;Reference:  Ribba, Kaloshi, Peyre, et al. A Tumor Growth Inhibition Model for Low-Grade Glioma Treated with Chemotherapy or Radiotherapy. Clin Cancer Res. 2012;18(18):5071-80.

[LONGITUDINAL]	
input={lambdaP, kPQ, kQPP, gamma, deltaQP, KDE, P0, Q0}

EQUATION:
; definition of the initial time
t_0 = 0
; initialization of the ODEs
P_0 = P0
Q_0 = Q0
C_0 = 0
QP_0 = 0

K = 100
PSTAR = P+Q+QP
ddt_C = -KDE*C
ddt_P = lambdaP*P*(1-PSTAR/K) + kQPP*QP - kPQ*P - gamma*P*KDE*C
ddt_Q = kPQ*P - gamma*Q*KDE*C
ddt_QP = gamma*Q*KDE*C - kQPP*QP - deltaQP*QP


[INDIVIDUAL]
input = {lambdaP_pop, kPQ_pop, kQPP_pop, gamma_pop, deltaQP_pop, KDE_pop, P0_pop, Q0_pop, omega_lambdaP, omega_kPQ, omega_kQPP, omega_gamma, omega_deltaQP, omega_KDE, omega_P0, omega_Q0}  

DEFINITION:
lambdaP 	= {distribution = lognormal, typical = lambdaP_pop,	sd = omega_lambdaP}
kPQ      	= {distribution = lognormal, typical = kPQ_pop, 	sd = omega_kPQ}
kQPP    	= {distribution = lognormal, typical = kQPP_pop, 	sd = omega_kQPP}
gamma	= {distribution = lognormal, typical = gamma_pop, 	sd = omega_gamma}
deltaQP 	= {distribution = lognormal, typical = deltaQP_pop,	sd = omega_deltaQP}
KDE 	= {distribution = lognormal, typical = KDE_pop, 	sd = omega_KDE}
P0	= {distribution = lognormal, typical = P0_pop, 	sd = omega_P0}
Q0 	= {distribution = lognormal, typical = Q0_pop, 	sd = omega_Q0}