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# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 9 sizeConstants = 11 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] = "Pfr in component Pfr (micromolar)" legend_states[1] = "Pr in component Pr (micromolar)" legend_constants[0] = "Ifr_sigma_fr_phi_fr in component model_parameters (dimensionless)" legend_constants[1] = "Ir_sigma_r_phi_r in component model_parameters (dimensionless)" legend_constants[2] = "kd in component Pr (first_order_rate_constant)" legend_states[2] = "Xi in component Xi (micromolar)" legend_states[3] = "Xa in component Xa (micromolar)" legend_constants[3] = "kia in component model_parameters (second_order_rate_constant)" legend_constants[4] = "kai in component model_parameters (first_order_rate_constant)" legend_states[4] = "prepreS in component prepreS (micromolar)" legend_constants[5] = "kx in component model_parameters (second_order_rate_constant)" legend_states[5] = "preS in component preS (micromolar)" legend_states[6] = "Ya in component Ya (micromolar)" legend_constants[6] = "ky in component model_parameters (second_order_rate_constant)" legend_states[7] = "S in component S (micromolar)" legend_constants[7] = "alpha1 in component S (micromolar)" legend_states[8] = "V in component V (micromolar)" legend_constants[8] = "alpha2 in component V (micromolar)" legend_constants[9] = "kG in component Ya (second_order_rate_constant)" legend_constants[10] = "glucose in component model_parameters (micromolar)" legend_rates[0] = "d/dt Pfr in component Pfr (micromolar)" legend_rates[1] = "d/dt Pr in component Pr (micromolar)" legend_rates[2] = "d/dt Xi in component Xi (micromolar)" legend_rates[3] = "d/dt Xa in component Xa (micromolar)" legend_rates[4] = "d/dt prepreS in component prepreS (micromolar)" legend_rates[5] = "d/dt preS in component preS (micromolar)" legend_rates[7] = "d/dt S in component S (micromolar)" legend_rates[8] = "d/dt V in component V (micromolar)" legend_rates[6] = "d/dt Ya in component Ya (micromolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 10.0 states[1] = 0.0 constants[0] = 0.1 constants[1] = 0.0 constants[2] = 0.1 states[2] = 6.0 states[3] = 0.0 constants[3] = 0.1 constants[4] = 0.8 states[4] = 200.0 constants[5] = 0.2 states[5] = 0.0 states[6] = 0.9 constants[6] = 1.0 states[7] = 0.0 constants[7] = 30.0 states[8] = 50.0 constants[8] = 50.0 constants[9] = 0.1 constants[10] = 1.0 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[1]*states[1]-constants[0]*states[0] rates[1] = constants[0]*states[1]-(constants[1]*states[1]+constants[2]*states[1]) rates[2] = constants[4]*states[3]-constants[3]*states[1]*states[2] rates[3] = constants[3]*states[1]*states[2]-constants[4]*states[3] rates[4] = -(constants[5]*states[3]*states[4]) rates[5] = constants[5]*states[3]*states[4]-constants[6]*states[6]*states[5] rates[7] = (constants[6]*states[6]*states[5]+constants[7]/(1.00000+power(states[8], 3.00000)))-states[7] rates[8] = constants[8]/(1.00000+power(states[7], 3.00000))-states[8] rates[6] = -(constants[9]*constants[10]*states[6]) 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)