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Leukopoiesis Model

Model Type
SES Library XPP model

# Eqn 1:

#β(Q) is the introduction rate

#β0 represents the maximal rate of introduction in the proliferating phase

#θ1 is the value for which β reaches half of its maximal value

#n is the sen- sitivity of the rate of reintroduction

#Q is the quiscent cells

# Eqn 2:

#k(W) is the differentiation rate

#k0 is a proportionality coefficiet

#m and θ2 depend on the growth factors responsible for maturation of considered white blood cells

#W is lymphocytes (T, B, or NK)

# Eqn 3:

#Kv is the differentiation rate to other blood cells

#γ1 is the apoptosis rate for prolif. haematopoietic stem cells

#τ1 is the proliferation phase duration

# Eqn 4:

#A is the amplification parameter

#γ2 is the death rate of matured blood cells

#τ2 is the amplification phase duration

B-Cell

Modeling B-Cell reporductions where:
β0 =1.77 day−1,θ1 =1×108 cells/kg,n =3 , τ1 =0.05 day,γ1 =0.1day−1

k0 =0.1day−1,θ2 =1×108 cells/kg,m =2 , τ2 =2day,K =0.02 day−1,A =20 .

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$$\beta(Q) = \frac{\beta_0 heta_1^n}{ heta_1^n + Q^n}, \beta_0, heta_1>0 \\\r k(W)= \frac{k_0 heta_2^m}{ heta_2^m + W^m}, k_0, heta_2>0 \\\r \frac{dQ}{dt} = -[K+k(W(t))+ \beta(Q(t))]Q(t)+ 2e^{- \gamma_1 au_1} \beta(Q(t- au_1)) Q(t- au_1) \\\r \frac{dW}{dt} = - \gamma_2 W(t)+Ak(W(t- au_2))Q(t- au_2)$$
leukopoiesis.ode
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