# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 17 sizeConstants = 18 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 (second)" legend_states[0] = "T in component T (dimensionless)" legend_constants[0] = "delta in component model_parameters (first_order_rate_constant)" legend_constants[1] = "gamma in component model_parameters (first_order_rate_constant)" legend_constants[2] = "lambda in component model_parameters (first_order_rate_constant)" legend_states[1] = "v in component v (dimensionless)" legend_states[2] = "I in component I (dimensionless)" legend_constants[3] = "alpha in component model_parameters (first_order_rate_constant)" legend_constants[4] = "p in component model_parameters (first_order_rate_constant)" legend_states[3] = "z in component z (dimensionless)" legend_states[4] = "w in component w (dimensionless)" legend_states[5] = "x in component x (dimensionless)" legend_constants[5] = "r in component model_parameters (first_order_rate_constant)" legend_states[6] = "y in component y (dimensionless)" legend_constants[6] = "k in component model_parameters (dimensionless)" legend_constants[7] = "d in component model_parameters (first_order_rate_constant)" legend_constants[8] = "beta in component model_parameters (first_order_rate_constant)" legend_constants[9] = "a in component model_parameters (first_order_rate_constant)" legend_constants[10] = "u in component model_parameters (first_order_rate_constant)" legend_constants[11] = "eta in component model_parameters (first_order_rate_constant)" legend_constants[12] = "xi in component model_parameters (first_order_rate_constant)" legend_constants[13] = "rho in component model_parameters (first_order_rate_constant)" legend_constants[14] = "phi in component model_parameters (first_order_rate_constant)" legend_states[7] = "m_9 in component m_9 (dimensionless)" legend_states[8] = "m_8 in component m_8 (dimensionless)" legend_states[9] = "m_7 in component m_7 (dimensionless)" legend_states[10] = "m_6 in component m_6 (dimensionless)" legend_states[11] = "m_5 in component m_5 (dimensionless)" legend_states[12] = "m_4 in component m_4 (dimensionless)" legend_states[13] = "m_3 in component m_3 (dimensionless)" legend_states[14] = "m_2 in component m_2 (dimensionless)" legend_states[15] = "m_1 in component m_1 (dimensionless)" legend_states[16] = "m_0 in component m_0 (dimensionless)" legend_constants[15] = "b in component model_parameters (first_order_rate_constant)" legend_constants[16] = "epsilon in component model_parameters (dimensionless)" legend_constants[17] = "c in component model_parameters (first_order_rate_constant)" legend_rates[0] = "d/dt T in component T (dimensionless)" legend_rates[2] = "d/dt I in component I (dimensionless)" legend_rates[5] = "d/dt x in component x (dimensionless)" legend_rates[6] = "d/dt y in component y (dimensionless)" legend_rates[1] = "d/dt v in component v (dimensionless)" legend_rates[4] = "d/dt w in component w (dimensionless)" legend_rates[7] = "d/dt m_9 in component m_9 (dimensionless)" legend_rates[8] = "d/dt m_8 in component m_8 (dimensionless)" legend_rates[9] = "d/dt m_7 in component m_7 (dimensionless)" legend_rates[10] = "d/dt m_6 in component m_6 (dimensionless)" legend_rates[11] = "d/dt m_5 in component m_5 (dimensionless)" legend_rates[12] = "d/dt m_4 in component m_4 (dimensionless)" legend_rates[13] = "d/dt m_3 in component m_3 (dimensionless)" legend_rates[14] = "d/dt m_2 in component m_2 (dimensionless)" legend_rates[15] = "d/dt m_1 in component m_1 (dimensionless)" legend_rates[16] = "d/dt m_0 in component m_0 (dimensionless)" legend_rates[3] = "d/dt z in component z (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 1000.0 constants[0] = 0.01 constants[1] = 0.01 constants[2] = 1.0 states[1] = 0.0001 states[2] = 0.0001 constants[3] = 0.2 constants[4] = 45.0 states[3] = 0.0 states[4] = 0.0 states[5] = 10.0 constants[5] = 1.0 states[6] = 0.0 constants[6] = 10.0 constants[7] = 0.001 constants[8] = 0.3 constants[9] = 0.2 constants[10] = 1.0 constants[11] = 1.0 constants[12] = 0.01 constants[13] = 0.3 constants[14] = 1.5 states[7] = 0.0 states[8] = 0.0 states[9] = 0.0 states[10] = 0.0 states[11] = 0.0 states[12] = 0.0 states[13] = 0.0 states[14] = 0.0 states[15] = 0.0 states[16] = 0.1 constants[15] = 0.1 constants[16] = 1.0 constants[17] = 1.0 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[2]-(constants[0]*states[0]+constants[1]*states[0]*states[1]) rates[2] = constants[1]*states[0]*states[1]-(constants[3]*states[2]+constants[4]*states[2]*(states[3]+states[4])) rates[5] = constants[5]*states[5]*states[1]*(1.00000-(states[5]+states[6])/constants[6])-(constants[7]*states[5]+constants[8]*states[5]*states[1]) rates[6] = (constants[8]*states[5]*states[1]+constants[5]*states[6]*states[1]*(1.00000-(states[5]+states[6])/constants[6]))-(constants[9]*states[6]+constants[4]*states[6]*(states[3]+states[4])) rates[1] = constants[11]*(states[6]+states[2])-constants[10]*states[1] rates[4] = 2.00000*constants[13]*states[7]-(constants[12]*states[4]+constants[14]*states[4]) rates[7] = 2.00000*constants[13]*states[8]-constants[13]*states[7] rates[8] = 2.00000*constants[13]*states[9]-constants[13]*states[8] rates[9] = 2.00000*constants[13]*states[10]-constants[13]*states[9] rates[10] = 2.00000*constants[13]*states[11]-constants[13]*states[10] rates[11] = 2.00000*constants[13]*states[12]-constants[13]*states[11] rates[12] = 2.00000*constants[13]*states[13]-constants[13]*states[12] rates[13] = 2.00000*constants[13]*states[14]-constants[13]*states[13] rates[14] = 2.00000*constants[13]*states[15]-constants[13]*states[14] rates[15] = 2.00000*constants[13]*states[16]-constants[13]*states[15] rates[16] = -(constants[13]*states[16]) rates[3] = (constants[12]*states[4]+constants[17]*states[5]*(states[6]+states[2])*(states[3]/(constants[16]*states[5]+1.00000)))-constants[15]*states[3] 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)