In[]:=
dtpts1a={{0,7.81},{7,11.00},{14,11.8},{15.38,11.875},{21,11.6},{28,10.9},{35,10.0},{42,9.11},{49,8.22},{56,7.38},{63,6.62},{70,5.92},{77,5.30},{84,4.74},{91,4.24},{98,3.79},{105,3.38},{112,3.02},{119,2.70}};(*RutherfordB,ProbableCure*)​​dtpts1b={{15.38,11.875},{21,11.6},{28,10.9},{35,10.0},{42,9.11},{49,8.22},{56,7.38},{63,6.62},{70,5.92},{77,5.30},{84,4.74},{91,4.24},{98,3.79},{105,3.38},{112,3.02},{119,2.70}};(*RutherfordB,ProbableCurefrommaxpointoutto120days*)​​dtpts1c={{10,11.7},{17,12.4},{24,9.91},{31,9.78},{38,10.1},{45,8.07},{52,7.80},{59,7.80},{66,6.17},{73,5.80},{80,5.59},{87,4.23},{94,3.78},{101,3.43},{108,2.26},{115,1.75}};(*DmpOsc*)​​​​dtpts1d={{0.0,10.8},{10,21.9},{20,50.2},{30,64.7},{40,60.4},{50,49.8},{60,44.4},{70,46.1},{80,50.1},{90,52.1},{100,51.4}};(*N049.9,Pf10.9,Pk-38.7k10.033,k20.105,c10.528,c24.12*)​​​​dtplt1a=ListPlot[dtpts1a,Frame->True,GridLines->Automatic,PlotRange->{{0,120},{0,15}},ImageSize->{575,366},Joined->True,Mesh->All,PlotStyle->{RGBColor[0,0,1],AbsolutePointSize[10]},AspectRatio->2/π,FrameLabel->{Style["Time (days)",Bold,Blue],Style["ProstateAg",Bold,Blue]},LabelStyle->Directive[Blue,Large]];​​​​dtplt1b=ListPlot[dtpts1b,Frame->True,GridLines->Automatic,PlotRange->{{0,120},{0,15}},ImageSize->{575,366},Joined->True,Mesh->All,PlotStyle->{RGBColor[0,0,1],AbsolutePointSize[10]},AspectRatio->2/π,FrameLabel->{Style["Time (days)",Bold,Blue],Style["ProstateAg",Bold,Blue]},LabelStyle->Directive[Blue,Large]];​​​​dtplt1c=ListPlot[dtpts1c,Frame->True,GridLines->Automatic,PlotRange->{{0,120},{0,15}},ImageSize->{575,366},Joined->True,Mesh->All,PlotStyle->{RGBColor[0,1,1],AbsolutePointSize[10]},AspectRatio->2/π,FrameLabel->{Style["Time (days)",Bold,Blue],Style["ProstateAg",Bold,Blue]},LabelStyle->Directive[Blue,Large]];​​dtplt1d=ListPlot[dtpts1d,Frame->True,GridLines->Automatic,PlotRange->{{0,120},{0,15}},ImageSize->{575,366},Joined->True,Mesh->All,PlotStyle->{RGBColor[0,0,1],AbsolutePointSize[10]},AspectRatio->2/π,FrameLabel->{Style["Time (days)",Bold,Blue],Style["ProstateAg",Bold,Blue]},LabelStyle->Directive[Blue,Large]];​​
In[]:=
E2aDampedOscillator:=N0+(Pf×((Exp[-(k1×t)])×((c1×Cos[k2×(t-Pk)]))));​​E2aDOsc[N0_,Pf_,Pk_,k1_,c1_,k2_]:=N0+(Pf×((Exp[-(k1×(t-Pk))])×((c1×Cos[k2×(t-Pk)]))));​​gRa[t_,r_,N0_,Pf_,Pk_,k1_,c1_,k2_]:=((t×r)+(E2aDOsc[N0,Pf,Pk,k1,c1,k2]));
In[]:=
​​Clear[t,E2DOsc,gR,r,N0,Pf,Pk,k1,c1,k2]​​E2DOsc[N0_,Pf_,Pk_,k1_,c1_,k2_]:=N0+(Pf×((Exp[-(k1×(t-Pk))])×((c1×Cos[k2×(t-Pk)]))));​​gR[t_,r_,N0_,Pf_,Pk_,k1_,c1_,k2_]:=((t×r)+(E2DOsc[N0,Pf,Pk,k1,c1,k2]));
In[]:=
Manipulate[Show[Plot[gR[t,r,N0,Pf,Pk,k1,c1,k2],{t,0.0,120.0},Frame->True,GridLines->Automatic,AxesOrigin->{0.0,0.0},PlotRange->{{0,120},{0,15}},ImageSize->{575,366},PlotStyle->{RGBColor[0,1,0],Thickness[0.01]},AspectRatio->2.0/π,FrameLabel->{Style["Time (days)",Bold,Blue],Style["ProstateAg",Bold,Blue]},LabelStyle->Directive[Blue,Large]],dtplt1b,dtplt1c],​​{{N0,13.0,Style["Initial (N0)",Blue,Bold,Medium]},0.0,20.0,0.00010,ControlType->Slider,ImageSize->Medium,DefaultBaseStyle->{Blue,Bold,Medium},Appearance->"Labeled"},{{Pf,1.0,Style["Power Factor (Pf)",Blue,Bold,Medium]},-10.0,10.0,0.00010,ControlType->Slider,ImageSize->Medium,DefaultBaseStyle->{Blue,Bold,Medium},Appearance->"Labeled"},{{Pk,16.0,Style["Peak Location (Pk)",Blue,Bold,Medium]},0.0,25.0,0.00010,ControlType->Slider,ImageSize->Medium,DefaultBaseStyle->{Blue,Bold,Medium},Appearance->"Labeled"},{{k1,0.016,Style["Damping (k1)",Blue,Bold,Medium]},-0.10,0.10,0.00010,ControlType->Slider,ImageSize->Medium,DefaultBaseStyle->{Blue,Bold,Medium},Appearance->"Labeled"},​​{{c1,1.5,Style["Cos (c1)",Blue,Bold,Medium]},0.0,5.0,0.00010,ControlType->Slider,ImageSize->Medium,DefaultBaseStyle->{Blue,Bold,Medium},Appearance->"Labeled"},{{k2,0.3,Style["Period (k2)",Blue,Bold,Medium]},0.010,0.50,0.00010,ControlType->Slider,ImageSize->Medium,DefaultBaseStyle->{Blue,Bold,Medium},Appearance->"Labeled"},{{r,-0.0975,Style["Rotate (r)",Blue,Bold,Medium]},-5,5,0.00010,ControlType->Slider,ImageSize->Medium,DefaultBaseStyle->{Blue,Bold,Medium},Appearance->"Labeled"},ControlPlacement->Top,Paneled->True,ImageMargins->0]​​​​
Out[]=
​
Initial (N0)
13.
Power Factor (Pf)
1.
Peak Location (Pk)
16.
Damping (k1)
0.016
Cos (c1)
1.5
Period (k2)
0.3
Rotate (r)
-0.0975
Show
,dtplt1b,dtplt1c
In[]:=
KinetE2DO=NonlinearModelFit[dtpts1c,gR[t,r,N0,Pf,Pk,k1,c1,k2],{{r,-0.0975},{N0,13},{Pf,1.0},{Pk,16},{k1,0.016},{c1,1.5},{k2,0.3}},t,Method->"Automatic"]
Out[]=
FittedModel
12.9925-0.0974099t+1.14724
-20(1)

Cos[0.300232(-16.0534+t)]

In[]:=
Normal[KinetE2DO]
Out[]=
12.9925-0.0974099t+1.14724
-0.0156507(-16.0534+t)

Cos[0.300232(-16.0534+t)]
In[]:=
KinetEBR["BestFitParameters"]
Out[]=
KinetEBR[BestFitParameters]
In[]:=
KinetE2DO["ParameterErrors"]
Out[]=
{0.000121521,0.00859839,0.00628255,0.0313888,0.000339868,0.0055232,0.000298436}
In[]:=
KinetE2DO["ParameterTable"]
Out[]=
Estimate
Standard Error
t-Statistic
P-Value
r
-0.0974099
0.000121521
-801.589
3.72634×
-23
10
N0
12.9925
0.00859839
1511.04
1.23985×
-25
10
Pf
1.00428
0.00628255
159.852
7.4608×
-17
10
Pk
16.0534
0.0313888
511.439
2.12652×
-21
10
k1
0.0156507
0.000339868
46.0494
5.37441×
-12
10
c1
1.14235
0.0055232
206.828
7.34551×
-18
10
k2
0.300232
0.000298436
1006.02
4.82386×
-24
10
In[]:=
KinetE2DOscMdl=Plot[{KinetE2DO[t]},{t,0,120},PlotRange->{{0,120},{0.0,15.0}},Frame->True,GridLines->Automatic,ImageSize->{575,366},PlotStyle->{Green,Thickness[0.01]},AspectRatio->2/π]
Out[]=
In[]:=
Show[dtplt1b,KinetE2DOscMdl]
Out[]=