b=μ-g;g=0.001037052​​μ=0.00616/12​​
μ
1
=0.544/12​​
η
1
=0.0002476904​​
η
2
=0.088256814​​
β
1
=0.005026665​​
β
2
=0.045262083​​
γ
1
=0​​
γ
2
=0.91924​​
γ
3
=0.456/12​​ρ=0.9384​​
ρ
1
=0​​ω=0.080716​​l=l​​h=h​​
Clear[c]
In[]:=
NDSolve[{S'[t]b-(
η
1
S[t]A[t]+
β
1
S[t]C[t])-(μ+g)S[t],Y'[t]gS[t]-(
η
2
Y[t]A[t]+
β
2
Y[t]C[t])-μY[t],L'[t](
η
1
S[t]+
η
2
Y[t])A[t]+(
β
1
S[t]+
β
2
Y[t])C[t]-(μ+
μ
1
+hρ)L[t],A'[t]hρL[t]+
ρ
1
C[t]-(μ+
γ
2
)A[t]-(1-l)ωA[t],C'[t](1-l)ωA[t]-(μ+
μ
1
+
ρ
1
+
γ
3
)C[t],​​R'[t](1-h)
γ
1
L[t]+l
γ
2
A[t]+
γ
3
C[t]-μR[t],​​S[0]657824,​​Y[0]32331634,​​L[0]0,​​A[0]20143,​​C[t]1745,​​R[0]0},​​{S[t],Y[t],L[t],A[t],C[t],R[t]},{t,0,12}]
NDSolve
:There are fewer dependent variables, {A[t],L[t],R[t],S[t],Y[t]}​, than equations, so the system is overdetermined.
Out[]=
NDSolve[{
′
S
[t]-0.000523719-0.00155039S[t]-0.00024769A[t]S[t]-0.00502667

t
S[t],
′
Y
[t]0.00103705S[t]-0.000513333Y[t]-0.0882568A[t]Y[t]-0.0452621

t
Y[t],
′
L
[t]-(0.0458467+0.9384h)L[t]+

t
(0.00502667S[t]+0.0452621Y[t])+A[t](0.00024769S[t]+0.0882568Y[t]),
′
A
[t]-0.919753A[t]-0.080716(1-l)A[t]+0.9384hL[t],
′
C
[t]0.080716(1-l)A[t]-0.0838467

t
,
′
R
[t]0.91924lA[t]+0.038

t
-0.000513333R[t],S[0]657824,Y[0]32331634,L[0]0,A[0]20143,

t
1745,R[0]0},{S[t],Y[t],L[t],A[t],

t
,R[t]},{t,0,12}]