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# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 5 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] = "x in component x (dimensionless)" legend_constants[0] = "d 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_constants[3] = "beta in component model_parameters (first_order_rate_constant)" legend_states[1] = "v in component v (dimensionless)" legend_states[2] = "y0 in component y0 (dimensionless)" legend_constants[4] = "a0 in component model_parameters (first_order_rate_constant)" legend_constants[5] = "eta in component model_parameters (first_order_rate_constant)" legend_constants[6] = "phi in component model_parameters (first_order_rate_constant)" legend_states[3] = "L in component L (dimensionless)" legend_states[4] = "y1 in component y1 (dimensionless)" legend_constants[7] = "a1 in component model_parameters (first_order_rate_constant)" legend_constants[8] = "k in component model_parameters (first_order_rate_constant)" legend_constants[9] = "u in component model_parameters (first_order_rate_constant)" legend_constants[10] = "R0 in component R0 (dimensionless)" legend_rates[0] = "d/dt x in component x (dimensionless)" legend_rates[2] = "d/dt y0 in component y0 (dimensionless)" legend_rates[4] = "d/dt y1 in component y1 (dimensionless)" legend_rates[3] = "d/dt L in component L (dimensionless)" legend_rates[1] = "d/dt v in component v (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] = 0.1 constants[1] = 0.5 constants[2] = 10 constants[3] = 0.1 states[1] = 1 states[2] = 0 constants[4] = 0.1 constants[5] = 0.01 constants[6] = 0.1 states[3] = 0 states[4] = 0 constants[7] = 0.2 constants[8] = 1 constants[9] = 1 constants[10] = ((constants[2]*constants[5])/(constants[0]*constants[7]*(constants[4]+constants[5])))*(constants[3]+(constants[1]*constants[6])/(constants[6]+constants[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[3]*states[0]*states[1]+constants[1]*states[0]*states[1]) rates[2] = (constants[3]*states[0]*states[1]-(constants[4]*states[2]+constants[5]*states[2]))+constants[6]*states[3] rates[4] = constants[5]*states[2]-constants[7]*states[4] rates[3] = constants[1]*states[0]*states[1]-(constants[6]*states[3]+constants[0]*states[3]) rates[1] = constants[8]*states[4]-constants[9]*states[1] 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)