def test_stochastic_well_mixed(self):
S, E, I, R = sympy.symbols("S E I R")
N = 75000
tmax = 100
model = SymbolicEpiModel([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, 10)
result_int = model.integrate(tt)
t, result_sim = model.simulate(tmax,
sampling_dt=1,
return_compartments=[S, R])
for c, res in result_sim.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)
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 test_time_dependent_rates(self):
B, t = sympy.symbols("B t")
epi = SymbolicEpiModel([B])
epi.add_fission_processes([
(B, t, B, B),
])
epi.set_initial_conditions({B: 1})
result = epi.integrate([0, 3], adopt_final_state=True)
assert (np.isclose(epi.y0[0], np.exp(3**2 / 2)))
epi.set_initial_conditions({B: 1})
result = epi.integrate(np.linspace(0, 3, 10000),
integrator='euler',
adopt_final_state=True)
eul = epi.y0[0]
real = np.exp(3**2 / 2)
assert (np.abs(1 - eul / real) < 1e-2)