How to fix Python Gekko equation error “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')

#optimise

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()

i tried running the code but failed in doing so and gained the following from the system

 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

di/dt term in your equation missed the parenthesis.

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

You can get a rough idea with the error message like below to address which part of the code raised the problem.

Please see the corrected code below.

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()