Sehingga diperoleh nilai eigen
2
J yaitu:
1 1
3 3
2 3
1 1
1 3
3 2
3 1
3 2
3 2
1 1
1 3
3 2
3 3
1 3
2 3
3 1
1 1
3 3
2 3
3 4
2 1
4 3 2
3 4
1 3
1 1
3 4
6 2 3 2
4 1
3 1
1 3
4 6 2
3 2 4
m m
m m
m m
v u
w w
v T
T w
w v
i v
u i
w w
v T
T w
w v
i v
u i
w w
v T
T w
w v
c
λ
λ
λ λ
⎡ ⎤
→ − − +
+ +
⎣ ⎦
⎡ ⎤
+ +
⎣ ⎦
+ ⎡
⎤ → − +
− −
+ +
⎣ ⎦
⎡ ⎤
+ +
⎣ ⎦
− ⎡
⎤ → − +
− +
+ +
⎣ ⎦
⎡ ⎤
+ +
⎣ ⎦
→ −
Lampiran 10 Gambar dinamika populasi virus HIV saat
1 R
dengan Mathematica 7
Untuk memperoleh gambar dinamika populasi Gambar 4.5 dapat program sebagai berikut
1. Saat
0.25
PI
η
=
m m
s:=3 ; p:=6 ; T :=10 ; d:=0.5 ; δ:=0.6 ; c:=9 ; k:=0.01 ; N1:=12 ;
: 0.25; Solve[{s + pT11- T1 T - dT1- kV1T1==0,
kV1T1- δT2==0, 1
N1 T2 -cV1==0, N1
δT2-cVni==0},{T1,T2,V1,Vni}]
pi pi
pi
η η
δ η
= −
m
spd=NDSolve[{ T1[t]==s +pT1[t]1-T1[t] T -dT1[t]-kV1[t]T1[t],
T2[t]==kV1[t]T1[t]- δT2[t],
V1[t]==1 N1 T2[t]-cV1[t],
Vni[t]== N1
δT2[t]-cVni[t], T1[0]==2,T2[0]==0.5,V1[0]==0.2, Vni[
pi pi
η δ
η −
0]==0.1}, {T1[t],T2[t],V1[t], Vni[t]},{t ,0,50}]
vta1=Plot[{T1[t].spd[[1,1]]},{t ,0,50},PlotRange {{0,1},{0,15}}, PlotStyle
{Dotdashed, Red,Thick}, FrameLabel
{Waktu,Sel Darah PutihSehat}, Frame {{True,Fals
→ →
→ →
e},{True, False}}] vta2=Plot[{T2[t].spd[[1,2]]},{t ,0,50},PlotRange
{{0,5},{0,1}}, PlotStyle {Dotdashed, Red,Thick},
FrameLabel {Waktu,Sel Darah Putih Terinfeksi}, Frame
{{True, False},{True,False}}] vta3=Pl
→ →
→ →
ot[{V1[t].spd[[1,3]]},{t ,0,50},PlotRange {{0,5},{0,0.5}},PlotStyle
{Dotdashed,Red,Thick}, FrameLabel
{Waktu,Virus yangdapat menginfeksi}, Frame {{True,False},{True, False}}]
vta4=Plot[{Vni[t].spd[[1,4 →
→ →
→ ]]},{t ,0,50}, PlotRange
{{0,5},{0,0.5}},PlotStyle {Dotdashed,Red,Thick},
FrameLabel {Waktu,Virus yang tidak dapat menginfeksi},Frame
{{True, False},{True, False}}] spd=NDSolve[{
T1[t]==s +pT1[t]1-T1[t] T →
→ →
→
m
-dT1[t]-kV1[t]T1[t], T2[t]==kV1[t]T1[t]-
δT2[t], V1[t]==1
N1 T2[t]-cV1[t], Vni[t]==
N1 δT2[t]-cVni[t],
T1[0]==6,T2[0]==0.8,V1[0]==0.4, Vni[0]==0.5}, {T1[t],T2[t],V1[t], Vni[t]},{t ,0,
pi pi
η δ
η −
50}]
vta5=Plot[{T1[t].spd[[1,1]]},{t ,0,50}, PlotRange {{0,1},{0,15}},
FrameLabel {Waktu,Sel Darah PutihSehat}, PlotStyle
{Dashed,Magenta ,Thick}, Frame
{{True, False},{True, False}}] vta6=Plot[{T2[t].spd[[1,2]
→ →
→ →
]},{t ,0,50}, PlotRange {{0,5},{0,1}},
FrameLabel {Waktu,Sel Darah Putih Terinfeksi}, PlotStyle
{Dashed,Magenta ,Thick}, Frame
{{True, False},{True, False}}] vta7=Plot[{V1[t].spd[[1,3]]},{t ,0,50}, PlotRange
{ →
→ →
→ → {0,5},{0,0.5}},
FrameLabel {Waktu,Virus yang dapat menginfeksi}, PlotStyle
{Dashed,Magenta ,Thick}, Frame
{{True, False},{True, False}}] vta8=Plot[{Vni[t].spd[[1,4]]},{t ,0,50}, PlotRange
{{0,5},{0,0.5}}, Fra
→ →
→ →
m
meLabel {Waktu,Virus yang tidak dapat menginfeksi}, PlotStyle
{Dashed,Magenta ,Thick}, Frame
{{True, False},{True, False}}] spd=NDSolve[{
T1[t]==s + pT1[t]1-T1[t] T -dT1[t]- kV1[t]T1[t], T2[t]==kV1[t]
→ →
→
T1[t]- δT2[t],
V1[t]==1 N1 T2[t]-cV1[t],
Vni[t]== N1
δT2[t]-cVni[t], T1[0]==12,T2[0]==0.2, V1[0]==0.1, Vni[0]==0.3},
{T1[t],T2[t], V1[t], Vni[t]},{t ,0,50}]
pi pi
η δ
η −
vta9=Plot [{T1[t] .spd[[1,1]]},{t ,0,50}, PlotRange {{0,1},{0,15}},
FrameLabel {Waktu,Sel Darah Putih Sehat}, PlotStyle
{Dotted ,Blue , Thick}, Frame
{{True , False},{True , False}}] vta10=Plot [{T2[t] .spd[[1,2]]}
→ →
→ →
,{t ,0,50}, PlotRange {{0,5},{0,1}},
FrameLabel {Waktu,Sel Darah Putih Terinfeksi}, PlotStyle
{Dotted ,Blue , Thick}, Frame
{{True , False},{True , False}}] vta11=Plot [{V1[t] .spd[[1,3]]},{t ,0, 50}, PlotRange
{{0, 5 →
→ →
→ →
},{0, 0.5}}, FrameLabel
{Waktu,Virus yang dapat menginfeksi}, PlotStyle {Dotted ,Blue , Thick},
Frame {{True , False},{True , False}}]
vta12=Plot [{Vni[t] .spd[[1,4]]},{t ,0,50}, PlotRange {{0,5},{0, 0.5}},
FrameLabe →
→ →
→ l
{Waktu,Virus yang tidak dapat menginfeksi}, PlotStyle {Dotted ,Blue , Thick},
Frame {{True , False},{True , False}}]
→ →
→ Show [ vta1, vta5, vta9 ]
Show [ vta2, vta6, vta10 ] Show [ vta3, vta7 , vta11]
Show [ vta4, vta8, vta12 ]
2. Saat
