def test_birth_death(self):
epi = EpiModel(list("SIR"))
R0 = 2
rho = 1
mu = 0.2
eta = R0 * rho
with self.assertWarns(UserWarning):
epi.set_processes([
("S", "I", eta, "I", "I"),
("I", rho, "R"),
(None, mu, "S"),
("S", mu, None),
("R", mu, None),
("I", mu, None),
])
epi.set_initial_conditions({'S': 0.8, 'I': 0.2})
t = [0, 1000]
res = epi.integrate(t)
assert (np.isclose(res['S'][-1], (mu + rho) / eta))
assert (np.isclose(res['I'][-1],
mu / eta * (eta - mu - rho) / (mu + rho)))
def test_dynamic_birth(self):
A = "A"
epi = EpiModel([A])
epi.set_initial_conditions({A: 1})
with self.assertWarns(UserWarning):
epi.set_processes([
(None, lambda t, y: 2 * t, A),
])
res = epi.integrate([0, 5])
assert (np.isclose(res[A][-1], 5**2 + 1))
def test_temporal_gillespie(self, plot=False):
scl = 40
def R0(t, y=None):
return 4 + np.cos(t * scl)
S, I = list("SI")
N = 100
rec = 1
model = EpiModel([S, I], N)
model.set_processes([
(S, I, R0, I, I),
(I, rec, S),
])
I0 = 1
S0 = N - I0
model.set_initial_conditions({
S: S0,
I: I0,
})
taus = []
N_sample = 10000
for sample in range(N_sample):
tau, _ = model.get_time_leap_and_proposed_compartment_changes(0)
taus.append(tau)
I = lambda t: (4 * t + 1 / scl * np.sin(t * scl))
I2 = lambda t: I(t) * S0 * I0 / N + I0 * rec * t
pdf = lambda t: (R0(t) * S0 * I0 / N + I0 * rec) * np.exp(-I2(t))
measured, bins = np.histogram(taus, bins=100, density=True)
theory = [
np.exp(-I2(bins[i - 1])) - np.exp(-I2(bins[i]))
for i in range(1, len(bins)) if measured[i - 1] > 0
]
experi = [
measured[i - 1] for i in range(1, len(bins)) if measured[i - 1] > 0
]
# make sure the kullback-leibler divergence is below some threshold
if plot: # pragma: no cover
import matplotlib.pyplot as pl
pl.figure()
pl.hist(taus, bins=100, density=True)
tt = np.linspace(0, 1, 100)
pl.plot(tt, pdf(tt))
pl.yscale('log')
pl.figure()
pl.hist(taus, bins=100, density=True)
tt = np.linspace(0, 1, 100)
pl.plot(tt, pdf(tt))
pl.show()
assert (entropy(theory, experi) < 0.01)
def test_initial_condition_warnings(self):
A, B, C = list("ABC")
epi = EpiModel(list("ABC"))
with self.assertWarns(UserWarning):
# this should raise a warning that rates do not sum to zero
epi.set_initial_conditions({A: 0.1, B: 0.2})
with self.assertWarns(UserWarning):
# this should raise a warning that initial conditions were set twice
epi.set_initial_conditions([(A, 0.1), (A, 0.2)])
def test_stochastic_fission(self):
A, B, C = list("ABC")
N = 10
epi = EpiModel([A, B, C],
N,
correct_for_dynamical_population_size=True)
epi.add_fusion_processes([
(A, B, 1.0, C),
])
epi.set_initial_conditions({A: 5, B: 5})
t, res = epi.simulate(1e9)
assert (res[C][-1] == 5)
def test_inference_of_temporal_dependence(self, plot=False):
data = np.array([
(1.0, 2.00),
(10000.0, 2.00),
(10001.0, -2.00),
])
times, rates = data[:, 0], data[:, 1]
f = interp1d(times, rates, kind='linear')
def infection_rate(t, y):
return f(t)
S, I = list("SI")
N = 100
rec = 1
model = EpiModel([S, I], N)
# first, initialize the time to t0 = 1, so
# column sum tests do not fail
model.set_initial_conditions({S: 99, I: 1}, initial_time=1)
# Here, the function will fail to evaluate time dependence
# but will warn the user that there were errors in time
# evaluation.
self.assertWarns(
UserWarning,
model.set_processes,
[
(S, I, infection_rate, I, I),
(I, infection_rate, S),
],
)
assert (not model.rates_have_explicit_time_dependence)
assert (model.rates_have_functional_dependence)
# this should warn the user that rates are functionally dependent
# but that no temporal dependence could be inferred, to in case
# they know that there's a time dependence, they have to state
# that explicitly
self.assertWarns(UserWarning, model.simulate, tmax=2)
model.set_initial_conditions({S: 99, I: 1}, initial_time=1)
# here, the time dependence is given explicitly and so
# the warning will not be shown
model.simulate(tmax=2, rates_have_explicit_time_dependence=True)
def test_correcting_for_declining_pop_size(self):
A, B = list("AB")
epi = EpiModel([A, B], 10, correct_for_dynamical_population_size=True)
epi.add_transition_processes([
#(None, 0.1, A),
])
epi.add_fusion_processes([
(A, B, 1, B),
])
epi.set_initial_conditions({B: 4, A: 6})
tt = np.linspace(0, 30)
result = epi.integrate(tt)
#from matplotlib import pyplot as pl
#pl.plot(tt, result[A], label=A)
#pl.plot(tt, result[B], label=B)
epi.correct_for_dynamical_population_size = False
result = epi.integrate(tt)
def test_stochastic_well_mixed(self):
S, E, I, R = list("SEIR")
N = 75000
tmax = 100
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)
t, result_sim = model.simulate(tmax,
sampling_dt=1,
return_compartments=[S, R])
model = StochasticEpiModel([S, E, I, R], N)
model.set_link_transmission_processes([
(I, S, 2, I, E),
])
model.set_node_transition_processes([
(I, 1, R),
(E, 1, I),
])
model.set_random_initial_conditions({S: N - 100, I: 100})
t, result_sim2 = model.simulate(tmax,
sampling_dt=1,
return_compartments=[S, R])
for c, res in result_sim2.items():
#print(c, np.abs(1-res[-1]/result_int[c][-1]))
#print(c, np.abs(1-res[-1]/result_sim[c][-1]))
assert (np.abs(1 - res[-1] / result_int[c][-1]) < 0.05)
assert (np.abs(1 - res[-1] / result_sim[c][-1]) < 0.05)
def test_birth_stochastics(self):
A, B, C = list("ABC")
epi = EpiModel([A, B, C],
10,
correct_for_dynamical_population_size=True)
epi.set_initial_conditions({A: 5, B: 5})
epi.set_processes([
(None, 1, A),
(A, 1, B),
(B, 1, None),
],
allow_nonzero_column_sums=True)
_, res = epi.simulate(200, sampling_dt=0.05)
vals = np.concatenate([res[A][_ > 10], res[B][_ > 10]])
rv = poisson(vals.mean())
measured, bins = np.histogram(vals,
bins=np.arange(10) - 0.5,
density=True)
theory = [
rv.pmf(i) for i in range(0,
len(bins) - 1) if measured[i] > 0
]
experi = [
measured[i] for i in range(0,
len(bins) - 1) if measured[i] > 0
]
# make sure the kullback-leibler divergence is below some threshold
#for a, b in zip(theory, experi):
# print(a,b)
assert (entropy(theory, experi) < 1e-2)
assert (np.median(res[A]) == 1)
from epipack.numeric_epi_models import EpiModel
from epipack import StochasticEpiModel
from time import time
S, E, I, R = list("SEIR")
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():
def test_temporal_gillespie_repeated_simulation(self, plot=False):
scl = 40
def R0(t, y=None):
return 4 + np.cos(t * scl)
S, I = list("SI")
N = 100
rec = 1
model = EpiModel([S, I], N)
model.set_processes([
(S, I, R0, I, I),
(I, rec, S),
])
I0 = 1
S0 = N - I0
model.set_initial_conditions({
S: S0,
I: I0,
})
taus = []
N_sample = 10000
if plot:
from tqdm import tqdm
else:
tqdm = lambda x: x
tt = np.linspace(0, 1, 100)
for sample in tqdm(range(N_sample)):
tau = None
model.set_initial_conditions({
S: S0,
I: I0,
})
for _t in tt[1:]:
time, result = model.simulate(_t, adopt_final_state=True)
#print(time, result['I'])
if result['I'][-1] != I0:
tau = time[1]
break
#print()
if tau is not None:
taus.append(tau)
I = lambda t: (4 * t + 1 / scl * np.sin(t * scl))
I2 = lambda t: I(t) * S0 * I0 / N + I0 * rec * t
pdf = lambda t: (R0(t) * S0 * I0 / N + I0 * rec) * np.exp(-I2(t))
measured, bins = np.histogram(taus, bins=100, density=True)
theory = [
np.exp(-I2(bins[i - 1])) - np.exp(-I2(bins[i]))
for i in range(1, len(bins)) if measured[i - 1] > 0
]
experi = [
measured[i - 1] for i in range(1, len(bins)) if measured[i - 1] > 0
]
# make sure the kullback-leibler divergence is below some threshold
if plot:
import matplotlib.pyplot as pl
pl.figure()
pl.hist(taus, bins=100, density=True)
tt = np.linspace(0, 1, 100)
pl.plot(tt, pdf(tt))
pl.yscale('log')
pl.figure()
pl.hist(taus, bins=100, density=True)
tt = np.linspace(0, 1, 100)
pl.plot(tt, pdf(tt))
pl.show()
assert (entropy(theory, experi) < 0.01)