Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 0
sizeStates = 10
sizeConstants = 28
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] = "T in component uninfected_CD4 (cells_per_mm3)"
legend_constants[0] = "s in component uninfected_CD4 (cells_per_mm3_day)"
legend_constants[1] = "lambda in component uninfected_CD4 (per_day)"
legend_states[1] = "T1_star in component productively_infected_CD4 (cells_per_mm3)"
legend_states[2] = "T2_star in component productively_infected_CD4 (cells_per_mm3)"
legend_constants[2] = "Tmax in component uninfected_CD4 (cells_per_mm3)"
legend_constants[3] = "mu in component uninfected_CD4 (per_day)"
legend_constants[4] = "k1 in component productively_infected_CD4 (ml_per_virons_day)"
legend_constants[5] = "r1 in component drug_parameters (dimensionless)"
legend_states[3] = "V1_I in component virus_strain1 (virons_per_ml)"
legend_constants[6] = "k2 in component productively_infected_CD4 (ml_per_virons_day)"
legend_constants[7] = "r2 in component drug_parameters (dimensionless)"
legend_states[4] = "V2_I in component virus_strain2 (virons_per_ml)"
legend_states[5] = "M in component uninfected_long_lived_cells (cells_per_mm3)"
legend_constants[8] = "lambda_M in component uninfected_long_lived_cells (cells_per_mm3_day)"
legend_constants[9] = "mu_M in component uninfected_long_lived_cells (per_day)"
legend_constants[10] = "k1_M in component productively_infected_long_lived_cells (ml_per_virons_day)"
legend_constants[11] = "k2_M in component productively_infected_long_lived_cells (ml_per_virons_day)"
legend_constants[12] = "m11 in component productively_infected_CD4 (dimensionless)"
legend_constants[13] = "m21 in component productively_infected_CD4 (dimensionless)"
legend_constants[14] = "delta1 in component productively_infected_CD4 (per_day)"
legend_constants[15] = "m22 in component productively_infected_CD4 (dimensionless)"
legend_constants[16] = "m12 in component productively_infected_CD4 (dimensionless)"
legend_constants[17] = "delta2 in component productively_infected_CD4 (per_day)"
legend_states[6] = "M1_star in component productively_infected_long_lived_cells (cells_per_mm3)"
legend_constants[18] = "delta1_M in component productively_infected_long_lived_cells (per_day)"
legend_states[7] = "M2_star in component productively_infected_long_lived_cells (cells_per_mm3)"
legend_constants[19] = "delta2_M in component productively_infected_long_lived_cells (per_day)"
legend_constants[20] = "p1 in component drug_parameters (dimensionless)"
legend_constants[21] = "N1 in component virus_strain1 (virons_per_cell)"
legend_constants[22] = "N1_M in component virus_strain1 (virons_per_cell)"
legend_states[8] = "V1 in component virus_strain1 (virons_per_ml)"
legend_constants[23] = "c1 in component virus_strain1 (per_day)"
legend_constants[24] = "p2 in component drug_parameters (dimensionless)"
legend_constants[25] = "N2 in component virus_strain2 (virons_per_cell)"
legend_constants[26] = "N2_M in component virus_strain2 (virons_per_cell)"
legend_constants[27] = "c2 in component virus_strain2 (per_day)"
legend_states[9] = "V2 in component virus_strain2 (virons_per_ml)"
legend_rates[0] = "d/dt T in component uninfected_CD4 (cells_per_mm3)"
legend_rates[5] = "d/dt M in component uninfected_long_lived_cells (cells_per_mm3)"
legend_rates[1] = "d/dt T1_star in component productively_infected_CD4 (cells_per_mm3)"
legend_rates[2] = "d/dt T2_star in component productively_infected_CD4 (cells_per_mm3)"
legend_rates[6] = "d/dt M1_star in component productively_infected_long_lived_cells (cells_per_mm3)"
legend_rates[7] = "d/dt M2_star in component productively_infected_long_lived_cells (cells_per_mm3)"
legend_rates[3] = "d/dt V1_I in component virus_strain1 (virons_per_ml)"
legend_rates[8] = "d/dt V1 in component virus_strain1 (virons_per_ml)"
legend_rates[4] = "d/dt V2_I in component virus_strain2 (virons_per_ml)"
legend_rates[9] = "d/dt V2 in component virus_strain2 (virons_per_ml)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 178.81
constants[0] = 0
constants[1] = 0.01
states[1] = 1.19
states[2] = 0.004
constants[2] = 450
constants[3] = 0.0014
constants[4] = 3.43E-8
constants[5] = 0.9
states[3] = 133500
constants[6] = 3.43E-8
constants[7] = 0.25
states[4] = 450
states[5] = 49.2
constants[8] = 2.0
constants[9] = 0.04
constants[10] = 4.67E-9
constants[11] = 4.67E-9
constants[12] = 1
constants[13] = 3.4E-5
constants[14] = 0.69
constants[15] = 1
constants[16] = 3.4E-5
constants[17] = 0.69
states[6] = 0.49
constants[18] = 0.062
states[7] = 1.7E-3
constants[19] = 0.062
constants[20] = 0.99
constants[21] = 480.1
constants[22] = 534.4
states[8] = 133500
constants[23] = 3.07
constants[24] = 0.25
constants[25] = 475.3
constants[26] = 529.0
constants[27] = 3.07
states[9] = 450
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[0] = (((constants[0]+constants[1]*states[0]*(1.00000-(states[0]+states[1]+states[2])/constants[2]))-constants[3]*states[0])-constants[4]*(1.00000-constants[5])*states[0]*states[3])-constants[6]*(1.00000-constants[7])*states[0]*states[4]
rates[5] = ((constants[8]-constants[9]*states[5])-constants[10]*(1.00000-constants[5])*states[5]*states[3])-constants[11]*(1.00000-constants[7])*states[5]*states[4]
rates[1] = (constants[12]*constants[4]*(1.00000-constants[5])*states[0]*states[3]+constants[13]*constants[6]*(1.00000-constants[7])*states[0]*states[4])-constants[14]*states[1]
rates[2] = (constants[15]*constants[6]*(1.00000-constants[7])*states[0]*states[4]+constants[16]*constants[4]*(1.00000-constants[5])*states[0]*states[3])-constants[17]*states[2]
rates[6] = (constants[12]*constants[10]*(1.00000-constants[5])*states[5]*states[3]+constants[13]*constants[11]*(1.00000-constants[7])*states[5]*states[4])-constants[18]*states[6]
rates[7] = (constants[15]*constants[11]*(1.00000-constants[7])*states[5]*states[4]+constants[16]*constants[10]*(1.00000-constants[5])*states[5]*states[3])-constants[19]*states[7]
rates[3] = ((1.00000-constants[20])*constants[21]*constants[14]*states[1]+(1.00000-constants[20])*constants[22]*constants[18]*states[6])-constants[23]*states[3]
rates[8] = (constants[21]*constants[14]*states[1]+constants[22]*constants[18]*states[6])-constants[23]*states[8]
rates[4] = ((1.00000-constants[24])*constants[25]*constants[17]*states[2]+(1.00000-constants[24])*constants[26]*constants[19]*states[7])-constants[27]*states[4]
rates[9] = (constants[25]*constants[17]*states[2]+constants[26]*constants[19]*states[7])-constants[27]*states[9]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
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)