DESCRIPTION: arthritis development model of Koch

[LONGITUDINAL]
input = {a, b, I0, alpha, beta, CL, V1, V2, sigma1, sigma2, sigma3, k1, k2, k3, k4, k5, tau}

EQUATION:
; initialization of the time
t0 = 0

; initialization of the variable of interest
I_0 = I0
D_0 = 0
G_0 = a*exp(b*t)

K12 = alpha*beta*V2/CL
K21 = alpha*beta*V1/CL
Cc = pkmodel(k12=K12,k21=K21,V=V1,Cl=CL)
E = (sigma1*exp(- sigma2*Cc) + sigma3)*Cc

ddt_G = k3 - E*G - (k1/k2)*(1- exp(- k2*t))*G
ddt_I = k4*G - k4*delay(G,tau)
ddt_D = - k5*D + k4*delay(G,tau)


TAS = I+D
AKS = D

[INDIVIDUAL]
input = {tau_pop, omega_tau}

DEFINITION:
tau = {distribution = normal, mean = tau_pop, sd = omega_tau}