def sin_test(n=8,text_position='start'):
"""Test the stuff from the modules"""
from bfmplot import pl
import bfmplot as bp
import numpy as np
#bp.set_color_cycle(bp.cccs_colors)
#pl.figure(figsize=bp.phys_rev_column())
pl.figure(figsize=bp.golden_ratio(5))
x = np.linspace(1,5*np.pi,100)
for i in range(n):
pl.plot(x, 1-np.sin(x[::-1]/np.sqrt(i+1)), marker=bp.markers[i],mfc='w',label='$i=%d$'%i)
bp.strip_axis(pl.gca())
leg = pl.legend()
bp.align_legend_right(leg)
bp.arrow(pl.gca(), r'$i$',
(3, 1.8),
(6, 0.8),
text_position=text_position)
pl.xlabel('hello')
pl.ylabel('hello')
bp.set_n_ticks(pl.gca(), 3, 2)
#pl.xscale('log')
pl.gcf().tight_layout()
def sin_test(n=8,text_position='start'):
pl.figure(figsize=bp.golden_ratio(5))
x = np.linspace(0,5*np.pi,100)
for i in range(n):
pl.plot(x, 1-np.sin(x[::-1]/np.sqrt(i+1)), marker=bp.markers[i],mfc='w',label='$i=%d$'%i)
bp.strip_axis(pl.gca())
leg = pl.legend()
bp.align_legend_right(leg)
bp.arrow(pl.gca(), r'$i$', (14, 0.8), (10, 0.15), text_position=text_position, rad=0.3)
pl.xlabel('this is the x-label')
pl.ylabel('this is the y-label')
pl.gcf().tight_layout()
def sin_test(n=8, text_position='start', with_legend=True):
pl.figure(figsize=bp.golden_ratio(5))
x = np.linspace(0, 5 * np.pi, 100)
for i in range(n):
pl.plot(x,
1 - np.sin(x[::-1] / np.sqrt(i + 1)),
marker=bp.markers[i],
mfc='w',
label='$i=%d$' % i)
bp.strip_axis(pl.gca())
if with_legend:
leg = pl.legend()
bp.align_legend_right(leg)
pl.xlabel('this is the x-label')
pl.ylabel('this is the y-label')
pl.gca().set_title(name)
pl.gcf().tight_layout()
})
print(agentmodel.conditional_link_transmission_events)
agentmodel.set_random_initial_conditions({
S: N - int(0.01*N),
I: int(0.005*N),
E: int(0.005*N),
})
print("simulating")
t, result = agentmodel.simulate(800)
from bfmplot import pl
for c, res in result.items():
pl.plot(t, res,label=c)
model = EpiModel([S, E, I, R, X, T_I, T_E, Q],N)
model.add_transition_processes([
(E, alpha, I),
(I, rho, R),
(I, kappa, T_I),
(T_I, chi, X),
(T_E, xi, R),
(T_E, chi, X),
#(Q, omega, S),
])
model.add_transmission_processes([
t = solve_t(np.mean(k), n)
rho = solve_rho(np.mean(k), np.mean(k**2), n)
ax = fig.add_subplot(1, 3, 1)
pl.hist(k,
bins=np.arange(0, kmax, 2),
density=True,
alpha=1,
align='left',
color=bp.brewer_qualitative[1],
label='data',
histtype='step')
p = pk(n, t, rho, kmax, X, W)
pl.plot(np.arange(kmax),
p,
lw=1,
c=bp.brewer_qualitative[2],
label='model fit')
pl.xlim(0, 30)
ax.text(0.04, 0.95, '(a)', va='top', ha='left', transform=ax.transAxes)
bp.strip_axis(ax)
leg = pl.legend()
bp.align_legend_right(leg)
ax.set_ylabel('probability density $p_k$')
ax.set_xlabel('node degree $k$')
#pl.show()
#sys.exit(0)
### collab network
print("loading", 'degree_sequences/cond-mat.degree_sequence', '...')
dtype=float), np.array(self.cascade_size, dtype=float) / self.N
if __name__ == "__main__":
from sixdegrees.utils import to_networkx_graph
from sixdegrees import small_world_network, modular_hierarchical_network
import sixdegrees as sixd
from bfmplot import pl
import netwulf
B = 10
L = 3
N = B**L
k = 10
mu = -0.8
thresholds = [0.1] * N
initially_infected = np.arange(10)
#G = to_networkx_graph(*modular_hierarchical_network(B,L,k,mu))
G = to_networkx_graph(*sixd.random_geometric_kleinberg_network(N, k, mu))
Thresh = ThreshModel(G, initially_infected, thresholds)
t, a = Thresh.simulate()
pl.plot(t, a)
pl.ylim([0, 1])
pl.show()
x = np.arange(1, max(k1pos))
a0 = 2.30753
a1 = 0.27061
b1 = 0.9929
fac = (a1 - a0 * b1 - 1)
s = np.sqrt(2 * x / (N - 1))
s = np.sqrt(np.log(1 / (1 - x / (N - 1))**2))
#pl.plot(x, 1/(N-1)*np.sqrt((1-covariance)/covariance) * np.exp(-t**2/2/covariance+np.sqrt(2)*t*a0)* np.exp(np.sqrt(2)*fac*t*np.sqrt(2*x/(N-1))))
#pl.plot(x, 1/(N-1)*np.sqrt((1-covariance)/covariance) * np.exp(-t**2/2/covariance+np.sqrt(2)*t*a0)* np.exp(-np.sqrt(2)*fac*t*s))
#pl.plot(x, 1/(N-1)*np.sqrt((1-covariance)/covariance) * np.exp(-t**2/2/covariance)*\
# np.exp(-fac*np.sqrt(2*np.log((N-1)/x)))
# )
rho = covariance
prefac = 1 / (N - 1) * np.sqrt((1 - rho) / rho) * np.exp(-t**2 / 2 / rho)
pl.plot(x, pk(x, N, t, covariance), label='asymptotic solution Eq. (29)')
pl.plot(x, 1 / x**(np.sqrt(2)) * 0.1, label='$1/k^{\sqrt{2}}$')
#pl.plot(x, prefac*np.exp(np.sqrt(2)*t*1/(x/(N-1))**0.5/3.25),label='stretched exponential')
pl.plot(x,
prefac * np.exp(np.sqrt(2) * t * np.sqrt(2 * np.log(
(N - 1) / x))) / 15,
label='mu log')
pl.legend()
pl.xscale('log')
pl.yscale('log')
pl.xlabel('degree $k$')
pl.ylabel('probability')
fig.tight_layout()
zorder=-1000,
)
ax[i].text(0.7,
0.03,
titlemap[province],
transform=ax[i].transAxes,
ha='right',
va='bottom',
bbox={
'facecolor': 'w',
'edgecolor': 'w',
'pad': 0
})
pl.plot(t,
cases,
marker=markers[i + 2],
c=colors[i + 2],
label='data',
mfc='None')
pl.plot(tt, f(tt, *p), c='k', lw=1, label='$Q_I$')
_c = i % (n_col)
_r = i // (n_col)
if _r == n_row - 1:
pl.xlabel('days since Jan. 20th')
if _c == 0 and _r == 0:
pl.ylabel('confirmed cases', )
pl.gca().yaxis.set_label_coords(-0.3, -0.2)
pl.xlim([1, 30])
pl.xscale('log')
pl.yscale('log')
tt2 = tt[tt > tswitch]
result = model.SIRX(
tt,
cases[0],
params['eta'],
params['rho'],
params['kappa'],
params['kappa0'],
N,
params['I0_factor'],
)
X = result[2, :] * N
I = result[1, :] * N
#S = result[0,:]*N
pl.plot(t, cases, marker=markers[i], c=colors[i], label='data', mfc='None')
pl.plot(t2, cases2, marker=markers[i], c='grey', label='data', mfc='None')
pl.plot(tt1,
X[tt <= tswitch],
'-',
c='k',
label='$Q_I$ (detected and quarantined)')
pl.plot(tt2,
X[tt > tswitch],
'-.',
c='k',
label='$Q_I$ (detected and quarantined)')
pl.plot(tt, I, '--', c=colors[2], lw=1.5, label='$I$ (undected infected)')
#pl.plot(tt, S,label='model')
rho = np.linspace(0, 0.5, 200)
k = 2**np.arange(0, 10, 2)
k = np.array(k, dtype=float)
variances = np.zeros((200, 5))
for i in range(200):
for j in range(5):
t = solve_t(k[j], n)
variances[i, j] = variance(t, rho[i], n, NMAX)
fig = plt.figure(2, figsize=(6, 6))
ax = fig.add_subplot(1, 1, 1)
plt.xlabel(r'$\rho$', size=16)
plt.ylabel(r'Var[k]', size=14)
for i in range(5):
plt.plot(rho, variances[:, i], label=r'$k=$' + str(k[i]))
ax.set_yscale('log')
#ax.set_xscale('log')
plt.legend(loc=4)
plt.savefig('figures/variance.pdf')
### triangle plots
n = 10**5
NMAX = 20 # increase this if needed
k = 10**np.linspace(0, 4.99, 20)
rho = np.linspace(0, 0.5, 6)
triangle_density = np.zeros((20, 6))
import numpy as np
from scipy.interpolate import interp1d
from bfmplot import pl
import bfmplot as bp
x = np.linspace(0, 6, 9)
y = 2 + np.sin(x)
x2 = np.linspace(0, 6, 1000)
for _x, _y in zip(x, y):
print(_x, _y)
interp_modes = ['zero', 'linear', 'nearest', 'quadratic']
pl.figure()
pl.plot(x, y, 's', label='data')
for kind in interp_modes:
f = interp1d(x, y, kind=kind)
pl.plot(x2, f(x2), label=kind)
pl.legend()
bp.strip_axis(pl.gca())
pl.xlabel('time')
pl.ylabel('value')
pl.gcf().tight_layout()
pl.show()
model.set_processes(quadratic_processes + linear_processes)
initial_conditions = {(node, "S"): 1.0 for node in nodes}
initial_conditions[(nodes[0], "S")] = 0.8
initial_conditions[(nodes[0], "I")] = 0.2
model.set_initial_conditions(initial_conditions,
allow_nonzero_column_sums=True)
# set compartments for which you want to obtain the
# result
plot_compartments = [(node, "I") for node in nodes]
# integrate
import numpy as np
t = np.linspace(0, 12, 1000)
result = model.integrate(t, return_compartments=plot_compartments)
# plot result
from bfmplot import pl as plt
plt.figure()
for (node, _), concentration in result.items():
plt.plot(t, concentration, label='node: ' + str(node))
plt.xlabel("time")
plt.ylabel("I")
plt.legend()
plt.gcf().tight_layout()
plt.gcf().savefig("chain_I.png", dpi=300)
plt.show()
tau_new = []
N_meas = 10000
for meas in tqdm(range(N_meas)):
tau_con.append(conservative_method(t0, y0))
tau_new.append(new_method(t0, y0))
from bfmplot import pl
from scipy.integrate import cumtrapz
pl.hist(tau_con, bins=200, density=True, histtype='step')
pl.hist(tau_new, bins=200, density=True, histtype='step')
t = np.linspace(0, 120, 1000)
lamb = np.array([get_event_rates(_t, y0).sum() for _t in t])
integral = cumtrapz(lamb, x=t, initial=0)
p = lamb * np.exp(-integral)
pl.plot(t, p)
pl.xlabel('tau')
pl.ylabel('pdf')
#pl.yscale('log')
pl.gcf().tight_layout()
pl.figure()
pl.plot(*cum_hist(tau_con))
pl.plot(*cum_hist(tau_new))
pl.plot(t, np.exp(-integral))
pl.ylabel('P(t>tau)')
pl.xlabel('tau')
#pl.yscale('log')
pl.gcf().tight_layout()
model.set_processes([
(S, I, alpha, I, I),
(I, beta, R),
(None, gamma, S),
(None, 1e-3, I),
])
model.set_initial_conditions({S: N - I0, I: I0})
t, result_sim = model.simulate(4000)
from bfmplot import pl
import bfmplot as bp
for iC, (C, res) in enumerate(result_sim.items()):
pl.plot(t, res, label=C, lw=1.5, c=bp.colors[iC])
model.set_processes([
(S, I, alpha, I, I),
(I, beta, R),
(None, gamma, S),
])
result = model.integrate(t)
for iC, (C, res) in enumerate(result.items()):
pl.plot(t, res, c=bp.colors[iC], ls='-.')
bp.strip_axis(pl.gca())
pl.xlim([0, 150])
pl.ylim([0, 1000])
initial_conditions = {(node, "S"): 1.0 for node in range(N)}
initial_conditions[(0, "S")] = 0.99
initial_conditions[(0, "I")] = 0.01
model.set_initial_conditions(initial_conditions,
allow_nonzero_column_sums=True)
t = np.linspace(0, 20, 100)
from bfmplot import pl
return_compartments = [(node, "I") for node in range(N)]
print("integrate")
result = model.integrate_and_return_by_index(
t,
return_compartments=return_compartments,
)
print("plot")
pl.figure()
for iC, C in enumerate(return_compartments):
pl.plot(t, result[iC, :])
end = time()
print("needed", end - start, "seconds")
pl.show()
pl.sca(ax[i])
tt = np.logspace(np.log(t[0]), np.log(35), base=np.exp(1))
result = model.SIRX(tt, cases[0],
params['eta'],
params['rho'],
params['kappa'],
params['kappa0'],
N,
params['I0_factor'],
)
X = result[2,:]*N
I = result[1,:]*N
#S = result[0,:]*N
pl.plot(t, cases,marker=markers[i],c=colors[i],label='data',mfc='None')
pl.plot(tt, X,c='k',label='$Q_I$ (detected and quarantined)')
pl.plot(tt, I,'--',c=colors[2],lw=1.5,label='$I$ (undected infected)')
#pl.plot(tt, S,label='model')
_c = i % n_col
_r = i // n_col
if _r == n_row-1:
pl.xlabel('days since Jan. 21st')
if _c == 0:
pl.ylabel('confirmed')
#pl.title(titlemap[province])
ax[i].text(0.03,0.97,
"{}.{}".format(letter[_r], roman[_c]),
transform=ax[i].transAxes,
set_lims[_ax](Ticks.lim)
set_ticks[_ax](Ticks.ticks)
if __name__ == "__main__":
import numpy as np
import bfmplot as bp
fig, ax = pl.subplots(1, 1)
x = np.linspace(1, 10, 100)
mus = np.linspace(1, 4, 4)
for mu in mus:
y = x**mu
pl.plot(x, y, c=bp.brewer_qualitative[0])
#pl.xscale('log')
bp.strip_axis(ax, horizontal='left')
pl.yscale('log')
ax.set_xlabel('x')
ax.set_ylabel('y')
pl.gcf().tight_layout()
pl.xlim([1, 10])
for mu in mus:
label = r'$\mu={:d}$'.format(int(mu))
y = x**mu
add_curve_label(ax, x, y, label, label_pos_rel=0.5 + mu / 50)
expected_counts[model.get_compartment_id(C0)] = N_measurements * ((N-1)*rateA / (rateB + rateE + rateA) * probAC0) expected_counts[model.get_compartment_id(C1)] = N_measurements * ((N-1)*rateA / (rateB + rateE + rateA) * probAC1) expected_counts[model.get_compartment_id(D)] = N_measurements * ((N-1)*rateB / (rateB + rateE + rateA) * probBD) expected_counts[model.get_compartment_id(F)] = (N-1) * expected_counts[model.get_compartment_id(E)] expected_counts[model.get_compartment_id(S)] = N_measurements * N - expected_counts.sum() pl.bar(x+width/2, expected_counts, width) pl.xticks(x) pl.gca().set_xticklabels(model.compartments) pl.figure() ndx = np.where(expected_counts==0) counts[ndx] = 1 expected_counts[ndx] = 1 pl.plot(x, np.abs(1-counts/expected_counts)) from scipy.stats import entropy _counts = np.delete(counts,1) _exp_counts = np.delete(expected_counts,1) print(entropy(_counts, _exp_counts)) pl.show()
import bfmplot as bp
data = np.array([
(0.0, 2.00),
(0.75, 2.68),
(1.5, 3.00),
(2.25, 2.78),
(3.0, 2.14),
(3.75, 1.43),
(4.5, 1.02),
(5.25, 1.14),
(6.0, 1.72),
])
times, rates = data[:, 0], data[:, 1]
x2 = np.linspace(times[0], times[-1], 1000)
interp_modes = ['zero', 'linear', 'nearest', 'quadratic']
pl.figure()
pl.plot(times, rates, 's', label='data')
for kind in interp_modes:
f = interp1d(times, rates, kind=kind)
pl.plot(x2, f(x2), label=kind)
pl.legend(frameon=False)
bp.strip_axis(pl.gca())
pl.xlabel('time')
pl.ylabel('value')
pl.gcf().tight_layout()
pl.gcf().savefig('interp1d.png', dpi=300)
pl.show()
(I, rho, None),
])
model.set_initial_conditions({
S: 190,
I: 10,
})
model.set_parameter_values({
eta: 4,
rho: 1,
})
def print_status():
print(model.t0/50*100)
t, result = model.simulate(50,sampling_dt=0.1,sampling_callback=print_status)
pl.plot(t, result[S],label='S')
pl.plot(t, result[I],label='I')
model.set_initial_conditions({
S: 190,
I: 10,
})
#tt = np.linspace(0,100,1000)
tt = t
result = model.integrate(tt)
pl.plot(tt, result[S],label='S')
pl.plot(tt, result[I],label='I')
pl.show()
(I, quarantine_rate, Q),
])
I0 = 0.01
model.set_initial_conditions({S: 1 - I0, I: I0})
import numpy as np
from bfmplot import pl as plt
import bfmplot as bp
t = np.linspace(0, 100, 1000)
result = model.integrate(t)
plt.figure()
for compartment, incidence in result.items():
plt.plot(t, incidence, label=compartment)
plt.xlabel('time [days]')
plt.ylabel('incidence')
plt.legend()
bp.strip_axis(plt.gca())
plt.gcf().tight_layout()
plt.savefig('SEIRQ.png', dpi=300)
N = 1000
I0 = 100
model = epk.EpiModel([S, E, I, R, Q], initial_population_size=N)
model.set_processes([
(S, I, infection_rate, E, I),
N = 200000
tmax = 50
model = EpiModel([S,E,I,R],N)
model.set_processes([
( S, I, 2, E, I ),
( I, 1, R),
( E, 1, I),
])
model.set_initial_conditions({S: N-100, I: 100})
tt = np.linspace(0,tmax,10000)
result_int = model.integrate(tt)
for c, res in result_int.items():
pl.plot(tt, res)
start = time()
t, result_sim = model.simulate(tmax,sampling_dt=1)
end = time()
print("numeric model needed", end-start, "s")
for c, res in result_sim.items():
pl.plot(t, res, '--')
model = StochasticEpiModel([S,E,I,R],N)
model.set_link_transmission_processes([
( I, S, 2, I, E ),
])
params['kappa0'],
N,
params['I0_factor'],
)
X = result[2,:]*N
I = result[1,:]*N
imax = np.argmax(I)
print(imax)
max_date = tt_dates[imax]
max_tt = tt[imax]
print(max_date)
#S = result[0,:]*N
pl.plot(t, cases,marker=markers[i+2],c=colors[i+2],label='data',mfc='None')
pl.plot(t2, cases2,marker='o',ms=5,c='grey',label='data',mfc='None')
pl.plot(tt, X,'-',c='k')
#pl.plot(tt1, X[tt<=tswitch],'-',c='k')
#pl.plot(tt2, X[tt>tswitch],'-',c='k')
pl.plot(tt, I,'--',c=colors[2],lw=1.5)
pl.plot([max_tt]*2, [0,max_dates_pos[i]],':',c=colors[0],lw=1.5)
pl.text(max_tt-1, max_dates_pos[i], max_dates[i],
transform=ax[i].transData,
ha='left',
va=max_dates_va[i],
color=colors[0],
fontsize=9,
bbox={'facecolor':'w','edgecolor':'w','pad':0}
)
ax[i].plot([22.5,22.5], [0,cases[-1]],':',c=colors[0],lw=1.5)
})
print(model.conditional_link_transmission_events)
model.set_random_initial_conditions({"S": N - I0, "I": I0})
print(model.node_and_link_events)
start = time()
t, result = model.simulate(300, sampling_dt=1)
end = time()
print("simulation took", end - start, "seconds")
from bfmplot import pl
for comp, series in result.items():
pl.plot(t, series, label=comp)
kw = {
'R0': R0,
'Q0': Q0,
'k0': k0,
'I0': I0 / N,
'waning_quarantine_rate': waning_quarantine_rate,
'recovery_rate': recovery_rate,
'infection_rate': infection_rate,
'app_participation_ratio': 1.0,
't': t,
}
t, result = mean_field_SIRX_tracing(kw)
if i == 0:
_d = 7
else:
_d = 4
pexp, _ = curve_fit(fexp, _t[_t <= _d], _cases[_t <= _d], [1, 1.])
print("pexp =", pexp)
print(p)
tt = np.logspace(np.log(t[0]), np.log(t[-1]), base=np.exp(1))
pl.sca(ax[i])
growth_rate = (6.2 - 1) / 8
pl.plot(t, cases, marker=markers[i], c=colors[i], label='data', mfc='None')
pl.plot(tt, f(tt, *p), c='k', lw=1, label='$Q_I$')
pl.plot(tt,
fexp(tt, growth_rate * 1.1, _cases[0] * 2.3),
c=colors[2],
lw=1,
label='$Q_I$',
ls='--')
_c = i % (n_col)
_r = i // (n_col)
if _r == n_row - 1:
pl.xlabel('days since Jan. 20th')
if _c == 0 and _r == 0:
pass
#pl.ylabel('confirmed cases',)
k = 2**np.arange(0, 10, 2)
k = np.array(k, dtype=float)
if not data_exists:
variances = np.zeros((len(rho), len(k)))
for i in range(len(rho)):
for j in range(len(k)):
t = solve_t(k[j], n)
variances[i, j] = variance(t, rho[i], n, NMAX)
fig, ax = pl.subplots(1, 1, figsize=(4, 2.5))
pl.xlabel(r'local edge weight correlation $\rho$')
pl.ylabel(r'node degree variance $\mathrm{Var}(k)$')
for i in range(len(k)):
pl.plot(rho, variances[:, i], c=bp.brewer_qualitative[1])
bp.strip_axis(ax)
ax.set_yscale('log')
#ax.set_xscale('log')
ax.set_xlim([0, 0.5])
fig.tight_layout()
for i in range(len(k)):
bp.add_curve_label(ax,
rho,
variances[:, i],
r'$\left\langle k\right\rangle={:d}$'.format(int(k[i])),
label_pos_rel=0.4)
if not data_exists:
b = p['rho'].value
a = p['eta'].value
I0f = p['I0_factor'].value
N = pdata['population'] / 1e6
print(p['kappa0'],p['kappa'])
Q = (k+k0)/(b+k+k0)
P = k0/(k+k0)
R0eff = a / (b+k+k0)
tabledata.append([titlemap[province], N, Q, P, R0eff, k, k0, I0f, ])
ks.append(k)
k0s.append(k0)
for i, (_k0, _ks) in enumerate(zip(k0s, ks)):
pl.plot([_k0],[_ks],marker=markers[i],color=colors[i],markersize=7)
pl.xlim([0,0.14])
pl.ylim([-.05,0.55])
pl.gcf().savefig('model_fit_figures/'+fn+'.png',dpi=300)
pl.show()
headers = [
'Province',
'$N/10^6$','$Q$',
'$P$',
'$R_{0,\mathrm{eff}}$',
'$\kappa$ [$\mathrm{d}^{-1}$]',
'$\kappa_{0}$ [$\mathrm{d}^{-1}$]',
'$I_0/X_0$',
