Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 4
sizeStates = 20
sizeConstants = 26
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 (hour)"
legend_states[0] = "S_0 in component S_0 (dimensionless)"
legend_constants[15] = "R_0 in component R (first_order_rate_constant)"
legend_constants[16] = "u_s in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[0] = "phi in component phi (first_order_rate_constant)"
legend_states[1] = "S_1 in component S_1 (dimensionless)"
legend_constants[17] = "R_1 in component R (first_order_rate_constant)"
legend_constants[0] = "epsilon_s in component kinetic_parameters (first_order_rate_constant)"
legend_constants[1] = "alpha in component kinetic_parameters (dimensionless)"
legend_constants[2] = "u in component kinetic_parameters (first_order_rate_constant)"
legend_states[2] = "S_2 in component S_2 (dimensionless)"
legend_constants[18] = "R_2 in component R (first_order_rate_constant)"
legend_states[3] = "S_3 in component S_3 (dimensionless)"
legend_constants[19] = "R_3 in component R (first_order_rate_constant)"
legend_states[4] = "S_4 in component S_4 (dimensionless)"
legend_constants[20] = "R_4 in component R (first_order_rate_constant)"
legend_states[5] = "S_5 in component S_5 (dimensionless)"
legend_constants[21] = "R_5 in component R (first_order_rate_constant)"
legend_states[6] = "S_6 in component S_6 (dimensionless)"
legend_constants[22] = "R_6 in component R (first_order_rate_constant)"
legend_states[7] = "S_7 in component S_7 (dimensionless)"
legend_constants[23] = "R_7 in component R (first_order_rate_constant)"
legend_states[8] = "S_8 in component S_8 (dimensionless)"
legend_constants[24] = "R_8 in component R (first_order_rate_constant)"
legend_states[9] = "M_0 in component M_0 (dimensionless)"
legend_constants[3] = "epsilon_m in component kinetic_parameters (first_order_rate_constant)"
legend_constants[25] = "u_m in component kinetic_parameters (first_order_rate_constant)"
legend_states[10] = "M_1 in component M_1 (dimensionless)"
legend_states[11] = "M_1_2 in component M_1 (dimensionless)"
legend_states[12] = "M_2 in component M_2 (dimensionless)"
legend_states[13] = "M_3 in component M_3 (dimensionless)"
legend_states[14] = "M_4 in component M_4 (dimensionless)"
legend_states[15] = "M_5 in component M_5 (dimensionless)"
legend_states[16] = "M_6 in component M_6 (dimensionless)"
legend_states[17] = "M_7 in component M_7 (dimensionless)"
legend_states[18] = "M_8 in component M_8 (dimensionless)"
legend_constants[4] = "r_0 in component R (first_order_rate_constant)"
legend_constants[5] = "r_1 in component R (first_order_rate_constant)"
legend_constants[6] = "r_2 in component R (first_order_rate_constant)"
legend_constants[7] = "r_3 in component R (first_order_rate_constant)"
legend_constants[8] = "r_4 in component R (first_order_rate_constant)"
legend_constants[9] = "r_5 in component R (first_order_rate_constant)"
legend_constants[10] = "r_6 in component R (first_order_rate_constant)"
legend_constants[11] = "r_7 in component R (first_order_rate_constant)"
legend_constants[12] = "r_8 in component R (first_order_rate_constant)"
legend_constants[13] = "a in component kinetic_parameters (dimensionless)"
legend_states[19] = "w in component w (dimensionless)"
legend_algebraic[1] = "total_cells in component total_cells (dimensionless)"
legend_algebraic[2] = "stable_total in component total_cells (dimensionless)"
legend_algebraic[3] = "mutant_total in component total_cells (dimensionless)"
legend_constants[14] = "beta in component kinetic_parameters (dimensionless)"
legend_rates[0] = "d/dt S_0 in component S_0 (dimensionless)"
legend_rates[1] = "d/dt S_1 in component S_1 (dimensionless)"
legend_rates[2] = "d/dt S_2 in component S_2 (dimensionless)"
legend_rates[3] = "d/dt S_3 in component S_3 (dimensionless)"
legend_rates[4] = "d/dt S_4 in component S_4 (dimensionless)"
legend_rates[5] = "d/dt S_5 in component S_5 (dimensionless)"
legend_rates[6] = "d/dt S_6 in component S_6 (dimensionless)"
legend_rates[7] = "d/dt S_7 in component S_7 (dimensionless)"
legend_rates[8] = "d/dt S_8 in component S_8 (dimensionless)"
legend_rates[9] = "d/dt M_0 in component M_0 (dimensionless)"
legend_rates[10] = "d/dt M_1 in component M_1 (dimensionless)"
legend_rates[11] = "d/dt M_1_2 in component M_1 (dimensionless)"
legend_rates[12] = "d/dt M_2 in component M_2 (dimensionless)"
legend_rates[13] = "d/dt M_3 in component M_3 (dimensionless)"
legend_rates[14] = "d/dt M_4 in component M_4 (dimensionless)"
legend_rates[15] = "d/dt M_5 in component M_5 (dimensionless)"
legend_rates[16] = "d/dt M_6 in component M_6 (dimensionless)"
legend_rates[17] = "d/dt M_7 in component M_7 (dimensionless)"
legend_rates[18] = "d/dt M_8 in component M_8 (dimensionless)"
legend_rates[19] = "d/dt w in component w (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 0.5
states[1] = 0
constants[0] = 0.99
constants[1] = 0.6
constants[2] = 0.07
states[2] = 0
states[3] = 0
states[4] = 0
states[5] = 0
states[6] = 0
states[7] = 0
states[8] = 0
states[9] = 0.5
constants[3] = 0.1
states[10] = 0
states[11] = 0
states[12] = 0
states[13] = 0
states[14] = 0
states[15] = 0
states[16] = 0
states[17] = 0
states[18] = 0
constants[4] = 0.5
constants[5] = 0.6
constants[6] = 0.7
constants[7] = 0.8
constants[8] = 0.9
constants[9] = 1
constants[10] = 1.1
constants[11] = 1.2
constants[12] = 1.3
constants[13] = 0.5
states[19] = 0
constants[14] = 0.2
constants[15] = constants[4]
constants[16] = constants[2]*(1.00000-(constants[14]*constants[0])/1.00000)
constants[17] = constants[5]*(1.00000-constants[13])
constants[18] = constants[6]*(1.00000-constants[13])
constants[19] = constants[7]*(1.00000-constants[13])
constants[20] = constants[8]*(1.00000-constants[13])
constants[21] = constants[9]*(1.00000-constants[13])
constants[22] = constants[10]*(1.00000-constants[13])
constants[23] = constants[11]*(1.00000-constants[13])
constants[24] = constants[12]*(1.00000-constants[13])
constants[25] = constants[2]*(1.00000-(constants[14]*constants[3])/1.00000)
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[10] = states[9]*1.00000
algebraic[0] = ((1.00000-constants[16])/1.00000)*(constants[15]*states[0]+constants[17]*states[1]+constants[18]*states[2]+constants[19]*states[3]+constants[20]*states[4])+((1.00000-constants[25])/1.00000)*(constants[17]*states[10]+constants[18]*states[12]+constants[19]*states[13]+constants[20]*states[14])
rates[0] = ((constants[15]*states[0])/1.00000)*(1.00000-constants[16])-algebraic[0]*states[0]
rates[1] = (((constants[1]*constants[2]*constants[15]*states[0])/1.00000)*(1.00000-constants[0])+((constants[17]*states[1])/1.00000)*(1.00000-constants[16]))-algebraic[0]*states[1]
rates[2] = (((constants[1]*constants[2]*constants[17]*states[1])/1.00000)*(1.00000-constants[0])+((constants[18]*states[2])/1.00000)*(1.00000-constants[16]))-algebraic[0]*states[2]
rates[3] = (((constants[1]*constants[2]*constants[18]*states[2])/1.00000)*(1.00000-constants[0])+((constants[19]*states[3])/1.00000)*(1.00000-constants[16]))-algebraic[0]*states[3]
rates[4] = (((constants[1]*constants[2]*constants[19]*states[3])/1.00000)*(1.00000-constants[0])+((constants[20]*states[4])/1.00000)*(1.00000-constants[16]))-algebraic[0]*states[4]
rates[5] = (((constants[1]*constants[2]*constants[20]*states[4])/1.00000)*(1.00000-constants[0])+((constants[21]*states[5])/1.00000)*(1.00000-constants[16]))-algebraic[0]*states[5]
rates[6] = (((constants[1]*constants[2]*constants[21]*states[5])/1.00000)*(1.00000-constants[0])+((constants[22]*states[6])/1.00000)*(1.00000-constants[16]))-algebraic[0]*states[6]
rates[7] = (((constants[1]*constants[2]*constants[22]*states[6])/1.00000)*(1.00000-constants[0])+((constants[23]*states[7])/1.00000)*(1.00000-constants[16]))-algebraic[0]*states[7]
rates[8] = (((constants[1]*constants[2]*constants[23]*states[7])/1.00000)*(1.00000-constants[0])+((constants[24]*states[8])/1.00000)*(1.00000-constants[16]))-algebraic[0]*states[8]
rates[9] = ((constants[15]*states[9])/1.00000)*(1.00000-constants[25])-algebraic[0]*states[9]
rates[11] = (((constants[1]*constants[2]*constants[15]*states[9])/1.00000)*(1.00000-constants[3])+((constants[17]*states[10])/1.00000)*(1.00000-constants[25]))-algebraic[0]*states[10]
rates[12] = (((constants[1]*constants[2]*constants[17]*states[10])/1.00000)*(1.00000-constants[3])+((constants[18]*states[12])/1.00000)*(1.00000-constants[25]))-algebraic[0]*states[12]
rates[13] = (((constants[1]*constants[2]*constants[18]*states[12])/1.00000)*(1.00000-constants[3])+((constants[19]*states[13])/1.00000)*(1.00000-constants[25]))-algebraic[0]*states[13]
rates[14] = (((constants[1]*constants[2]*constants[19]*states[14])/1.00000)*(1.00000-constants[3])+((constants[20]*states[14])/1.00000)*(1.00000-constants[25]))-algebraic[0]*states[14]
rates[15] = (((constants[1]*constants[2]*constants[20]*states[14])/1.00000)*(1.00000-constants[3])+((constants[21]*states[15])/1.00000)*(1.00000-constants[25]))-algebraic[0]*states[15]
rates[16] = (((constants[1]*constants[2]*constants[21]*states[15])/1.00000)*(1.00000-constants[3])+((constants[22]*states[16])/1.00000)*(1.00000-constants[25]))-algebraic[0]*states[16]
rates[17] = (((constants[1]*constants[2]*constants[22]*states[16])/1.00000)*(1.00000-constants[3])+((constants[23]*states[17])/1.00000)*(1.00000-constants[25]))-algebraic[0]*states[17]
rates[18] = (((constants[1]*constants[2]*constants[23]*states[17])/1.00000)*(1.00000-constants[3])+((constants[24]*states[18])/1.00000)*((1.00000-constants[25])+((constants[1]*constants[2])/1.00000)*(1.00000-constants[3])))-algebraic[0]*states[8]
rates[19] = (((1.00000-constants[1])*constants[2])/1.00000)*((1.00000-constants[0])*(constants[15]*states[0]+constants[17]*states[1]+constants[18]*states[2]+constants[19]*states[3]+constants[20]*states[4]+constants[21]*states[5]+constants[22]*states[6]+constants[23]*states[7]+constants[24]*states[8])+(1.00000-constants[3])*(constants[15]*states[9]+constants[17]*states[10]+constants[18]*states[12]+constants[19]*states[13]+constants[20]*states[14]+constants[21]*states[15]+constants[22]*states[16]+constants[23]*states[17]+constants[24]*states[18]))-algebraic[0]*states[19]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = ((1.00000-constants[16])/1.00000)*(constants[15]*states[0]+constants[17]*states[1]+constants[18]*states[2]+constants[19]*states[3]+constants[20]*states[4])+((1.00000-constants[25])/1.00000)*(constants[17]*states[10]+constants[18]*states[12]+constants[19]*states[13]+constants[20]*states[14])
algebraic[1] = states[0]+states[1]+states[2]+states[3]+states[4]+states[5]+states[6]+states[7]+states[8]+states[9]+states[12]+states[13]+states[14]+states[15]+states[16]+states[17]+states[18]
algebraic[2] = states[0]+states[1]+states[2]+states[3]+states[4]+states[5]+states[6]+states[7]+states[8]
algebraic[3] = states[9]+states[12]+states[13]+states[14]+states[15]+states[16]+states[17]+states[18]
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)