# Size of variable arrays: sizeAlgebraic = 2 sizeStates = 5 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 (second)" legend_states[0] = "R in component R (dimensionless)" legend_constants[19] = "phi_1 in component reaction_rate_constants (first_order_rate_constant)" legend_constants[20] = "phi_2 in component reaction_rate_constants (second_order_rate_constant)" legend_constants[21] = "phi_2b in component reaction_rate_constants (first_order_rate_constant)" legend_constants[0] = "k_1b in component reaction_rate_constants (first_order_rate_constant)" legend_constants[1] = "l_2b in component reaction_rate_constants (first_order_rate_constant)" legend_states[1] = "I_1 in component I_1 (dimensionless)" legend_states[2] = "O in component O (dimensionless)" legend_constants[2] = "p in component reaction_rate_constants (micromolar)" legend_constants[22] = "phi_3 in component reaction_rate_constants (second_order_rate_constant)" legend_constants[23] = "phi_4 in component reaction_rate_constants (first_order_rate_constant)" legend_constants[24] = "phi_4b in component reaction_rate_constants (first_order_rate_constant)" legend_constants[3] = "k_3b in component reaction_rate_constants (first_order_rate_constant)" legend_states[3] = "A in component A (dimensionless)" legend_algebraic[0] = "S in component S (dimensionless)" legend_states[4] = "I_2 in component I_2 (dimensionless)" legend_constants[25] = "phi_5 in component reaction_rate_constants (first_order_rate_constant)" legend_algebraic[1] = "open_probability in component open_probability (dimensionless)" legend_constants[4] = "k_1a in component reaction_rate_constants (second_order_rate_constant)" legend_constants[5] = "k_2a in component reaction_rate_constants (second_order_rate_constant)" legend_constants[6] = "k_2b in component reaction_rate_constants (first_order_rate_constant)" legend_constants[7] = "k_3a in component reaction_rate_constants (second_order_rate_constant)" legend_constants[8] = "k_4a in component reaction_rate_constants (second_order_rate_constant)" legend_constants[9] = "k_4b in component reaction_rate_constants (first_order_rate_constant)" legend_constants[10] = "l_2a in component reaction_rate_constants (first_order_rate_constant)" legend_constants[11] = "l_4a in component reaction_rate_constants (second_order_rate_constant)" legend_constants[12] = "l_4b in component reaction_rate_constants (second_order_rate_constant)" legend_constants[13] = "l_6a in component reaction_rate_constants (first_order_rate_constant)" legend_constants[14] = "l_6b in component reaction_rate_constants (first_order_rate_constant)" legend_constants[15] = "L_1 in component reaction_rate_constants (micromolar)" legend_constants[16] = "L_3 in component reaction_rate_constants (micromolar)" legend_constants[17] = "L_5 in component reaction_rate_constants (micromolar)" legend_constants[18] = "c in component reaction_rate_constants (micromolar)" legend_rates[0] = "d/dt R in component R (dimensionless)" legend_rates[2] = "d/dt O in component O (dimensionless)" legend_rates[1] = "d/dt I_1 in component I_1 (dimensionless)" legend_rates[4] = "d/dt I_2 in component I_2 (dimensionless)" legend_rates[3] = "d/dt A in component A (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 1 constants[0] = 0.04 constants[1] = 0.8 states[1] = 0 states[2] = 0 constants[2] = 10 constants[3] = 29.8 states[3] = 0 states[4] = 0 constants[4] = 0.64 constants[5] = 37.4 constants[6] = 1.4 constants[7] = 0.11 constants[8] = 4 constants[9] = 0.54 constants[10] = 1.7 constants[11] = 1.7 constants[12] = 2.5 constants[13] = 4707 constants[14] = 11.4 constants[15] = 0.12 constants[16] = 0.025 constants[17] = 54.7 constants[18] = 1 constants[19] = ((constants[4]*constants[15]+constants[10])*constants[18])/(constants[15]+constants[18]*(1.00000+constants[15]/constants[16])) constants[20] = (constants[5]*constants[16]+constants[11]*constants[18])/(constants[16]+constants[18]*(1.00000+constants[16]/constants[15])) constants[21] = (constants[6]+constants[12]*constants[18])/(1.00000+constants[18]/constants[17]) constants[22] = (constants[7]*constants[17])/(constants[18]+constants[17]) constants[23] = ((constants[8]*constants[17]+constants[13])*constants[18])/(constants[18]+constants[17]) constants[24] = (constants[15]*(constants[9]+constants[14]))/(constants[18]+constants[15]) constants[25] = ((constants[4]*constants[15]+constants[10])*constants[18])/(constants[18]+constants[15]) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = (constants[21]*states[2]+(constants[0]+constants[1])*states[1])-(constants[20]*constants[2]*states[0]+constants[19]*states[0]) rates[1] = constants[19]*states[0]-(constants[0]+constants[1])*states[1] rates[4] = constants[25]*states[3]-(constants[0]+constants[1])*states[4] rates[3] = (constants[23]*states[2]+(constants[0]+constants[1])*states[4])-(constants[24]*states[3]+constants[25]*states[3]) algebraic[0] = 1.00000-(states[0]+states[2]+states[3]+states[1]+states[4]) rates[2] = (constants[20]*constants[2]*states[0]+constants[24]*states[3]+constants[3]*algebraic[0])-(constants[21]+constants[23]+1.00000*constants[22])*states[2] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = 1.00000-(states[0]+states[2]+states[3]+states[1]+states[4]) algebraic[1] = power(0.100000*states[2]+0.900000*states[3], 4.00000) 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)