# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 5 sizeConstants = 13 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] = "Y in component Y (dimensionless)" legend_constants[0] = "C1 in component model_parameters (dimensionless)" legend_constants[1] = "k1 in component model_parameters (first_order_rate_constant)" legend_states[1] = "P in component P (dimensionless)" legend_constants[2] = "K in component model_parameters (dimensionless)" legend_constants[3] = "C in component model_parameters (dimensionless)" legend_constants[4] = "C2 in component model_parameters (dimensionless)" legend_constants[5] = "k2 in component model_parameters (first_order_rate_constant)" legend_constants[6] = "ky in component model_parameters (first_order_rate_constant)" legend_states[2] = "X in component X (dimensionless)" legend_constants[7] = "k3 in component model_parameters (first_order_rate_constant)" legend_constants[8] = "k4 in component model_parameters (first_order_rate_constant)" legend_states[3] = "Z in component Z (dimensionless)" legend_constants[9] = "C3 in component model_parameters (dimensionless)" legend_constants[10] = "k5 in component model_parameters (first_order_rate_constant)" legend_constants[11] = "K2 in component model_parameters (dimensionless)" legend_states[4] = "IL6 in component IL6 (dimensionless)" legend_constants[12] = "k6 in component model_parameters (first_order_rate_constant)" legend_rates[0] = "d/dt Y in component Y (dimensionless)" legend_rates[2] = "d/dt X in component X (dimensionless)" legend_rates[1] = "d/dt P in component P (dimensionless)" legend_rates[3] = "d/dt Z in component Z (dimensionless)" legend_rates[4] = "d/dt IL6 in component IL6 (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 10.0 constants[0] = 1.0 constants[1] = 1.0 states[1] = 10.0 constants[2] = 5.0 constants[3] = 50.0 constants[4] = 1.0 constants[5] = 1.3 constants[6] = 0.01 states[2] = 500.0 constants[7] = 0.05 constants[8] = 0.9 states[3] = 200.0 constants[9] = 1.0 constants[10] = 5.0 constants[11] = 2.0 states[4] = 1.9 constants[12] = 0.02 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[1]*constants[0]*(states[1]/(constants[2]+states[1]))*constants[3]-(constants[5]*constants[4]*(1.00000-states[1]/(constants[2]+states[1]))*states[0]+constants[6]*states[0]) rates[2] = constants[5]*constants[4]*(1.00000-states[1]/(constants[2]+states[1]))*states[0]-constants[7]*states[2] rates[1] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , 6.00000), 10.0000-constants[8]*states[1] , greater_equal(voi , 6.00000) & less(voi , 12.0000), -(constants[8]*states[1]) , greater_equal(voi , 12.0000) & less(voi , 18.0000), 10.0000-constants[8]*states[1] , greater_equal(voi , 18.0000) & less(voi , 24.0000), -(constants[8]*states[1]) , greater_equal(voi , 24.0000) & less(voi , 30.0000), 10.0000-constants[8]*states[1] , greater_equal(voi , 30.0000) & less(voi , 36.0000), -(constants[8]*states[1]) , greater_equal(voi , 36.0000) & less(voi , 42.0000), 10.0000-constants[8]*states[1] , greater_equal(voi , 42.0000) & less(voi , 48.0000), -(constants[8]*states[1]) , greater_equal(voi , 48.0000) & less(voi , 54.0000), 10.0000-constants[8]*states[1] , greater_equal(voi , 54.0000) & less(voi , 60.0000), -(constants[8]*states[1]) , greater_equal(voi , 60.0000) & less(voi , 66.0000), 10.0000-constants[8]*states[1] , greater_equal(voi , 66.0000) & less(voi , 72.0000), -(constants[8]*states[1]) , greater_equal(voi , 72.0000) & less(voi , 78.0000), 10.0000-constants[8]*states[1] , greater_equal(voi , 78.0000) & less(voi , 84.0000), -(constants[8]*states[1]) , greater_equal(voi , 84.0000) & less(voi , 90.0000), 10.0000-constants[8]*states[1] , greater_equal(voi , 90.0000) & less(voi , 96.0000), -(constants[8]*states[1]) , True, float('nan')]) rates[3] = constants[10]*constants[9]*(states[4]/(constants[11]+states[4]))-constants[12]*states[3] rates[4] = 0.100000*states[2]-10.0000*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 custom_piecewise(cases): """Compute result of a piecewise function""" return select(cases[0::2],cases[1::2]) 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)