/
betafit.py
73 lines (67 loc) · 2.1 KB
/
betafit.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
import numpy as np
import scipy as sp
import scipy.integrate as spint
from scipy.optimize import minimize
import warnings
import matplotlib.pyplot as plt
import tabular
def odeint(f,u0,t0,tb):
r = spint.ode(f)
r.set_integrator('dopri5',atol=1e-10,rtol=1e-10)
r.set_initial_value(u0,t0)
y = []
t = []
dt = 1e-2
warnings.filterwarnings("ignore",category=UserWarning)
while r.successful() and r.t < tb:
r.integrate(min(r.t+dt,tb))
y.append(r.y)
t.append(r.t)
return np.array(t),np.array(y)
# kernel(c) returns f(t,u)
def odefit(kernel,c_init,u0,t0,tb,u_star):
F = lambda c: npla.norm(odeint(kernel(c),u0,t0,tb) - U_star)
c_star = minimize(F,c_init)
return c_star
def ebola_kernel(beta):
br,mu,eps,gamma, ddr = .037/365, 0.012/365, 1./6, 0.1, 0.70/10
def f(t,Y):
S,E,I,R,D, I_c = tuple(Y)
N = sum(Y[0:4])
return np.array([
br*N-beta*S*I/N-mu*S,
beta*S*I/N - (eps+mu)*E,
eps*E - (gamma+ddr)*I,
(1./10 -ddr)*I- mu*R,
ddr*I,
eps*E
])
return f
if __name__ == "__main__":
rfields = ['t','C']
realdata = np.array(tabular.tbarr('mcm2015files/betatest.csv',rfields,{field:'float' for field in rfields},{}))
initState = np.array([22e6,0,86,0,0,86])
lobound,hibound = 0.0, 1.0
guess = lobound*0.5+hibound*0.5
T,Y = odeint(ebola_kernel(guess),initState,0,317)
ret = Y[-1][5]
print guess, ret
while abs(ret-22460) > 0.1:
if ret-22460 < 0:
lobound = guess
else:
hibound = guess
guess = lobound*0.5 + hibound*0.5
T,Y = odeint(ebola_kernel(guess),initState,0,317)
ret = Y[-1][5]
print guess, ret
#f = ebola_kernel(guess)
#T,Y = odeint(ebola_kernel(guess),initState,0,365*12)
fig,ax = plt.subplots()
pltlist = ((1,'E'),(2,'I'),(4,'D'),(5,'C'))
for k, s in pltlist[3:]:
ax.plot(T,Y[:,k],label=s)
ax.plot(realdata[:,0],realdata[:,1],label='real C')
legend = ax.legend(shadow=True,loc=2)
print Y[-1]
plt.show()