# Size of variable arrays: sizeAlgebraic = 4 sizeStates = 10 sizeConstants = 14 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 (day)" legend_states[0] = "S in component S (dimensionless)" legend_constants[0] = "r in component S (first_order_rate_constant)" legend_constants[1] = "epsilon in component S (dimensionless)" legend_algebraic[0] = "H in component S (dimensionless)" legend_constants[2] = "d in component kinetic_parameters (first_order_rate_constant)" legend_constants[3] = "g in component memory_duration (first_order_rate_constant)" legend_constants[4] = "beta_1 in component kinetic_parameters (first_order_rate_constant)" legend_constants[5] = "beta_2 in component kinetic_parameters (first_order_rate_constant)" legend_states[1] = "R_1 in component R1 (dimensionless)" legend_states[2] = "R_2 in component R2 (dimensionless)" legend_states[3] = "R_12 in component R12 (dimensionless)" legend_states[4] = "P_1 in component P1 (dimensionless)" legend_states[5] = "P_2 in component P2 (dimensionless)" legend_states[6] = "I_1 in component I1 (dimensionless)" legend_states[7] = "I_2 in component I2 (dimensionless)" legend_states[8] = "I_12 in component I12 (dimensionless)" legend_states[9] = "I_21 in component I21 (dimensionless)" legend_algebraic[1] = "P in component S (dimensionless)" legend_constants[6] = "a_1 in component kinetic_parameters (first_order_rate_constant)" legend_constants[7] = "alpha_1 in component kinetic_parameters (first_order_rate_constant)" legend_constants[8] = "a_2 in component kinetic_parameters (first_order_rate_constant)" legend_constants[9] = "alpha_2 in component kinetic_parameters (first_order_rate_constant)" legend_constants[10] = "k_1 in component P1 (first_order_rate_constant)" legend_constants[11] = "u in component kinetic_parameters (first_order_rate_constant)" legend_algebraic[2] = "log_P1 in component P1 (dimensionless)" legend_constants[12] = "k_2 in component P2 (first_order_rate_constant)" legend_algebraic[3] = "log_P2 in component P2 (dimensionless)" legend_constants[13] = "G in component memory_duration (dimensionless)" legend_rates[0] = "d/dt S in component S (dimensionless)" legend_rates[6] = "d/dt I_1 in component I1 (dimensionless)" legend_rates[7] = "d/dt I_2 in component I2 (dimensionless)" legend_rates[8] = "d/dt I_12 in component I12 (dimensionless)" legend_rates[9] = "d/dt I_21 in component I21 (dimensionless)" legend_rates[1] = "d/dt R_1 in component R1 (dimensionless)" legend_rates[2] = "d/dt R_2 in component R2 (dimensionless)" legend_rates[3] = "d/dt R_12 in component R12 (dimensionless)" legend_rates[4] = "d/dt P_1 in component P1 (dimensionless)" legend_rates[5] = "d/dt P_2 in component P2 (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 100 constants[0] = 0.5 constants[1] = 0.1 constants[2] = 0.01 constants[3] = 0.01 constants[4] = 1 constants[5] = 1 states[1] = 0 states[2] = 0 states[3] = 0 states[4] = 1 states[5] = 1 states[6] = 0 states[7] = 0 states[8] = 0 states[9] = 0 constants[6] = 0.03 constants[7] = 0.1 constants[8] = 1 constants[9] = 0.1 constants[10] = 1 constants[11] = 0.5 constants[12] = 1 constants[13] = 1.00000/constants[3] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[6] = (constants[4]*states[0]*states[4]-constants[6]*states[6])-constants[7]*states[6] rates[7] = (constants[5]*states[0]*states[5]-constants[8]*states[7])-constants[9]*states[7] rates[8] = (constants[5]*states[1]*states[5]-constants[8]*states[8])-constants[9]*states[8] rates[9] = (constants[4]*states[2]*states[4]-constants[6]*states[9])-constants[7]*states[9] rates[1] = ((constants[7]*states[6]-constants[2]*states[1])-constants[3]*states[1])-constants[5]*states[1]*states[5] rates[2] = ((constants[9]*states[7]-constants[2]*states[2])-constants[3]*states[2])-constants[4]*states[2]*states[4] rates[3] = ((constants[9]*states[8]+constants[7]*states[9])-constants[2]*states[3])-constants[3]*states[3] rates[4] = constants[10]*(states[6]+states[9])-constants[11]*states[4] rates[5] = constants[12]*(states[7]+states[8])-constants[11]*states[5] algebraic[0] = states[0]+states[6]+states[1]+states[7]+states[2]+states[8]+states[9]+states[3] rates[0] = ((((constants[0]*algebraic[0])/(constants[1]*algebraic[0]+1.00000)-constants[2]*states[0])-constants[4]*states[0]*states[4])-constants[5]*states[0]*states[5])+constants[3]*(states[1]+states[2]+states[3]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = states[0]+states[6]+states[1]+states[7]+states[2]+states[8]+states[9]+states[3] algebraic[1] = states[4]+states[5] algebraic[2] = log(states[4], 10) algebraic[3] = log(states[5], 10) 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)