def network_simulation():
from epipack import StochasticEpiModel
from epipack.plottools import plot
import matplotlib.pyplot as pl
import networkx as nx
k0 = 50
R0 = 2.5
rho = 1
eta = R0 * rho / k0
omega = 1 / 14
N = int(1e4)
edges = [ (e[0], e[1], 1.0) for e in \
nx.fast_gnp_random_graph(N,k0/(N-1)).edges() ]
SIRS = StochasticEpiModel(
compartments=list('SIR'),
N=N,
edge_weight_tuples=edges
)\
.set_link_transmission_processes([
('I', 'S', eta, 'I', 'I'),
])\
.set_node_transition_processes([
('I', rho, 'R'),
('R', omega, 'S'),
])\
.set_random_initial_conditions({
'S': N-100,
'I': 100
})
t_s, result_s = SIRS.simulate(40)
ax = plot(t_s, result_s)
ax.get_figure().savefig('network_simulation.png', dpi=300)
def test_network(self):
N = 1000
k = 4
links = []
for i in range(N):
neighs = np.random.randint(0, N - 1, size=(k, ), dtype=int)
neighs[neighs >= i] += 1
for neigh in neighs:
links.append((i, int(neigh), 1.0))
network = get_random_layout(N, links, windowwidth=500)
model = StochasticEpiModel(
list("SIRXTQ"),
N=len(network['nodes']),
directed=True,
edge_weight_tuples=links,
)
k0 = model.out_degree.mean()
R0 = 10
recovery_rate = 1 / 8
quarantine_rate = 1 / 16
tracing_rate = 1 / 2
waning_immunity_rate = 1 / 14
infection_rate = R0 * (recovery_rate) / k0
model.set_node_transition_processes([
("I", recovery_rate, "R"),
("I", quarantine_rate, "T"),
("T", tracing_rate, "X"),
("Q", waning_immunity_rate, "S"),
("X", recovery_rate, "R"),
])
model.set_link_transmission_processes([("I", "S", infection_rate, "I",
"I")])
model.set_conditional_link_transmission_processes({
("T", "->", "X"): [
("X", "I", 0.5, "X", "T"),
#("X","S",0.5,"X","Q"),
],
})
model.set_random_initial_conditions({'I': 20, 'S': N - 20})
sampling_dt = 0.08
visualize(model,
network,
sampling_dt,
ignore_plot_compartments=['S'],
quarantine_compartments=['X', 'T', 'Q'])
def test_temporal_gillespie(self,plot=False):
infection_rate = 1.0
recovery_rate = 0.2
model = StochasticEpiModel(["S","I","R"],3)\
.set_link_transmission_processes([
("I", "S", infection_rate, "I", "I"),
])\
.set_node_transition_processes([
("I", recovery_rate, "R"),
])\
.set_node_statuses([1,0,0])
edges = [ [ (0,1) ], [ (0,1), (0,2) ], [] ]
temporal_network = TemporalNetwork(3,edges,[0,0.5,1.2],1.5)
sim = TemporalNetworkSimulation(temporal_network, model)
N_meas = 10000
taus = []
for meas in range(N_meas):
sim.reset()
t, res = sim.simulate(1000)
if t[-1] == 0:
continue
else:
taus.append(t[1])
def rate(t):
t = t % 1.5
if t < 0.5:
return infection_rate + recovery_rate
elif t < 1.2:
return 2*infection_rate + recovery_rate
elif t < 1.5:
return recovery_rate
measured, bins = np.histogram(taus,bins=100,density=True)
rates = np.array([rate(_t) for _t in bins])
I2 = cumtrapz(rates,bins,initial=0.0)
theory = [ np.exp(-I2[i-1])-np.exp(-I2[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,max(taus),10000)
rates = np.array([rate(_t) for _t in tt])
I2 = cumtrapz(rates,tt,initial=0.0)
pl.plot(tt, rates*np.exp(-I2))
pl.yscale('log')
pl.figure()
pl.hist(taus,bins=100,density=True)
pl.plot(tt, rates*np.exp(-I2))
pl.show()
assert(entropy(theory, experi) < 0.02)
def network_simulation_visualization():
from epipack import StochasticEpiModel
from epipack.plottools import plot
import matplotlib.pyplot as pl
import networkx as nx
k0 = 50
R0 = 2.5
rho = 1
eta = R0 * rho / k0
omega = 1 / 14
N = int(1e4)
edges = [ (e[0], e[1], 1.0) for e in \
nx.fast_gnp_random_graph(N,k0/(N-1)).edges() ]
SIRS = StochasticEpiModel(
compartments=list('SIR'),
N=N,
edge_weight_tuples=edges
)\
.set_link_transmission_processes([
('I', 'S', eta, 'I', 'I'),
])\
.set_node_transition_processes([
('I', rho, 'R'),
('R', omega, 'S'),
])\
.set_random_initial_conditions({
'S': N-100,
'I': 100
})
from epipack.vis import visualize
from epipack.networks import get_random_layout
layouted_network = get_random_layout(N, edges)
visualize(SIRS,
layouted_network,
sampling_dt=0.1,
config={'draw_links': False})
I0 = 50
k0 = 100
R0 = 2.5
Q0 = 0.5
waning_quarantine_rate = omega = 1 / 14
recovery_rate = rho = 1 / 2
quarantine_rate = kappa = rho * Q0 / (1 - Q0)
infection_rate = eta = R0 * (rho) / k0
p = k0 / (N - 1)
G = nx.fast_gnp_random_graph(N, p)
edges = [(e[0], e[1], 1.0) for e in G.edges()]
#model = StochasticEpiModel(list("SIXRQ"),N,edge_weight_tuples=edges)
model = StochasticEpiModel(list("SIXRQ"),
N,
well_mixed_mean_contact_number=k0)
model.set_node_transition_processes([
("I", rho, "R"),
("I", kappa, "X"),
("Q", omega, "S"),
])
model.set_link_transmission_processes([
("I", "S", eta, "I", "I"),
])
model.set_conditional_link_transmission_processes({
("I", "->", "X"): [
("X", "S", Q0, "X", "Q"),
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 ),
])
model.set_node_transition_processes([
( I, 1, R),
( E, 1, I),
])
model.set_random_initial_conditions({S: N-100, I: 100})
start = time()
t, result_sim = model.simulate(tmax,sampling_dt=1)
end = time()
for c, res in result_sim.items():
pl.plot(t, res, ':')
from epipack.vis import visualize
from epipack import StochasticEpiModel
# load network
network, config, _ = nw.load('./MHRN.json')
# get the network properties
N = len(network['nodes'])
edge_list = [(link['source'], link['target'], 1.0)
for link in network['links']]
# define model
model = StochasticEpiModel(
list("SIRXTQ"),
N=N,
edge_weight_tuples=edge_list,
)
k0 = model.out_degree.mean()
R0 = 5
recovery_rate = 1 / 8
quarantine_rate = 1.5 * recovery_rate
infection_rate = R0 * (recovery_rate) / k0
R0 = 3
recovery_rate = 1 / 8
quarantine_rate = 1 / 16
tracing_rate = 1 / 2
waning_immunity_rate = 1 / 14
infection_rate = R0 * (recovery_rate) / k0
('A', 'S', 0.5 * infection_rate * 0.7, 'A', 'I'),
('A', 'S', 0.5 * infection_rate * 0.3, 'A', 'A'),
]
conditional_transmission = {
('I', '->', 'X'): [
('X', 'I', p, 'X', 'X'),
]
}
model = StochasticEpiModel(
compartments=compartments,
N=N,
well_mixed_mean_contact_number=k0,
)\
.set_link_transmission_processes(link_transmission)\
.set_node_transition_processes(node_transition)\
.set_conditional_link_transmission_processes(conditional_transmission)\
.set_random_initial_conditions({
'S': N-100,
'I': 100
})
t, result = model.simulate(80)
from epipack.plottools import plot
ax = plot(t, result)
ax.set_yscale('log')
ax.set_ylim([1, N])
ax.set_xlabel('time [d]')
ax.legend()
from epipack.vis import visualize
from epipack import StochasticEpiModel
from epipack.colors import palettes, colors, bg_colors, hex_bg_colors
# load network
network, config, _ = nw.load('/Users/bfmaier/pythonlib/facebook/FB.json')
# get the network properties
N = len(network['nodes'])
edge_list = [(link['source'], link['target'], 1.0)
for link in network['links']]
# define model
model = StochasticEpiModel(
list("SIRX"),
N=N,
edge_weight_tuples=edge_list,
)
k0 = model.out_degree.mean()
R0 = 5
recovery_rate = 1 / 8
quarantine_rate = 1.5 * recovery_rate
infection_rate = R0 * (recovery_rate) / k0
# usual infection process
model.set_link_transmission_processes([("I", "S", infection_rate, "I", "I")])
# standard SIR dynamic with additional quarantine of symptomatic infecteds
model.set_node_transition_processes([
("I", recovery_rate, "R"),
("I", quarantine_rate, "X"),
break
print(t, next_t, edge_list)
print("Delta T =", temporal_network._Delta_t)
for edge_list, t, next_t in temporal_network:
print("DeltaT =", temporal_network._Delta_t)
break
from epipack import StochasticEpiModel
infection_rate = 1.0
recovery_rate = 0.2
model = StochasticEpiModel(["S","I","R"],3)\
.set_link_transmission_processes([
("I", "S", infection_rate, "I", "I"),
])\
.set_node_transition_processes([
("I", recovery_rate, "R"),
])\
.set_node_statuses([1,0,0])
temporal_network = TemporalNetwork(3, edges, [0, 0.5, 1.2], 1.5)
sim = TemporalNetworkSimulation(temporal_network, model)
t, res = sim.simulate(100)
print(t, res)
sim.reset()
print(sim.model.node_status)
t, res = sim.simulate(100)
print(t, res)
import matplotlib.pyplot as pl
from tqdm import tqdm
S, I, A, B, C0, C1, D, E, F = "S I A B C0 C1 D E F".split(" ")
rateA = 3.0
rateB = 2.0
rateE = 1.0
probAC0 = 0.2
probAC1 = 0.8
probBD = 0.2
N = 6
edges = [ (0, i, 1.0) for i in range(1,N) ]
model = StochasticEpiModel([S,I,A,B,C0,C1,D, E, F], N, edges)
model.set_node_transition_processes([
(I, rateA, A),
(I, rateB, B),
(I, rateE, E),
])
model.set_conditional_link_transmission_processes({
(I, "->", A) : [
( A, S, probAC0, A, C0),
( A, S, probAC1, A, C1),
],
(I, "->", B): [
( B, S, probBD, B, D),
],
alpha = 1/5
rho = 1/8
eta = R0 * rho / k0
kappa = Q0/(1-Q0) * rho
chi = 1/2
xi = (1-Q0)/Q0 * chi
omega = 1/14
S, E, I, R, X, T_I, T_E, Q = "S E I R X T_I T_E Q".split(" ")
N = 20000
print("generating network")
edges = [(e[0],e[1],1.0) for e in (nx.fast_gnp_random_graph(N,k0/(N-1))).edges() ]
agentmodel = StochasticEpiModel([S, E, I, R, X, T_I, T_E, Q], N, edges)
#model = StochasticEpiModel([S, E, I, R, X, T_I, T_E, Q], N, well_mixed_mean_contact_number=k0)
agentmodel.set_node_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),
])
agentmodel.set_link_transmission_processes([
(I, S, R0*rho/k0, I, E),
])
import numpy as np
from epipack import StochasticEpiModel
S, S0, S1, I, A, B, C0, C1, D, E, F = "S S0 S1 I A B C0 C1 D E F".split(" ")
rateA = 3.0
rateB = 2.0
rateE = 1.0
rateF = 5.0
rateC = 10.0
N = 6
edges = [(0, i, 1.0) for i in range(1, N)]
edges.extend([(N + 1, 0, 1.0), (N, 0, 1.0), (N + 1, 1, 1.0), (N + 1, 2, 1.0)])
model = StochasticEpiModel([S, S0, S1, I, A, B, C0, C1, D, E, F], N + 2, edges)
model.set_node_transition_processes([
(S0, rateC, E),
(I, rateF, F),
])
model.set_link_transmission_processes([
(S0, I, rateA, S0, A),
(S0, I, rateB, S0, B),
(S1, I, rateE, S1, E),
])
statuses = np.zeros(N + 2, dtype=int)
statuses[0] = model.get_compartment_id(I)
statuses[N] = model.get_compartment_id(S0)
if __name__ == "__main__":
import netwulf as nw
from epipack import StochasticEpiModel
import networkx as nx
N = 301 * 299
network = get_grid_layout(N)
edge_list = [(link['source'], link['target'], 1.0)
for link in network['links']]
k0 = 25
model = StochasticEpiModel(
list("SIRXTQ"),
N=N,
well_mixed_mean_contact_number=k0,
)
Reff = 3
R0 = 3
recovery_rate = 1 / 8
quarantine_rate = 1 / 32
tracing_rate = 1 / 2
waning_immunity_rate = 1 / 14
infection_rate = Reff * (recovery_rate + quarantine_rate) / k0
infection_rate = R0 * (recovery_rate) / k0
model.set_node_transition_processes([
("I", recovery_rate, "R"),
("I", quarantine_rate, "T"),
("T", tracing_rate, "X"),
("Q", waning_immunity_rate, "S"),
('A', 'S', 0.5 * infection_rate * 0.7, 'A', 'I'),
('A', 'S', 0.5 * infection_rate * 0.3, 'A', 'A'),
]
conditional_transmission = {
('I', '->', 'X'): [
('X', 'I', p, 'X', 'X'),
]
}
model = StochasticEpiModel(
compartments=compartments,
N=N,
edge_weight_tuples=edges
)\
.set_link_transmission_processes(link_transmission)\
.set_node_transition_processes(node_transition)\
.set_conditional_link_transmission_processes(conditional_transmission)\
.set_random_initial_conditions({
'S': N-100,
'I': 100
})
t, result = model.simulate(100)
from epipack.plottools import plot
from bfmplot import pl
ax = plot(t, result)
ax.set_yscale('log')
ax.set_ylim([1, N])
ax.set_ylim([1, N])
from epipack import StochasticEpiModel
import numpy as np
if __name__ == "__main__":
N = 3
edge_weight_tuples = [
(0, 1, 1 / 3),
(0, 2, 2 / 3),
]
directed = False
S, I, R = list("SIR")
model = StochasticEpiModel(
compartments=[S, I, R],
N=N,
edge_weight_tuples=edge_weight_tuples,
directed=directed,
)
infection_rate = 3.0
model.set_link_transmission_processes([
('I', 'S', infection_rate, 'I', 'I'),
])
recovery_rate = 2.0
model.set_node_transition_processes([
('I', recovery_rate, 'R'),
])
model.set_random_initial_conditions({S: N - 1, I: 1})