我试图在python中解决基于延迟微分方程和常微分方程的模型，但遇到了几个错误

Question

ii was trying to solve model based on delayed differential equation and ordinary differential equation to generate simulations and graphs. but encountered several errors such as module is not callable. in the TypeError Traceback (most recent call last) in () 36 g=lambda t:0 37 y0 = c1_0, c2_0, c3_0, c4_0, c5_0, c6_0 ,c7_0, c8_0, c9_0, c10_0, c11_0, c12_0, c13_0, c14_0, c15_0, c16_0 ,c17_0, c18_0, c19_0, c20_0, c21_0, c22_0, c23_0, c24_0, c25_0, c26_0 ,c27_0, c28_0, c29_0, c30_0, c31_0 ---> 38 results= ddeint(TNF_alpha_model, g, tt, args=(k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, k17, k18, k19, k20, k21, k22, k23, k24, k25, k26, k27, k28, k29, p, t0)) 39 c1, c2, c3, c4, c5, c6 ,c7, c8, c9, c10, c11, c12, c13, c14, c15, c16 ,c17, c18, c19, c20, c21, c22, c23, c24, c25, c26 ,c27, c28, c29, c30, c31 = results.T 40

TypeError: 'module' object is not callable

import numpy as np
import matplotlib.pyplot as plt

import math as m
import pylab
import ddeint as ddeint
# VALUES OF PARAMETERS
k1 = 0.185*10**(-3)
k2 = 0.00125*10**(-3)
k3 = 0.185*10**(-3)
k4 = 0.00125*10**(-3) 
k5 = 0.185*10**(-3)
k6 = 0.00125*10**(-3)
k7 = 0.185*10**(-3)
k8 = 0.00125*10**(-3) 
k9 = 0.185*10**(-3)
k10 = 0.00125*10**(-3)
k11 = 0.37*10**(-3)
k12 = 0.014*10**(-3)
k13 = 0.00125*10**(-3) 
k14 = 0.37*10**(-3)
k15 = 0.185*10**(-3)
k16 = 0.00125*10**(-3)
k17 = 0.37*10**(-3)
k18 = 0.5*10**(-3)
k19 = 0.2*10**(-3)
k20 = 0.1*10**(-3)
k21 = 0.1*10**(-3)
k22 = 0.06*10**(-3)
k23 = 100*10**(-3)
k24 = 0.185*10**(-3)
k25 = 0.00125*10**(-3)
k26 = 0.37*10**(-3)
k27 = 0.37*10**(-3)
k28 = 0.5*10**(-3)
k29 = 750*10**(-3)
p = 1.75*10**(-3)


# initial values
c1_list = np.array([ 1, 10]) #TNF-a 
c2_0 = 100 #TNFR1 
c3_0 = 0 # TNF-a/TNFR1
c4_0 = 150 #TRADD
c5_0 = 0 # TNF-a/TNFR1/TRADD
c6_0 = 100 #TRAF2
c7_0 = 0 #TNF-a/TNFR1/TRADD/TRAF2
c8_0 = 100 #RIP-1
c9_0 = 0 # TNF-a/TNFR1/TRADD/TRAF2/RIP-1, early complex
c10_0 = 100 # IKK
c11_0 = 0 #TNF-a/TNFR1/TRADD/TRAF2/RIP-1/IKK, survival complex
c12_0 = 0 # IKK
c13_0 = 250 # Ik-B/NF-kB
c14_0 = 0 #Ik-B/NF-kB/IKK
c15_0 = 0 # Ik-B-P
c16_0 = 0 #NF-kB
c17_0 = 100 #FADD
c18_0 = 0 #TNF-a/TNFR1/TRADD/TRAF2/RIP-1/FADD
c19_0 = 0 #TRADD/TRAF2/RIP-1/FADD
c20_0 = 80 #Caspase-8
c21_0 = 0 #TRADD/TRAF2/RIP-1/FADD/caspase-8, death complex (death-inducing signaling complex—DISC)
c22_0 = 0 #Caspase-8
c23_0 = 200 #Caspase-3
c24_0 = 0 #Caspase-8/caspase-3
c25_0 = 0 #Caspase-3
c26_0 = 0 #DNA-fragmentation
c27_0 = 0 #c-IAP
c28_0 = 0 #Caspase-3/c-IAP
c29_0 = 800 #DNA (intact)
c30_0 = 0 # Caspase-3/DNA
c31_0 = 0 #IkB

t_max=36000
tt= np.linspace(0, t_max + 1, t_max+1)
t0 = 20
for c1_0 in c1_list:
    def TNF_alpha_model(y, t, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, k17, k18, k19, k20, k21, k22, k23, k24, k25, k26, k27,k28, k29, p, t0):
      c1, c2, c3, c4, c5, c6 ,c7, c8, c9, c10, c11, c12, c13, c14, c15, c16 ,c17, c18, c19, c20, c21, c22, c23, c24, c25, c26 ,c27, c28, c29, c30, c31 = y
      dc1dt = -k1*c1*c2 + k2*c3
      dc2dt = -k1*c1*c2 + k2*c3 + k17*c18 + k11*c11
      dc3dt = k1*c1*c2 - k2*c3 - k3*c3*c4 + k4*c5
      dc4dt = -k3*c3*c4 + k4*c5 + k11*c11 + k20*c21
      dc5dt =  k3*c3*c4 - k4*c5 - k5*c5*c6 + k6*c7
      dc6dt = -k5*c5*c6 + k6*c7 + k11*c11 + k20*c21
      dc7dt = k5*c5*c6 - k6*c7 - k7*c7*c8 + k8*c9
      dc8dt = -k7*c7*c8 + k8*c9 + k11*c11 + k20*c21
      dc9dt = k7*c7*c8 - k8*c9 - k9*c9*c10 + k10*c11 - k15*c9*c17 + k16*c18
      dc10dt = - k9*c9*c10 + k10*c11 + k14*c14
      dc11dt = k9*c9*c10 - k10*c11 - k11*c11
      dc12dt = -k12*c12*c13 + k13*c14 + k11*c11
      dc13dt = -k12*c12*c13 + k13*c14 + k29*c16*c31
      dc14dt = k12*c12*c13 - k13*c14 - k14*c14
      dc15dt = k14*c14
      dc16dt = k14*c14 - k29*c16*c31
      dc17dt = -k15*c9*c17 + k16*c18 + k20*c21
      dc18dt = k15*c9*c17 - k16*c18 - k17*c18
      dc19dt = k17*c18 - k18*c19*c20 + k19*c21
      dc20dt = -k18*c19*c20 + k19*c21
      dc21dt = k18*c19*c20 - k19*c21 - k20*c21
      dc22dt = k20*c21 - k21*c22*c23 + k22*c24 + k23*c24
      dc23dt = -k21*c22*c23 + k22*c24
      dc24dt = k21*c22*c23 - k22*c24 - k23*c24
      dc25dt = k23*c24 - k28*c27*c25 - k24*c29*c25 + k25*c30 + k26*c30
      dc26dt = k26*c30
      dc27dt = p*c16(t - t0) - k28*c27*c25
      dc28dt = k28*c27*c25
      dc29dt = -k24*c29*c25 + k25*c30
      dc30dt = k24*c29*c25 - k25*c30 - k26*c30
      dc31dt = p*c16(t - t0) - k29*c16*c31
      return dc1dt, dc2dt, dc3dt, dc4dt, dc5dt, dc6dt, dc7dt, dc8dt, dc9dt, dc10dt, dc11dt, dc12dt, dc13dt, dc14dt, dc15dt, dc16dt, dc17dt, dc18dt, dc19dt, dc20dt, dc21dt, dc22dt, dc23dt, dc24dt, dc25dt, dc26dt, dc27dt, dc28dt, dc29dt, dc30dt, dc31dt
    g=lambda t:0
    y0 = c1_0, c2_0, c3_0, c4_0, c5_0, c6_0 ,c7_0, c8_0, c9_0, c10_0, c11_0, c12_0, c13_0, c14_0, c15_0, c16_0 ,c17_0, c18_0, c19_0, c20_0, c21_0, c22_0, c23_0, c24_0, c25_0, c26_0 ,c27_0, c28_0, c29_0, c30_0, c31_0
    results= ddeint(TNF_alpha_model, g, tt, args=(k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, k17, k18, k19, k20, k21, k22, k23, k24, k25, k26, k27, k28, k29, p, t0))
    c1, c2, c3, c4, c5, c6 ,c7, c8, c9, c10, c11, c12, c13, c14, c15, c16 ,c17, c18, c19, c20, c21, c22, c23, c24, c25, c26 ,c27, c28, c29, c30, c31 = results.T
    
   
    
    plt.figure()
    plt.plot(t, c11, label='Survival complex' , c= 'g')
    plt.scatter(t, c11, label='Survival complex' , c= 'g')
    plt.title('complex evolution at ligand conc.  nM')
    plt.xlabel('Time in seconds' )
    plt.ylabel('Conc.[in nM] of complex formed')
    plt.figure()
    plt.scatter(t, c21, label='death complex' , c= 'r')
    plt.plot(t, c21, label='death complex' , c= 'r')
    plt.title('complex evolution at ligand conc. ' + '  nM')
    plt.xlabel('Time in seconds' )
    plt.ylabel('Conc.[in nM] of complex formed')
    plt.legend()

Answer 1

You have a typo when you call ddeint , you have imported the module as itself, when I believe you wanted to import the function ddeint from the module. You should replace:

import ddeint as ddeint

With:

from ddeint import ddeint