# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 5 sizeConstants = 36 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 (minute)" legend_states[0] = "x1 in component x1 (microg_l)" legend_constants[0] = "lambda_1 in component model_parameters (first_order_rate_constant)" legend_states[1] = "x3 in component x3 (microg_l)" legend_constants[1] = "a1 in component model_parameters (flux)" legend_constants[2] = "a2 in component model_parameters (flux)" legend_constants[3] = "a3 in component model_parameters (first_order_rate_constant)" legend_constants[4] = "a4 in component model_parameters (second_order_rate_constant)" legend_constants[5] = "a5 in component model_parameters (per_microg_l)" legend_constants[6] = "a6 in component model_parameters (per_microg_l2)" legend_constants[7] = "a7 in component model_parameters (per_microg_l)" legend_constants[8] = "a8 in component model_parameters (per_microg_l2)" legend_states[2] = "x2 in component x2 (microg_l)" legend_constants[9] = "lambda_2 in component model_parameters (first_order_rate_constant)" legend_constants[10] = "a9 in component model_parameters (flux)" legend_constants[11] = "a10 in component model_parameters (first_order_rate_constant)" legend_constants[12] = "a11 in component model_parameters (second_order_rate_constant)" legend_constants[13] = "a12 in component model_parameters (per_microg_l)" legend_constants[14] = "a13 in component model_parameters (per_microg_l2)" legend_constants[15] = "a14 in component model_parameters (per_microg_l)" legend_constants[16] = "a15 in component model_parameters (per_microg_l2)" legend_constants[33] = "lambda_3_ in component model_parameters (first_order_rate_constant)" legend_states[3] = "x4 in component x4 (microg_l)" legend_states[4] = "x5 in component x5 (microg_l)" legend_constants[17] = "a16 in component model_parameters (flux)" legend_constants[18] = "a17 in component model_parameters (first_order_rate_constant)" legend_constants[19] = "a18 in component model_parameters (second_order_rate_constant)" legend_constants[20] = "a19 in component model_parameters (first_order_rate_constant)" legend_constants[21] = "a20 in component model_parameters (second_order_rate_constant)" legend_constants[22] = "a21 in component model_parameters (per_microg_l)" legend_constants[23] = "a22 in component model_parameters (per_microg_l2)" legend_constants[24] = "a23 in component model_parameters (per_microg_l)" legend_constants[25] = "a24 in component model_parameters (per_microg_l2)" legend_constants[26] = "a25 in component model_parameters (first_order_rate_constant)" legend_constants[27] = "a26 in component model_parameters (first_order_rate_constant)" legend_constants[34] = "lambda_4_ in component model_parameters (first_order_rate_constant)" legend_constants[28] = "a27 in component model_parameters (first_order_rate_constant)" legend_constants[35] = "lambda_5_ in component model_parameters (first_order_rate_constant)" legend_constants[29] = "a28 in component model_parameters (first_order_rate_constant)" legend_constants[30] = "lambda_3 in component model_parameters (first_order_rate_constant)" legend_constants[31] = "lambda_4 in component model_parameters (first_order_rate_constant)" legend_constants[32] = "lambda_5 in component model_parameters (first_order_rate_constant)" legend_rates[0] = "d/dt x1 in component x1 (microg_l)" legend_rates[2] = "d/dt x2 in component x2 (microg_l)" legend_rates[1] = "d/dt x3 in component x3 (microg_l)" legend_rates[3] = "d/dt x4 in component x4 (microg_l)" legend_rates[4] = "d/dt x5 in component x5 (microg_l)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.01067 constants[0] = 0.059 states[1] = 6.51 constants[1] = 0.000017 constants[2] = 0.0023 constants[3] = 0.6 constants[4] = 45 constants[5] = 36 constants[6] = 216 constants[7] = 0.28 constants[8] = 0.36 states[2] = 0.04665 constants[9] = 0.028 constants[10] = 0.0003 constants[11] = 0.18 constants[12] = 150 constants[13] = 18 constants[14] = 460 constants[15] = 0.46 constants[16] = 0.1 states[3] = 60.61 states[4] = 12.61 constants[17] = 0.04 constants[18] = 150 constants[19] = 3800 constants[20] = 57 constants[21] = 2600 constants[22] = 200 constants[23] = 9400 constants[24] = 10 constants[25] = 320 constants[26] = 0.04 constants[27] = 0.00097 constants[28] = 0.57 constants[29] = 0.0017 constants[30] = 0.0986 constants[31] = 0.024 constants[32] = 3e-5 constants[33] = constants[30]+constants[28]+constants[29] constants[34] = constants[31]+constants[26] constants[35] = constants[32]+constants[27] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = (constants[1]+(constants[2]+constants[3]*states[0]+constants[4]*(power(states[0], 2.00000)))/(1.00000+constants[5]*states[0]+constants[6]*(power(states[0], 2.00000))+constants[7]*states[1]+constants[8]*(power(states[1], 2.00000))))-constants[0]*states[0] rates[2] = (constants[10]+constants[11]*states[0]+constants[12]*(power(states[0], 2.00000)))/(1.00000+constants[13]*states[0]+constants[14]*(power(states[0], 2.00000))+constants[15]*states[1]+constants[16]*(power(states[1], 2.00000)))-constants[9]*states[2] rates[1] = (constants[17]+(constants[18]*states[0]+constants[19]*(power(states[0], 2.00000))+constants[20]*states[2]+constants[21]*(power(states[2], 2.00000)))/(1.00000+constants[22]*states[0]+constants[23]*(power(states[0], 2.00000))+constants[24]*states[2]+constants[25]*(power(states[2], 2.00000)))+constants[26]*states[3]+constants[27]*states[4])-constants[33]*states[1] rates[3] = constants[28]*states[1]-constants[34]*states[3] rates[4] = constants[29]*states[1]-constants[35]*states[4] 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)