def default_numeric_models():
from epipack import EpiModel
import matplotlib.pyplot as pl
from epipack.plottools import plot
import numpy as np
S, I, R = list("SIR")
N = 1000
SIRS = EpiModel([S,I,R],N)\
.set_processes([
#### transmission process ####
# S + I (eta=2.5/d)-> I + I
(S, I, 2.5, I, I),
#### transition processes ####
# I (rho=1/d)-> R
# R (omega=1/14d)-> S
(I, 1, R),
(R, 1/14, S),
])\
.set_initial_conditions({S:N-10, I:10})
t = np.linspace(0, 40, 1000)
result_int = SIRS.integrate(t)
t_sim, result_sim = SIRS.simulate(t[-1])
ax = plot(t_sim, result_sim)
ax = plot(t, result_int, ax=ax)
ax.get_figure().savefig('numeric_model.png', dpi=300)
def symbolic_simulation_temporally_forced():
from epipack import SymbolicEpiModel
import sympy as sy
from epipack.plottools import plot
import numpy as np
S, I, R, eta, rho, omega, t, T = \
sy.symbols("S I R eta rho omega t T")
N = 1000
SIRS = SymbolicEpiModel([S,I,R],N)\
.set_processes([
(S, I, 3+sy.cos(2*sy.pi*t/T), I, I),
(I, rho, R),
(R, omega, S),
])
SIRS.set_parameter_values({
rho: 1,
omega: 1 / 14,
T: 100,
})
SIRS.set_initial_conditions({S: N - 100, I: 100})
_t = np.linspace(0, 150, 1000)
result = SIRS.integrate(_t)
t_sim, result_sim = SIRS.simulate(max(_t))
ax = plot(_t, result)
plot(t_sim, result_sim, ax=ax)
ax.get_figure().savefig('symbolic_model_time_varying_rate.png', dpi=300)
def varying_rate_numeric_models():
import numpy as np
from epipack import SISModel
from epipack.plottools import plot
N = 100
recovery_rate = 1.0
def infection_rate(t, y, *args, **kwargs):
return 3 + np.sin(2 * np.pi * t / 100)
SIS = SISModel(
infection_rate=infection_rate,
recovery_rate=recovery_rate,
initial_population_size=N
)\
.set_initial_conditions({
'S': 90,
'I': 10,
})
t = np.arange(200)
result_int = SIS.integrate(t)
t_sim, result_sim = SIS.simulate(199)
ax = plot(t_sim, result_sim)
ax = plot(t, result_int, ax=ax)
ax.get_figure().savefig('numeric_model_time_varying_rate.png', dpi=300)
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)
(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]
f = get_temporal_interpolation(times, rates, interpolation_degree=1)
S, I, R, t, rho = sympy.symbols("S I R t rho")
model = SymbolicEpiModel([S,I,R])
model.set_processes([
(S, I, f, I, I),
(I, rho, R),
])\
.set_initial_conditions({S:0.99,I:0.01})\
.set_parameter_values({rho:1})
t = np.linspace(0,6,1000)
result = model.integrate(t)
ax = plot(t,result)
ax.legend()
ax.get_figure().savefig('interp_SIR_symbolic.png',dpi=300)
pl.show()
f = interp1d(times, rates, kind='linear', bounds_error=False)
def infection_rate(t,y):
return f(t)
model = EpiModel(list("SIR"))
model.set_processes([
('S', 'I', infection_rate, 'I', 'I'),
('I', 1.0, 'R'),
])\
.set_initial_conditions({'S':0.99,'I':0.01})\
t = np.linspace(0,6,1000)
result = model.integrate(t)
ax = plot(t,result)
ax.legend(frameon=False)
model = EpiModel(list("SIR"))
model.set_processes([
('S', 'I', 2.0, 'I', 'I'),
('I', 1.0, 'R'),
])\
.set_initial_conditions({'S':0.99,'I':0.01})\
t = np.linspace(0,6,1000)
result = model.integrate(t,return_compartments='I')
ax = plot(t,result,ax=ax,curve_label_format='constant rate {}')
ax.set_ylim([0,1])
ax.legend(frameon=False)
