# coding: utf-8
"""
Implementation of a model for epidemics propagation.
"""
import numpy.random
from ._base_sir import BaseSIR
from .covid_sird import CovidSIRD
[docs]class CovidSIRDMixture(BaseSIR):
"""
The model extends model @see cl CovidSIRD and assumes
there are two variants of the same virus.
The term `beta1 * beta2 * S * I1 / N * I2 / N` means
that for all people being in contact with both
virus, the second one wins as it is more contagious.
.. runpython::
:showcode:
:rst:
from aftercovid.models import CovidSIRDMixture
model = CovidSIRDMixture()
print(model.to_rst())
.. exref::
:title: Mixture of SIRD simulation and plotting
.. plot::
from pandas import DataFrame
import matplotlib.pyplot as plt
from aftercovid.models import CovidSIRDMixture
model = CovidSIRDMixture()
sims = list(model.iterate(60))
df = DataFrame(sims)
print(df.head())
ax = df.plot(y=['S', 'I1', 'I2', 'R', 'D'], kind='line')
ax.set_xlabel("jours")
ax.set_ylabel("population")
r0 = model.R0()
ax.set_title("Simulation SIRD\\nR0=%f" % r0)
plt.show()
Visual representation:
.. gdot::
:script:
from aftercovid.models import CovidSIRDMixture
model = CovidSIRDMixture()
print(model.to_dot())
See :ref:`l-base-model-sir` to get the methods
common to SIRx models.
"""
P0 = [
('beta1', 0.5, 'taux de transmission dans la population'),
('beta2', 0.7, 'second taux de transmission dans la population'),
('mu', 1 / 14., '1/. : durée moyenne jusque la guérison'),
('nu', 1 / 21., '1/. : durée moyenne jusqu\'au décès'),
]
Q0 = [
('S', 9990., 'personnes non contaminées'),
('I1', 8., 'nombre de personnes malades ou contaminantes '
'pour le premier variant'),
('I2', 2., 'nombre de personnes malades ou contaminantes '
'pour le second variant'),
('R', 0., 'personnes guéries (recovered)'),
('D', 0., 'personnes décédées'),
]
C0 = [
('N', 10000., 'population'),
]
eq = {
'S': ('- beta1 * S / N * I1 - beta2 * S / N * I2 '
'+ beta1 * beta2 * S * I1 / N * I2 / N'),
'I1': ('beta1 * S / N * I1 - mu * I1 - nu * I1 '
'- beta1 * beta2 * S * I1 / N * I2 / N'),
'I2': 'beta2 * S / N * I2 - mu * I2 - nu * I2',
'R': 'mu * (I1 + I2)',
'D': 'nu * (I1 + I2)'
}
def __init__(self):
BaseSIR.__init__(
self,
p=CovidSIRDMixture.P0.copy(),
q=CovidSIRDMixture.Q0.copy(),
c=CovidSIRDMixture.C0.copy(),
eq=CovidSIRDMixture.eq.copy())
[docs] def R0(self, t=0):
'''
Returns R0 coefficient.
:param t: unused
'''
return (self['beta1'] + self['beta2']) / (self['nu'] + self['mu'])
[docs] def correctness(self, X=None):
"""
Unused.
"""
if X is None:
X = self.vect().reshape((1, -1))
return numpy.zeros(X.shape)
[docs] def rnd(self):
'''
Draws random parameters.
Not perfect.
'''
self['beta1'] = numpy.random.randn(1) * 0.1 + 0.5
self['beta2'] = numpy.random.randn(1) * 0.1 + 0.7
self['mu'] = numpy.random.randn(1) * 0.1 + 1. / 14
self['nu'] = numpy.random.randn(1) * 0.1 + 1. / 21
[docs] @staticmethod
def add_noise(X, epsilon=1.):
"""
Tries to add reasonable noise to the quantities stored in *X*.
:param epsilon: amplitude
:return: new X
"""
return CovidSIRD.add_noise(X, epsilon=epsilon)
