DESCRIPTION: Model cell reconstitution after Hematopoietic Stem Cell Transplant (HSCT) before  ATI
[LONGITUDINAL]

input = {ke,rp,rs,rm,re,qdns,lambdap,lambdanss,lambdasns,lambdame,log10Kp,log10Kps,log10Kpm,log10Kpe, log10P0 ,log10NS0,log10S0,log10M0,log10E0,GM,fp100,T01}

fp100 = {use=regressor}
T01 = {use=regressor}

EQUATION:
odeType = stiff

fp = fp100/100


lambdapns=lambdap
lambdapm = lambdap

dns = (qdns+1)*lambdanss
dnsp = qdns*lambdanss

W = 5
pb = 1
VolB = 60*W*1e3

Kp = 10^log10Kp
Ks = 10^(log10Kp-log10Kps)
Km = 10^(log10Kp-log10Kpm)
Ke = 10^(log10Kp-log10Kpe)

t0 = 0

if(GM==0)
  qNSS = (rs/lambdanss)*(Kp/Ks-1)
  qPS  = (1/lambdapns)*(dns*qNSS-lambdasns)
  qPM  = (rm/lambdapm)*(Kp/Km-1)
  qME  = (re/lambdame)*(Kp/Ke-1)

  Ei  = Kp/(qNSS*qPM*qME/qPS + qPM*qME/qPS + qME +1)
  Mi  = qME*Ei
  Si  = (qPM/qPS)*Mi
  NSi = qNSS*Si
  Pi  = qPS*Si

  T0  = 0
  P0  = Pi
  NS0 = NSi
  S0  = Si
  M0  = Mi
  E0  = Ei
else 
  T0 = T01*W
  P0  = 10^log10P0
  S0  = 10^log10S0
  NS0 = 10^log10NS0
  M0  = 10^log10M0
  E0  = 10^log10E0
end

Pp_0 = 0
NSp_0 = 0
NSp2_0 = 0
Tp_0 = fp*T0

T_0 = (1-fp)*T0
P_0 = P0
NS_0 = NS0
S_0 = S0
M_0 = M0
E_0 = E0


ddt_Tp   =  -ke*Tp
ddt_Pp   =  ke*Tp + rp*(1-(NS+NSp+ NSp2 +S+M+E)/Kp)*Pp
ddt_NSp  =  lambdapns*Pp - dns*NSp+ lambdasns*NSp2
ddt_NSp2 =  lambdanss*NSp  + rs*(1-(NS+NSp+NSp2+S+M+E)/Ks)*NSp2
    

ddt_T   =  -ke*T
ddt_P   =  ke*T + rp*(1-(NS+NSp+ NSp2 +S+M+E)/Kp)*P

ddt_NS  =  lambdapns*P  - dns*NS  + lambdasns*S
ddt_S   =  lambdanss*NS + rs*(1-(NS+NSp+ NSp2 +S+M+E)/Ks)*S

ddt_M   =  lambdapm*(P+Pp) + rm*(1-(NS+NSp+ NSp2 +S+M+E)/Km)*M
ddt_E   =  lambdame*M + re*(1-(NS+NSp+ NSp2 +S+M+E)/Ke)*E

S_b = log10(max(pb*(S)/VolB, 1e-3))
NS_b = log10(max(pb*(NS+NSp+ NSp2)/VolB, 1e-3))
NSp_b = log10(max(pb*(NSp+ NSp2)/VolB, 1e-3))
CD8_b =log10(max(pb*(M+E)/VolB, 1e-3))
E_b = log10(max(pb*(E)/VolB, 1e-3))
M_b = log10(max(pb*(M)/VolB, 1e-3))


OUTPUT:
output = {S_b,NS_b,CD8_b,E_b,M_b,NSp_b}
