,Δ2->2, t3->132,Δ3->4, t4->216 +2,Δ4->9,t5->tOct1+30(*tOct1+17*),Δ5->11 ,t6->tNov1+27-2,Δ6->8 ,(*t10->tNov1+27-2,Δ10->8 ,*)t7 ->tDec1+13+2,Δ7->6   ,  t8-> tMar12021+7-1, Δ8->7 (*    t9->   tFeb12021+9+2 ,Δ9->13 ,t10->tMar12021+4-1, Δ10->11 *)};
datet1=DatePlus[datet0, -1+t1/.parT];
datet2=DatePlus[datet0, -1+t2/.parT];
datet3=DatePlus[datet0, -1+t3/.parT];
datet4=DatePlus[datet0, -1+t4/.parT];
datet5=DatePlus[datet0, -1+t5/.parT];
datet6=DatePlus[datet0, -1+t6/.parT];
datet7=DatePlus[datet0, -1+t7/.parT];
datet8=DatePlus[datet0, -1+t8/.parT];
(*datet9=DatePlus[datet0, -1+t9/.parT];
datet10=DatePlus[datet0, -1+t10/.parT];
datet11=DatePlus[datet0, -1+t11/.parT];
datet12=DatePlus[datet0, -1+t12/.parT];
datet13=DatePlus[datet0, -1+t13/.parT];*)
eod=DatePlus[datet0, Length[QJHU]-1];
Print["t0=",t0/.parT, ",  t0JHU=",  t0JHU,",  i.e. ", datet0];
Print["t1=",t1/.parT, ",  t1JHU=",  t0JHU+t1/.parT,",  i.e. ", datet1];
Print["t2=",t2/.parT, ",  t2JHU=",  t0JHU+t2/.parT,",  i.e. ", datet2];Print["t3=",t3/.parT, ",  t3JHU=",  t0JHU+t3/.parT,",  i.e. ", datet3];
Print["t4=",t4/.parT, ",  t4JHU=",  t0JHU+t4/.parT,",  i.e. ", datet4];Print["t5=",t5/.parT, ",  t5JHU=",  t0JHU+t5/.parT,",  i.e. ", datet5];
Print["t6=",t6/.parT, ",  t6JHU=",  t0JHU+t6/.parT,",  i.e. ", datet6];
Print["t7=",t7/.parT, ",  t7JHU=",  t0JHU+t7/.parT,",  i.e. ", datet7];
Print["t8=",t8/.parT, ",  t8JHU=",  t0JHU+t8/.parT,",  i.e. ", datet8];
(*Print["t9=",t9/.parT, ",  t9JHU=",  t0JHU+t9/.parT,",  i.e. ", datet9];Print["t10=",t10/.parT, ",  t10JHU=",  t0JHU+t10/.parT,",  i.e. ", datet10];Print["t11=",t11/.parT, ",  t10JHU=",  t0JHU+t11/.parT,",  i.e. ", datet11];
Print["t12=",t12/.parT, ",  t10JHU=",  t0JHU+t12/.parT,",  i.e. ", datet12];Print["t13=",t13/.parT, ",  t10JHU=",  t0JHU+t13/.parT,",  i.e. ", datet13];*)
Print["eod=",Length[QJHU]," i.e. ",eod];(*Intervall-Mittelwerte der a-quer(k) *)
κ=N[{Mean[Take[kappa7,{t0,t1}/.parT]],
Mean[Take[kappa7,{t1,t2-Δ2}/.parT]],
Mean[Take[kappa7,{t2,t3-Δ3}/.parT]],
Mean[Take[kappa7,{t3,t4-Δ4}/.parT]],
Mean[Take[kappa7,{t4,t5-Δ5}/.parT]], 
Mean[Take[kappa7,{t5,t6-Δ6}/.parT]], 
Mean[Take[kappa7,{t6,t7-Δ7}/.parT]], 
Mean[Take[kappa7,{t7,t8-Δ8}/.parT]],
 Mean[Take[kappa7,{t8,Length[kappa7]}/.parT]](*,
Mean[Take[kappa7,{t9,Length[kappa7]}/.parT]],
Mean[Take[kappa7,{t10,Length[kappa7]}/.parT]] (
 Mean[Take[kappa7,{t11,t12}/.parT]]
  Mean[Take[kappa7,{t12,t13-Δ13}/.parT]], 
Mean[Take[kappa7,{t13,Length[kappa7]}/.parT]]*)
}] ;

sigmaκ={StandardDeviation[Take[kappa7,{t0,t1-1}/.parT]],
StandardDeviation[Take[kappa7,{t1,t2-Δ2}/.parT]],
StandardDeviation[Take[kappa7,{t2,t3-Δ3}/.parT]],
StandardDeviation[Take[kappa7,{t3,t4-Δ4}/.parT]],
StandardDeviation[Take[kappa7,{t4,t5-Δ5}/.parT]],StandardDeviation[Take[kappa7,{t5,t6-Δ6}/.parT]],
StandardDeviation[Take[kappa7,{t6,t7-Δ7}/.parT]],
StandardDeviation[Take[kappa7,{t7,t8-Δ8}/.parT]],
StandardDeviation[Take[kappa7,{t8,Length[kappa7]}/.parT]] (*,
StandardDeviation[Take[kappa7,{t9,Length[kappa7]}/.parT]],
StandardDeviation[Take[kappa7,{t10,Length[kappa7]}/.parT]],
StandardDeviation[Take[kappa7,{t11,t12}/.parT]],
StandardDeviation[Take[kappa7,{t12,t13-Δ13}/.parT]],
StandardDeviation[Take[kappa7,{t13,Length[kappa7]}/.parT]]*)
} ;

Print["letztes κ am ", datendkappa]

Print["κ = ",κ];

Print["sigmaκ = ", sigmaκ];

Length[κ]

faktor1=1;faktor2=1;
a1=κ[[2]](*-0.3sigmaκ[[2]]*); a2=κ[[3]]-0.1sigmaκ[[3]] ; a3=κ[[4]](*-0.6sigmaκ[[4]]*); a4=κ[[5]]-0.6sigmaκ[[5]]; a5=κ[[6]]  -0.2sigmaκ[[6]]; a6=κ[[7]] (*-0.1sigmaκ[[7]]*);a7=κ[[8]]  -0.15sigmaκ[[8]];
 a8=  κ[[9]] +0.25sigmaκ[[9]];
aa[x_]=a1 suppMult[x,t2-Δ2,t2,(a2/a1)]suppMult[x,t3-Δ3,t3,(a3/a2)]suppMult[x,t4-Δ4,t4,(a4/a3)]*suppMult[x,t5-Δ5,t5,(a5/a4)] suppMult[x,t6-Δ6,t6,(a6/a5)] suppMult[x,t7-Δ7,t7,(a7/a6)]suppMult[x,t8-Δ8,t8,(a8/a7)](*suppMult[x,t10-Δ10,t10,(a10/a9)]suppMult[x,t11-Δ11,t11,(a11/a10)]suppMult[x,t12-Δ12,t12,(a12/a11)]*)/.parT;aModel=Table[aa[k],{k,t1/.parT,kend}];
GraphaModel=DateListPlot[Take[aModel,Length[kappa7]+15],datet1,PlotStyle->{Black,Dashed},Sequence[PlotTheme->"Detailed", ImageSize->Medium],GridLines->{{"{2020,03,24}" ,"{2020,04,26}","{2020,07,05}","{2020,09,27}","{2020,10,31}","{2020,12,6}","{2021,03,02}"},Automatic},PlotRange->{0,0.4}];
Graphkappa7A=DateListPlot[Take[kappa7,Length[kappa7] ],datet0,(*Joined->False,*)  PlotStyle->{Colorkappa},Sequence[PlotTheme->"Detailed", ImageSize->Medium] ,  PlotRange->{0, 0.8},FrameLabel->{None,"kappa"}];Graphcrit=DateListPlot[Table[1/ptilde[k],{k,1,tMay12021+60}],datet0,Sequence[PlotTheme->"Detailed", ImageSize->Medium], PlotStyle->{Black, Thin, Dotted}];

Print["a1=", a1, " a2=", a2,   "  a3 =" , a3, " a4 =" , a4, " a5 =" , a5, " a6 =" , a6,  " a7 =" , a7 (*,  " a8 =" , a8  ,  " a9 =" , a9   ,   " a10 =" , a10 ,   " a11 =" , a11 ,   " a12 =" , a12,   " a13 =" , a13*)];Show[GraphaModel,Graphkappa7A,Graphcrit]

Export["/file-path/Check-Lehrach-2021-06-07kappa-Mod-2021-06-07.pdf",%]

Print["κ Szenario 1 " ,Show[GraphaModel,Graphkappa7A,Graphcrit]]

a8/a7

______________________________________________________________

Vergleich von zwei Teststrategien , beide mit täglichem Test, beide  nur mit Kontaktbeschränkungen wie im späten September 2020 
Szenarion 1: “PCR” 
Szenario 2  “Antigen”

abgeänderte Kontaktraten (fiktiv)  
kappa4 ab t4,

(*kappa1=0.25;*)
a1=κ[[2]](*-0.3sigmaκ[[2]]*); a2=κ[[3]]-0.1sigmaκ[[3]] ; a3=κ[[4]](*-0.6sigmaκ[[4]]*);  a4=κ[[5]]-0.6sigmaκ[[5]];
(*κ[[5]]-0.6sigmaκ[[5]]; a5=κ[[6]]  -0.2sigmaκ[[6]]; a6=κ[[7]] (*-0.1sigmaκ[[7]]*);a7=κ[[8]]  -0.15sigmaκ[[8]];
 a8=  κ[[9]] +0.4sigmaκ[[9]]*)

aa[x_]=a1 suppMult[x,t2-Δ2,t2,(a2/a1)]suppMult[x,t3-Δ3,t3,(a3/a2)]suppMult[x,t4-Δ4,t4,(a4/a3)](*suppMult[x,t4-Δ4,t4,(a4/a3)]suppMult[x,t5-Δ5,t5,(a5/a4)] suppMult[x,t6-Δ6,t6,(a6/a5)] suppMult[x,t7-Δ7,t7,(a5/a6)]suppMult[x,t8-Δ8,t8,(a8/a7)]suppMult[x,t10-Δ10,t10,(a10/a9)]suppMult[x,t11-Δ11,t11,(a11/a10)]suppMult[x,t12-Δ12,t12,(a12/a11)]*)/.parT;
aModel=Table[aa[k],{k,t1/.parT,kend}];
GraphaModel=DateListPlot[Take[aModel,Length[kappa7]+15],datet1,PlotStyle->{Black,Dashed},Sequence[PlotTheme->"Detailed", ImageSize->Medium],(*GridLines->{{{"{2020,03,24}" ,Thick},{"{2020,04,26}",Thick},{"{2020,07,05}",Thick},{"{2020,09,27}",Thick},{"{2020,10,31}",Thick},{"{2020,12,6}",Thick},{"{2021,03,02}",Thick}},{0.1,0.2,0.3,0.4}},*)GridLines->{{"{2020,03,24}" ,"{2020,04,26}","{2020,07,05}","{2020,09,27}","{2020,10,31}","{2020,12,6}","{2021,03,02}"},Automatic},PlotRange->{0,0.7}];
Graphkappa7A=DateListPlot[Take[kappa7,Length[kappa7] ],datet0,(*Joined->False,*)  PlotStyle->{Colorkappa},Sequence[PlotTheme->"Detailed", ImageSize->Medium] ,  (*GridLines->{{{"{2020,03,24}",Thick},{"{2020,04,26}",Thick},{"{2020,07,05}",Thick},{"{2020,09,27}",Thick},{"{2020,10,31}",Thick},{"{2020,12,6}",Thick},{"{2021,03,02}",Thick}},{0.1,0.2,0.3,0.4,0.5,0.6,0.7}},*)PlotRange->{0, 0.8},FrameLabel->{None,"kappa"}];Graphcrit=DateListPlot[Table[1/ptilde[k],{k,1,tMay12021+60}],datet0,Sequence[PlotTheme->"Detailed", ImageSize->Medium], PlotStyle->{Black, Thin, Dotted}];

Print["a1=", a1, " a2=", a2,   "  a3 =" , a3, " a4 =" , a4, " a5 =" , a5 (*, " a6 =" , a6 ,  " a7 =" , a7 ,  " a8 =" , a8  ,  " a9 =" , a9   ,   " a10 =" , a10 ,   " a11 =" , a11 ,   " a12 =" , a12,   " a13 =" , a13*)];Print["κ Szenario 2  "Show[GraphaModel,Graphkappa7A,Graphcrit]];Print["Kontakraten mit social distancing wie Sep 2020 ohne weitere Massnahmen"]

Show[GraphaModel,Graphkappa7A,Graphcrit]

Export["//kappa-Mod-Test-2021-06-07.pdf",%]

"/file-path//kappa-Mod-Test-2021-06-07.pdf"

Szenario 1 “PCR”,  tägliche Tests  η = 0.9

Szenario 1a,  Testquote β=100%,  tägliche Tests

β=1  (*Testquote*);  η=0.9 (*reliability des Tests*);
 l=1(*erster Tag der Sensibilität des Tests*);
ta=tOct1+15-1; 
xTestA[x_]=Piecewise[{{0,x<ta},{1,x≥ta}}] (*Anschaltfunktion des Tests*);
Testzykel={1,0,0,1,0,0,0};
TestB=Join[Table[0,ta-1],Table[η,kend]] (*Definition der Testfreuqenz und -effektivität*);Take[TestB,{ta-5,ta+15}]

___ ___ ___ ___ ___ __
Run <SEPAR-recursion-2014-04-17.nb>  version (iv)

NotebookEvaluate["/file-path/SEPAR-recursion-Version-iv-2021-05-31.nb"]

Qneurek1a=Qneurek;
RhoMod1a=RhoMod7;

___ ___ ___ ___ ___ ___ ___ ___ __

Szenario 1b,  Testquote β=80%,

β=0.8  (*Testquote*);  η=0.9 (*reliability des Tests*);
 l=1(*erster Tag der Sensibilität des Tests*);
ta=tOct1+15-1; 
xTestA[x_]=Piecewise[{{0,x<ta},{1,x≥ta}}] (*Anschaltfunktion des Tests*);
(*Testzykel={1,0,0,0,0,0,0};
TestB=Join[Table[0,ta-1],Flatten[Table[η Testzykel,Floor[(kend/7)]]]] ;*)
(*TestB=Join[Table[0,ta-1],Table[η,kend]] *)

TestB=Join[Table[0,ta-1],Table[η,kend]] (*Definition der Testfreuqenz und -effektivität*);Take[TestB,{ta-5,ta+15}]

___ ___ ___ ___ ___ __
Run <SEPAR-recursion-2014-04-17.nb>  version (iv)

NotebookEvaluate["//home/erhard/Dropbox/Mathematica_notebooks/Corona/0-Standardmoduln/SEPAR-recursion-Version-iv-2021-05-31.nb"]

Qneurek1b=Qneurek7;
RhoMod1b=RhoMod7;

___ ___ ___ ___ ___ ___ ___ ___ __

Szenario 2c,  Testquote β=60%,

β=0.6  (*Testquote*);  η=0.9 (*reliability des Tests*);
 l=1(*erster Tag der Sensibilität des Tests*);
ta=tOct1+15-1; 
xTestA[x_]=Piecewise[{{0,x<ta},{1,x≥ta}}] (*Anschaltfunktion des Tests*);

Testzykel={1,0,0,0,0,0,0};
TestB=Join[Table[0,ta-1],Table[η,kend]] (*Definition der Testfreuqenz und -effektivität*);Take[TestB,{ta-5,ta+15}]

___ ___ ___ ___ ___ __
Run <SEPAR-recursion-2014-04-17.nb>  version (iv)

NotebookEvaluate["/file-path/SEPAR-recursion-Version-iv-2021-05-31.nb"]

___ ___ ___ ___ ___ ___ ___ __

Qneurek1c=Qneurek7;
RhoMod1c=RhoMod7;

___ ___ ___ ___ ___ __

GraphQneurek1a=DateListPlot[{ Take[Qneurek1a,{1,Length[QJHU]+5}] },datet0,PlotStyle->{Black,Dashed},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium],PlotRange->{1,3.2 (10^4)}];GraphQneurek1b=DateListPlot[{ Take[Qneurek1b,{1,Length[QJHU]+5}] },datet0,PlotStyle->{Black,Dotted},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium],PlotRange->{1,45 (10^3)}];
GraphQneurek1c=DateListPlot[{ Take[Qneurek1c,{1,Length[QJHU]+5}] },datet0,PlotStyle->{Black,Dotted,Thin},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium]];Show[GraphQneurek1a,GraphQneurek1b,GraphQneurek1c,GraphQneu7JHU]

Export["/file-path/graph-Qneu-Test-Szen-1a-b-c-2021-04-23.pdf",%]

GraphLogQneurek1a=DateListLogPlot[{ Take[Qneurek1a,{1,Length[QJHU]+5}] },datet0,PlotStyle->{Black,Dashed},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium],PlotRange->{1,1 (10^6)}];GraphLogQneurek1b=DateListLogPlot[{ Take[Qneurek1b,{1,Length[QJHU]+5}] },datet0,PlotStyle->{Black,Dotted},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium]];
GraphLogQneurek1c=DateListLogPlot[{ Take[Qneurek1c,{1,Length[QJHU]+5}] },datet0,PlotStyle->{Black,Dotted,Thin},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium]];Show[GraphLogQneu7JHU,GraphLogQneurek1a,GraphLogQneurek1b,GraphLogQneurek1c]

Export["/file-path/graph-LogQneu-Test-Szen-1a-b-c-2021-06-07.pdf",%]

GraphRhoMod1a=DateListPlot[{ Take[RhoMod1a,{1,Length[QJHU]}] },datet0,PlotStyle->{ColorRho,Dashed},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium]];GraphRhoMod1b=DateListPlot[{ Take[RhoMod1b,{1,Length[QJHU]}] },datet0,PlotStyle->{ColorRho,Dotted},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium]];
GraphRhoMod1c=DateListPlot[{ Take[RhoMod1c,{1,Length[QJHU]-3}] },datet0,PlotStyle->{ColorRho,Dotted, Thin},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium]];Show[GraphRhoMod1a,GraphRhoMod1b ,GraphRhoMod1c]

Export["/file-path/graph-RhoMod-Test-Szen-1a-b-c-2021-06-07.pdf",%]

_____________________________________________________________

Szenario 2 “Antigen”,  tägliche Test,  η = 0.7 ,

Szenario 2a,  Testquote β=100%,  tägliche Tests

β=1  (*Testquote*);  η=0.7 (*reliability des Tests*);
 l=4(*erster Tag der Sensibilität des Tests*);
ta=tOct1+15-1; 
xTestA[x_]=Piecewise[{{0,x<ta},{1,x≥ta}}] (*Anschaltfunktion des Tests*);
Testzykel={1,0,0,1,0,0,0};
TestB=Join[Table[0,ta-1],Table[η,kend]] (*Definition der Testfreuqenz und -effektivität*);Take[TestB,{ta-5,ta+15}]

___ ___ ___ ___ ___ __
Run <SEPAR-recursion-2014-04-17.nb>  version (iv)

NotebookEvaluate["/file-path/SEPAR-recursion-Version-iv-2021-05-31.nb"]

Qneurek2a=Qneurek;
RhoMod2a=RhoMod7;

___ ___ ___ ___ ___ ___ ___ ___ __

Szenario 2b,  Testquote β=80%,

β=0.8  (*Testquote*);  η=0.7 (*reliability des Tests*);
 l=4(*erster Tag der Sensibilität des Tests*);
ta=tOct1+15-1; 
xTestA[x_]=Piecewise[{{0,x<ta},{1,x≥ta}}] (*Anschaltfunktion des Tests*);
(*Testzykel={1,0,0,0,0,0,0};
TestB=Join[Table[0,ta-1],Flatten[Table[η Testzykel,Floor[(kend/7)]]]] ;*)
(*TestB=Join[Table[0,ta-1],Table[η,kend]] *)

TestB=Join[Table[0,ta-1],Table[η,kend]] (*Definition der Testfreuqenz und -effektivität*);Take[TestB,{ta-5,ta+15}]

___ ___ ___ ___ ___ __
Run <SEPAR-recursion-2014-04-17.nb>  version (iv)

NotebookEvaluate["/file-path/SEPAR-recursion-Version-iv-2021-05-31.nb"]

Qneurek2b=Qneurek7;
RhoMod2b=RhoMod7;

___ ___ ___ ___ ___ ___ ___ ___ __

Szenario 2c,  Testquote β=60%,

β=0.6  (*Testquote*);  η=0.7 (*reliability des Tests*);
 l=4(*erster Tag der Sensibilität des Tests*);
ta=tOct1+15-1; 
xTestA[x_]=Piecewise[{{0,x<ta},{1,x≥ta}}] (*Anschaltfunktion des Tests*);

Testzykel={1,0,0,0,0,0,0};
TestB=Join[Table[0,ta-1],Table[η,kend]] (*Definition der Testfreuqenz und -effektivität*);Take[TestB,{ta-5,ta+15}]

___ ___ ___ ___ ___ __
Run <SEPAR-recursion-2014-04-17.nb>  version (iv)

NotebookEvaluate["/file-path/SEPAR-recursion-Version-iv-2021-05-31.nb"]

Qneurek2c=Qneurek7;
RhoMod2c=RhoMod7;

___ ___ ___ ___ ___ __

GraphQneurek2a=DateListPlot[{ Take[Qneurek2a,{1,Length[QJHU]+5}] },datet0,PlotStyle->{Black,Dashed},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium],PlotRange->{1,3.2 (10^4)}];GraphQneurek2b=DateListPlot[{ Take[Qneurek2b,{1,Length[QJHU]+5}] },datet0,PlotStyle->{Black,Dotted},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium],PlotRange->{1,45 (10^3)}];
GraphQneurek2c=DateListPlot[{ Take[Qneurek2c,{1,Length[QJHU]+5}] },datet0,PlotStyle->{Black,Dotted,Thin},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium]];Show[GraphQneurek2a,GraphQneurek2b,GraphQneurek2c,GraphQneu7JHU]

Export["/file-path/graph-Qneu-Test-Szen-2a-b-c-2021-06-07.pdf",%]

GraphLogQneurek2a=DateListLogPlot[{ Take[Qneurek2a,{1,Length[QJHU]+5}] },datet0,PlotStyle->{Black,Dashed},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium],PlotRange->{1,1 (10^6)}];GraphLogQneurek2b=DateListLogPlot[{ Take[Qneurek2b,{1,Length[QJHU]+5}] },datet0,PlotStyle->{Black,Dotted},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium]];
GraphLogQneurek2c=DateListLogPlot[{ Take[Qneurek2c,{1,Length[QJHU]+5}] },datet0,PlotStyle->{Black,Dotted,Thin},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium]];Show[GraphLogQneurek2a,GraphLogQneurek2b,GraphLogQneurek2c,GraphLogQneu7JHU]

Export["/file-path/graph-LogQneu-Test-Szen-2a-b-c-2021-06-07.pdf",%]

GraphRhoMod2a=DateListPlot[{ Take[RhoMod2a,{1,Length[QJHU]}] },datet0,PlotStyle->{ColorRho,Dashed},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium]];GraphRhoMod2b=DateListPlot[{ Take[RhoMod2b,{1,Length[QJHU]}] },datet0,PlotStyle->{ColorRho,Dotted},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium]];
GraphRhoMod2c=DateListPlot[{ Take[RhoMod2c,{1,Length[QJHU]-3}] },datet0,PlotStyle->{ColorRho,Dotted, Thin},Joined->True,Sequence[PlotTheme->"Detailed", ImageSize->Medium]];Show[GraphRhoMod2a,GraphRhoMod2b ,GraphRhoMod2c]

Export["/file-path/graph-RhoMod-Test-Szen-2a-b-c-2021-06-07.pdf",%]