Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 9
sizeStates = 16
sizeConstants = 14
from math import *
from numpy import *
def createLegends():
legend_states = [""] * sizeStates
legend_rates = [""] * sizeStates
legend_algebraic = [""] * sizeAlgebraic
legend_voi = ""
legend_constants = [""] * sizeConstants
legend_voi = "time in component environment (day)"
legend_states[0] = "B0 in component B0 (cells_per_GC)"
legend_constants[0] = "pr in component kinetic_parameters (dimensionless)"
legend_constants[1] = "mu in component kinetic_parameters (first_order_rate_constant)"
legend_constants[2] = "rho in component kinetic_parameters (first_order_rate_constant)"
legend_constants[3] = "delta_B in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[0] = "CT_star in component CT_star (cells_per_GC)"
legend_states[1] = "B1 in component B1 (cells_per_GC)"
legend_algebraic[4] = "alpha_B in component alpha_B (dimensionless)"
legend_states[2] = "B2 in component B2 (cells_per_GC)"
legend_states[3] = "B3 in component B3 (cells_per_GC)"
legend_states[4] = "B4 in component B4 (cells_per_GC)"
legend_states[5] = "B5 in component B5 (cells_per_GC)"
legend_states[6] = "B6 in component B6 (cells_per_GC)"
legend_states[7] = "B7 in component B7 (cells_per_GC)"
legend_states[8] = "B8 in component B8 (cells_per_GC)"
legend_states[9] = "B9 in component B9 (cells_per_GC)"
legend_states[10] = "B10 in component B10 (cells_per_GC)"
legend_algebraic[1] = "B_sum in component centroblasts_sum (cells_per_GC)"
legend_states[11] = "C in component C (cells_per_GC)"
legend_constants[4] = "d in component C (first_order_rate_constant)"
legend_states[12] = "C_star in component C_star (cells_per_GC)"
legend_algebraic[2] = "CA in component CA (cells_per_GC)"
legend_algebraic[5] = "C_starsum in component centrocytes_sum (cells_per_GC)"
legend_states[13] = "M in component M (cells_per_GC)"
legend_states[14] = "A in component A (cells_per_GC)"
legend_constants[5] = "z in component A (first_order_rate_constant)"
legend_constants[6] = "u in component A (dimensionless)"
legend_algebraic[3] = "log_A in component A (dimensionless)"
legend_states[15] = "T in component T (cells_per_GC)"
legend_constants[7] = "p in component T (first_order_rate_constant)"
legend_constants[8] = "sigma in component T (first_order_rate_constant)"
legend_constants[9] = "delta_T in component T (first_order_rate_constant)"
legend_algebraic[6] = "alpha_T in component alpha_T (dimensionless)"
legend_constants[10] = "SA in component CA (dimensionless)"
legend_constants[11] = "ST in component CT_star (dimensionless)"
legend_constants[12] = "KB in component alpha_B (dimensionless)"
legend_constants[13] = "KT in component alpha_T (dimensionless)"
legend_algebraic[7] = "total in component total (cells_per_GC)"
legend_algebraic[8] = "log_total in component total (dimensionless)"
legend_rates[0] = "d/dt B0 in component B0 (cells_per_GC)"
legend_rates[1] = "d/dt B1 in component B1 (cells_per_GC)"
legend_rates[2] = "d/dt B2 in component B2 (cells_per_GC)"
legend_rates[3] = "d/dt B3 in component B3 (cells_per_GC)"
legend_rates[4] = "d/dt B4 in component B4 (cells_per_GC)"
legend_rates[5] = "d/dt B5 in component B5 (cells_per_GC)"
legend_rates[6] = "d/dt B6 in component B6 (cells_per_GC)"
legend_rates[7] = "d/dt B7 in component B7 (cells_per_GC)"
legend_rates[8] = "d/dt B8 in component B8 (cells_per_GC)"
legend_rates[9] = "d/dt B9 in component B9 (cells_per_GC)"
legend_rates[10] = "d/dt B10 in component B10 (cells_per_GC)"
legend_rates[11] = "d/dt C in component C (cells_per_GC)"
legend_rates[12] = "d/dt C_star in component C_star (cells_per_GC)"
legend_rates[13] = "d/dt M in component M (cells_per_GC)"
legend_rates[14] = "d/dt A in component A (cells_per_GC)"
legend_rates[15] = "d/dt T in component T (cells_per_GC)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 3
constants[0] = 0.15
constants[1] = 3
constants[2] = 4
constants[3] = 0.8
states[1] = 0
states[2] = 0
states[3] = 0
states[4] = 0
states[5] = 0
states[6] = 0
states[7] = 0
states[8] = 0
states[9] = 0
states[10] = 0
states[11] = 0
constants[4] = 2
states[12] = 0
states[13] = 0
states[14] = 500
constants[5] = 0.02
constants[6] = 0.15
states[15] = 0
constants[7] = 2
constants[8] = 5
constants[9] = 0.8
constants[10] = 500
constants[11] = 50
constants[12] = 1e4
constants[13] = 100
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[11] = constants[4]*constants[2]*states[10]*1.00000-constants[1]*states[11]
algebraic[0] = (states[12]*states[15])/(constants[11]*1.00000+states[12])
rates[0] = constants[0]*constants[1]*algebraic[0]-(constants[2]*states[0]+constants[3]*states[0])
algebraic[2] = (states[11]*states[14])/(constants[10]*1.00000+states[14])
rates[12] = constants[1]*algebraic[2]-constants[1]*states[12]
rates[13] = (1.00000-constants[0])*constants[1]*algebraic[0]
rates[14] = -constants[5]*states[14]-constants[6]*algebraic[2]*1.00000
algebraic[1] = states[1]+states[1]+states[3]+states[4]+states[5]+states[6]+states[6]+states[7]+states[8]+states[9]+states[10]
algebraic[4] = constants[12]/(constants[12]+algebraic[1]/1.00000)
rates[1] = constants[2]*(1.00000+algebraic[4])*states[0]-(constants[2]*states[1]+constants[3]*states[1])
rates[2] = constants[2]*(1.00000+algebraic[4])*states[1]-(constants[2]*states[2]+constants[3]*states[2])
rates[3] = constants[2]*(1.00000+algebraic[4])*states[2]-(constants[2]*states[3]+constants[3]*states[3])
rates[4] = constants[2]*(1.00000+algebraic[4])*states[3]-(constants[2]*states[4]+constants[3]*states[4])
rates[5] = constants[2]*(1.00000+algebraic[4])*states[4]-(constants[2]*states[5]+constants[3]*states[5])
rates[6] = constants[2]*(1.00000+algebraic[4])*states[5]-(constants[2]*states[6]+constants[3]*states[6])
rates[7] = constants[2]*(1.00000+algebraic[4])*states[6]-(constants[2]*states[7]+constants[3]*states[7])
rates[8] = constants[2]*(1.00000+algebraic[4])*states[7]-(constants[2]*states[8]+constants[3]*states[8])
rates[9] = constants[2]*(1.00000+algebraic[4])*states[8]-(constants[2]*states[9]+constants[3]*states[9])
rates[10] = constants[2]*(1.00000+algebraic[4])*states[9]-(constants[2]*states[10]+constants[3]*states[10])
algebraic[6] = constants[13]/(constants[13]+states[15]/1.00000)
rates[15] = (constants[8]*1.00000+constants[7]*algebraic[6]*algebraic[0])-constants[9]*states[15]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = (states[12]*states[15])/(constants[11]*1.00000+states[12])
algebraic[2] = (states[11]*states[14])/(constants[10]*1.00000+states[14])
algebraic[1] = states[1]+states[1]+states[3]+states[4]+states[5]+states[6]+states[6]+states[7]+states[8]+states[9]+states[10]
algebraic[4] = constants[12]/(constants[12]+algebraic[1]/1.00000)
algebraic[6] = constants[13]/(constants[13]+states[15]/1.00000)
algebraic[3] = log(states[14]/1.00000, 10)
algebraic[5] = states[11]+states[12]
algebraic[7] = algebraic[1]+algebraic[5]
algebraic[8] = log(algebraic[7]/1.00000+1.00000e-12, 10)
return algebraic
def solve_model():
"""Solve model with ODE solver"""
from scipy.integrate import ode
# Initialise constants and state variables
(init_states, constants) = initConsts()
# Set timespan to solve over
voi = linspace(0, 10, 500)
# Construct ODE object to solve
r = ode(computeRates)
r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1)
r.set_initial_value(init_states, voi[0])
r.set_f_params(constants)
# Solve model
states = array([[0.0] * len(voi)] * sizeStates)
states[:,0] = init_states
for (i,t) in enumerate(voi[1:]):
if r.successful():
r.integrate(t)
states[:,i+1] = r.y
else:
break
# Compute algebraic variables
algebraic = computeAlgebraic(constants, states, voi)
return (voi, states, algebraic)
def plot_model(voi, states, algebraic):
"""Plot variables against variable of integration"""
import pylab
(legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends()
pylab.figure(1)
pylab.plot(voi,vstack((states,algebraic)).T)
pylab.xlabel(legend_voi)
pylab.legend(legend_states + legend_algebraic, loc='best')
pylab.show()
if __name__ == "__main__":
(voi, states, algebraic) = solve_model()
plot_model(voi, states, algebraic)