# Immune HIV Dynamics
# Kirschner, D (1996)

# bifurcation parameter
p gV=2

p muT=0.02,muTi=0.24
p kV=2.4e-5,kT=7.4e-4
p r=0.01,N=1000,C=100
p b=10,amax=12,a1=0.25

# treatment parameters
#p p=0,p chemo=0,k=16.66

# Langevin eqs
#wiener w
#gV=gV0+sigma*w
#p gV0=7
#p sigma=0
# ------------

prolif(x,y)=r*x*y/(C+y)
s(V)=5+5/(1+V)

dTn/dt=s(V)-muT*Tn+prolif(Tn,V)-kV*Tn*V
dTi/dt=kV*Tn*V-muTi*Ti-prolif(Ti,V)
dV/dt=N*prolif(Ti,V)-kT*Tn*V+gV*V/(b+V)

init Tn=1000,Ti=0,V=1e-3

# XPP settings
@ bound=1000000,total=500
# Langevin eqs
#@ meth=euler
# ------------
# ODEs
@ meth=quadlk
# ------------
@ maxstor=100000
@ xp=t,yp=Tn,xlo=0,ylo=0,xhi=500,yhi=2500

# AUTO bifurcation settings
@ autoxmin=0,autoxmax=22,autoymin=-1,autoymax=600
@ dsmax=1.0,dsmin=.001,parmin=0.5,parmax=20

done