# Size of variable arrays: sizeAlgebraic = 9 sizeStates = 8 sizeConstants = 20 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_constants[0] = "mu_T in component uninfected_CD4 (per_day)" legend_constants[1] = "r in component uninfected_CD4 (per_day)" legend_states[0] = "T_1 in component latently_infected_CD4 (per_micro_L)" legend_constants[2] = "T_max in component uninfected_CD4 (per_micro_L)" legend_constants[3] = "k_1 in component HIV1 (micro_L_per_day)" legend_states[1] = "V in component HIV1 (per_micro_L)" legend_constants[4] = "k_1_ in component hybrid_HIV1 (micro_L_per_day)" legend_states[2] = "V_ in component hybrid_HIV1 (per_micro_L)" legend_constants[5] = "s_0 in component uninfected_CD4 (per_micro_L_day)" legend_constants[6] = "theta in component uninfected_CD4 (per_micro_L)" legend_algebraic[0] = "s_V in component uninfected_CD4 (per_micro_L_day)" legend_states[3] = "T in component uninfected_CD4 (per_micro_L)" legend_constants[7] = "k_2 in component latently_infected_CD4 (per_day)" legend_constants[8] = "k_1D in component actively_infected_CD4 (micro_L_per_day)" legend_algebraic[1] = "D in component DIV (per_micro_L)" legend_constants[9] = "mu_b in component actively_infected_CD4 (per_day)" legend_states[4] = "T_2 in component actively_infected_CD4 (per_micro_L)" legend_constants[10] = "k_s in component actively_coinfected_CD4 (per_day)" legend_constants[11] = "mu_bD in component actively_coinfected_CD4 (per_day)" legend_states[5] = "T_D2 in component actively_coinfected_CD4 (per_micro_L)" legend_constants[12] = "mu_TD in component stably_coinfected_CD4 (per_day)" legend_states[6] = "T_D1 in component stably_coinfected_CD4 (per_micro_L)" legend_algebraic[4] = "N_D_t in component DIV (dimensionless)" legend_algebraic[7] = "pi_D_t in component DIV (per_day)" legend_constants[13] = "mu_D in component DIV (per_day)" legend_algebraic[2] = "N_t in component production_function (dimensionless)" legend_constants[14] = "t_DIV in component DIV (day)" legend_states[7] = "D_ode in component DIV (per_micro_L)" legend_constants[15] = "D_0 in component DIV (per_micro_L)" legend_algebraic[5] = "N_2_t in component HIV1 (dimensionless)" legend_constants[16] = "mu_V in component HIV1 (per_day)" legend_algebraic[6] = "N_t_ in component hybrid_HIV1 (dimensionless)" legend_algebraic[8] = "pi_t_ in component hybrid_HIV1 (per_day)" legend_constants[17] = "N_0 in component production_function (dimensionless)" legend_constants[18] = "gamma in component production_function (dimensionless)" legend_constants[19] = "t_c in component production_function (day)" legend_algebraic[3] = "T_tot in component cell_population (per_micro_L)" legend_rates[3] = "d/dt T in component uninfected_CD4 (per_micro_L)" legend_rates[0] = "d/dt T_1 in component latently_infected_CD4 (per_micro_L)" legend_rates[4] = "d/dt T_2 in component actively_infected_CD4 (per_micro_L)" legend_rates[5] = "d/dt T_D2 in component actively_coinfected_CD4 (per_micro_L)" legend_rates[6] = "d/dt T_D1 in component stably_coinfected_CD4 (per_micro_L)" legend_rates[7] = "d/dt D_ode in component DIV (per_micro_L)" legend_rates[1] = "d/dt V in component HIV1 (per_micro_L)" legend_rates[2] = "d/dt V_ in component hybrid_HIV1 (per_micro_L)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 0.02 constants[1] = 0.03 states[0] = 0 constants[2] = 1500 constants[3] = 2.4E-5 states[1] = 1E-3 constants[4] = 2.4E-7 states[2] = 0 constants[5] = 10 constants[6] = 1 states[3] = 1000 constants[7] = 0.017 constants[8] = 2.4E-5 constants[9] = 0.24 states[4] = 0 constants[10] = 0.48 constants[11] = 0.12 states[5] = 0 constants[12] = 0.02 states[6] = 0 constants[13] = 0.76 constants[14] = 2557 states[7] = 0 constants[15] = 0.1 constants[16] = 2.4 constants[17] = 300 constants[18] = 25 constants[19] = 7305 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = ((constants[3]*states[1]*states[3]+constants[4]*states[2]*states[3])-constants[0]*states[0])-constants[7]*states[0] rates[6] = constants[10]*states[5]-constants[12]*states[6] algebraic[0] = (constants[5]*constants[6])/(constants[6]+states[1]) rates[3] = (((algebraic[0]-constants[0]*states[3])+constants[1]*states[3]*(1.00000-(states[3]+states[0])/constants[2]))-constants[3]*states[1]*states[3])-constants[4]*states[2]*states[3] algebraic[1] = custom_piecewise([less(voi , constants[14]), 0.00000 , True, states[7]]) rates[4] = (constants[7]*states[0]-constants[8]*algebraic[1]*states[4])-constants[9]*states[4] rates[5] = (constants[8]*algebraic[1]*states[4]-constants[10]*states[5])-constants[11]*states[5] algebraic[2] = constants[17]*(1.00000+constants[18]*((power(voi, 2.00000))/(power(voi, 2.00000)+power(constants[19], 2.00000)))) algebraic[5] = 0.100000*algebraic[2] rates[1] = ((algebraic[2]*constants[9]*states[4]+algebraic[5]*constants[11]*states[5])-constants[3]*states[1]*states[3])-constants[16]*states[1] algebraic[4] = 0.200000*algebraic[2] algebraic[7] = 0.500000*constants[9]*algebraic[2] rates[7] = custom_piecewise([less(voi , constants[14]), constants[15]/constants[14] , True, (algebraic[4]*constants[11]*states[5]+algebraic[7]*states[6])-constants[13]*states[7]]) algebraic[6] = 0.100000*algebraic[2] algebraic[8] = 0.0100000*constants[9]*algebraic[2] rates[2] = ((algebraic[6]*constants[11]*states[5]+algebraic[8]*states[6])-constants[16]*states[2])-constants[4]*states[3]*states[2] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = (constants[5]*constants[6])/(constants[6]+states[1]) algebraic[1] = custom_piecewise([less(voi , constants[14]), 0.00000 , True, states[7]]) algebraic[2] = constants[17]*(1.00000+constants[18]*((power(voi, 2.00000))/(power(voi, 2.00000)+power(constants[19], 2.00000)))) algebraic[5] = 0.100000*algebraic[2] algebraic[4] = 0.200000*algebraic[2] algebraic[7] = 0.500000*constants[9]*algebraic[2] algebraic[6] = 0.100000*algebraic[2] algebraic[8] = 0.0100000*constants[9]*algebraic[2] algebraic[3] = states[3]+states[0]+states[4]+states[5]+states[6] 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)