如何修复Python Gekko方程错误“m.solve(disp=False)”？

Question

import numpy as np
from gekko import GEKKO 
import matplotlib.pyplot as plt

t_incubation = 5.1
t_infective = 3.3
R0= 2.4
N = 100000

e_initial=1/N
i_initial=0.00
r_initial=0.00
s_initial= 1- e_initial - i_initial - r_initial

alpha = 1/t_incubation
gamma = 1/t_infective
beta= R0*gamma

m = GEKKO()
u = m.MV(0,lb=0.0, ub=0.8)

s,e,i,r = m.Array(m.Var,4)
s.value= s_initial
e.value= e_initial
i.value=i_initial
r.value=r_initial
m.Equations([s.dt()== -(1-u)*beta * s * i,\
            e.dt()== (1-u)*beta * s * i - alpha * e,\
            i.dt== alpha * e - gamma * i,\
            r.dt()==gamma *i])
t= np.linspace(0,200,101)
t= np.insert(t,1,[0.001,0.002,0.004,0.008,0.02,0.04,0.08,\
                  0.2,0.4,0.8])
m.time=t
m.options.IMODE=7
m.options.NODES=3
m.solve(disp=False)

# plot the data
plt.figure(figsize=(8,5))

plt.subplot(3,1,1)
plt.plot(m.time, s.value, color='blue', lw=3, label='Susceptible')
plt.plot(m.time, r.value, color='red', lw=3, label='Recovered')


plt.subplot(3,1,2)
plt.plot(m.time, i.value, color='orange', lw=3, label='Infective')
plt.plot(m.time, e.value, color='purple', lw=3, label='Exposed')

#优化

m.options.IMODE=6
i.UPPER= 0.02
u.STATUS=1
m.options.SOLVER=3
m.options.TIME_SHIFT=0
s.value=s.value.value
e.value=e.value.value
i.value=i.value.value
r.value=r.value.value
m.Minimize(u)
m.solve(disp=True)

plt.subplot(3,1,1)
plt.plot(m.time, s.value, color='blue', lw=3, ls='--', label='Optimal susceptible')
plt.plot(m.time, r.value, color='red', lw=3, ls='--',label='optimal Recovered')


plt.subplot(3,1,2)
plt.plot(m.time, i.value, color='orange',ls='--', lw=3, label='Infective<2000')
plt.plot(m.time, e.value, color='purple',ls='--', lw=3, label='Optimal Exposed')
plt.ylim(0,0.2)
plt.ylabel('Fraction')
plt.legend()

plt.subplot(3,1,3)
plt.plot(m.time, u.value, 'k:',lw=3, label='Optimal (0=None, 1=No Interactions)')
plt.ylabel('Social Distancing')
plt.legend()

plt.xlabel('Time (days)')

plt.show()

我尝试运行代码，但失败了，并从系统中获得了以下内容

 m.solve(disp=False) and raise Exception(response)
Exception:  @error: Model Expression
 *** Error in syntax of function string: Invalid element: <boundmethodgkvariable
 .dtof0.0>

Answer 1

方程式中的di/dt项错过了parenthesis。

i.dt()== alpha * e - gamma * I

您可以大致了解下面的错误消息，以解决代码的哪一部分引发了问题。

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请看下面更正后的代码。

import numpy as np
from gekko import GEKKO 
import matplotlib.pyplot as plt

t_incubation = 5.1
t_infective = 3.3
R0= 2.4
N = 100000

e_initial=1/N
i_initial=0.00
r_initial=0.00
s_initial= 1- e_initial - i_initial - r_initial

alpha = 1/t_incubation
gamma = 1/t_infective
beta= R0*gamma

m = GEKKO(remote=True)
u = m.MV(0,lb=0.0, ub=0.8)

s,e,i,r = m.Array(m.Var,4)
s.value= s_initial
e.value= e_initial
i.value=i_initial
r.value=r_initial
m.Equations([s.dt()== -(1-u)*beta * s * i,
            e.dt()== (1-u)*beta * s * i - alpha * e,
            i.dt()== alpha * e - gamma * i,
            r.dt()==gamma *i])
t= np.linspace(0,200,101)
t= np.insert(t,1,[0.001,0.002,0.004,0.008,0.02,0.04,0.08,\
                  0.2,0.4,0.8])
m.time=t
m.options.IMODE=4
m.options.NODES=3
m.solve(disp=True)

# plot the data
plt.figure(figsize=(8,5))

plt.subplot(3,1,1)
plt.plot(m.time, s.value, color='blue', lw=3, label='Susceptible')
plt.plot(m.time, r.value, color='red', lw=3, label='Recovered')


plt.subplot(3,1,2)
plt.plot(m.time, i.value, color='orange', lw=3, label='Infective')
plt.plot(m.time, e.value, color='purple', lw=3, label='Exposed')

plt.show()

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