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from __future__ import division
"""
Library of discrete time Epidemic models
copyright 2012 Flávio Codeco Coelho
License: GPL-v3
"""
__author__ = 'fccoelho'
from numpy.random import poisson
from numpy import inf, nan, nan_to_num
import sys
import redis
redisclient = redis.StrictRedis()
vnames = {
'SIR': ['Exposed', 'Infectious', 'Susceptible'],
'SIR_s': ['Exposed', 'Infectious', 'Susceptible'],
'SIS': ['Exposed', 'Infectious', 'Susceptible'],
'SIS_s': ['Exposed', 'Infectious', 'Susceptible'],
'SEIS': ['Exposed', 'Infectious', 'Susceptible'],
'SEIS_s': ['Exposed', 'Infectious', 'Susceptible'],
'SEIR': ['Exposed', 'Infectious', 'Susceptible'],
'SEIR_s': ['Exposed', 'Infectious', 'Susceptible'],
'SIpRpS': ['Exposed', 'Infectious', 'Susceptible'],
'SIpRpS_s': ['Exposed', 'Infectious', 'Susceptible'],
'SEIpRpS': ['Exposed', 'Infectious', 'Susceptible'],
'SEIpRpS_s': ['Exposed', 'Infectious', 'Susceptible'],
'SEIpR': ['Exposed', 'Infectious', 'Susceptible'],
'SEIpR_s': ['Exposed', 'Infectious', 'Susceptible'],
'SIpR': ['Exposed', 'Infectious', 'Susceptible'],
'SIpR_s': ['Exposed', 'Infectious', 'Susceptible'],
'SIRS': ['Exposed', 'Infectious', 'Susceptible'],
'SIRS_s': ['Exposed', 'Infectious', 'Susceptible'],
'Custom': ['Exposed', 'Infectious', 'Susceptible'],
'Influenza': ('Susc_age1', 'Incub_age1', 'Subc_age1', 'Sympt_age1', 'Comp_age1',
'Susc_age2', 'Incub_age2', 'Subc_age2', 'Sympt_age2', 'Comp_age2',
'Susc_age3', 'Incub_age3', 'Subc_age3', 'Sympt_age3', 'Comp_age3',
'Susc_age4', 'Incub_age4', 'Subc_age4', 'Sympt_age4', 'Comp_age4',),
}
class Epimodel(object):
"""
Defines a library of discrete time population models
"""
def __init__(self, geocode, modtype='', parallel=True):
"""
defines which models a given site will use
and set variable names accordingly.
:param modtype:
"""
self.step = selectModel(modtype)
self.geocode = geocode
self.parallel = parallel
def __call__(self, *args, **kwargs):
args = self.get_args_from_redis()
res = self.step(*args)
self.update_redis(res)
#return res
def get_args_from_redis(self):
"""
get updated parameters from the redis database.
:param geocode: geocode of the site running this model.
"""
inits = [int(nan_to_num(i)) for i in eval(redisclient.lindex("{}:inits".format(self.geocode), -1))]
simstep = int(redisclient.get("simstep"))
totpop = int(float(redisclient.get("{}:totpop".format(self.geocode))))
theta = int(nan_to_num(float(redisclient.get("{}:theta".format(self.geocode)))))
npass = int(float(redisclient.get("{}:npass".format(self.geocode))))
bi = redisclient.hgetall("{}:bi".format(self.geocode))
bi = {k: float(v) for k, v in bi.items()}
bp = redisclient.hgetall("{}:bp".format(self.geocode))
bp = {k: float(v) for k, v in bp.items()}
values = [float(i) for i in redisclient.lrange("{}:values".format(self.geocode), 0, -1)]
return inits, simstep, totpop, theta, npass, bi, bp, values
def update_redis(self, results):
"""
Update redis database with the results of the model
:param results: results tuple.
"""
# Site state
state, Lpos, migInf = results
redisclient.rpush("{}:inits".format(self.geocode), state) # updating inits
redisclient.rpush('{}:ts'.format(self.geocode), state)
redisclient.set('{}:Lpos'.format(self.geocode), Lpos)
totc = int(nan_to_num(float(redisclient.get('{}:totalcases'.format(self.geocode)))))
redisclient.set('{}:totalcases'.format(self.geocode), Lpos+totc)
redisclient.rpush('{}:incidence'.format(self.geocode), Lpos)
redisclient.set('{}:migInf'.format(self.geocode), migInf)
# Graph state
if Lpos > 0:
infected = int(redisclient.get("simstep"))
redisclient.rpush("epipath", (infected, self.geocode, {})) #TODO: replace empty dict with infectors
# self.parentGraph.epipath.append((self.parentGraph.simstep, self.geocode, self.infector))
#TODO: have infector be stated in terms of geocodes
def selectModel(Type):
"""
Sets the model engine
"""
if Type == 'SIR':
return stepSIR
elif Type == 'SIR_s':
return stepSIR_s
elif Type == 'SIS':
return stepSIS
elif Type == 'SIS_s':
return stepSIS_s
elif Type == 'SEIS':
return stepSEIS
elif Type == 'SEIS_s':
return stepSEIS_s
elif Type == 'SEIR':
return stepSEIR
elif Type == 'SEIR_s':
return stepSEIR_s
elif Type == 'SIpRpS':
return stepSIpRpS
elif Type == 'SIpRpS_s':
return stepSIpRpS_s
elif Type == 'SEIpRpS':
return stepSEIpRpS
elif Type == 'SEIpRpS_s':
return stepSEIpRpS_s
elif Type == 'SIpR':
return stepSIpR
elif Type == 'SIpR_s':
return stepSIpR_s
elif Type == 'SEIpR':
return stepSEIpR
elif Type == 'SEIpR_s':
return stepSEIpR_s
elif Type == 'SIRS':
return stepSIRS
elif Type == 'SIRS_s':
return stepSIRS_s
elif Type == 'Influenza':
return stepFlu
elif Type == 'Custom':
#adds the user model as a method of instance self
try:
#TODO: move this import to the graph level
import CustomModel
vnames['Custom'] = CustomModel.vnames
return CustomModel.Model
except ImportError:
print "You have to Create a CustomModel.py file before you can select\nthe Custom model type"
else:
sys.exit('Model type specified in .epg file is invalid')
def stepFlu(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=()):
"""
Flu model with classes S,E,I subclinical, I mild, I medium, I serious, deaths
"""
#Variable long names to be used in the database output.
vnames = ('Susc_age1', 'Incub_age1', 'Subc_age1', 'Sympt_age1', 'Comp_age1',
'Susc_age2', 'Incub_age2', 'Subc_age2', 'Sympt_age2', 'Comp_age2',
'Susc_age3', 'Incub_age3', 'Subc_age3', 'Sympt_age3', 'Comp_age3',
'Susc_age4', 'Incub_age4', 'Subc_age4', 'Sympt_age4', 'Comp_age4',)
if simstep == 1: #get initial values
S1, E1, Is1, Ic1, Ig1 = (bi['susc_age1'], bi['incub_age1'], bi['subc_age1'], bi['sympt_age1'], bi['comp_age1'])
S2, E2, Is2, Ic2, Ig2 = (bi['susc_age2'], bi['incub_age2'], bi['subc_age2'], bi['sympt_age2'], bi['comp_age2'])
S3, E3, Is3, Ic3, Ig3 = (bi['susc_age3'], bi['incub_age3'], bi['subc_age3'], bi['sympt_age3'], bi['comp_age3'])
S4, E4, Is4, Ic4, Ig4 = (bi['susc_age4'], bi['incub_age4'], bi['subc_age4'], bi['sympt_age4'], bi['comp_age4'])
else: #get values from last time step
S1, E1, Is1, Ic1, Ig1, S2, E2, Is2, Ic2, Ig2, S3, E3, Is3, Ic3, Ig3, S4, E4, Is4, Ic4, Ig4 = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
#parameters: alpha,beta,r,e,c,g,d,pc1,pc2,pc3,pc4,pp1,pp2,pp3,pp4,b
#Vacination event
if vaccineNow: #TODO: add to bp when creating model
S1 -= vaccov * S1
S2 -= vaccov * S2
S3 -= vaccov * S3
S4 -= vaccov * S4
#New cases by age class
#beta=eval(values[2])
Infectantes = Ig1 + Ig2 + Ig3 + Ig4 + Ic1 + Ic2 + Ic3 + Ic4 + 0.5 * (Is1 + Is2 + Is3 + Is4) + theta
L1pos = float(beta) * S1 * (Infectantes / (N + npass)) ** alpha
L2pos = float(beta) * S2 * (Infectantes / (N + npass)) ** alpha
L3pos = float(beta) * S3 * (Infectantes / (N + npass)) ** alpha
L4pos = float(beta) * S4 * (Infectantes / (N + npass)) ** alpha
######################
Lpos = L1pos + L2pos + L3pos + L4pos
# Model
# 0-2 years old
E1pos = L1pos + (1 - e) * E1
Is1pos = (1 - (pc1 * c + (1 - pc1) * r)) * Is1 + e * E1
Ic1pos = (1 - (pp1 * g + (1 - pp1) * r)) * Ic1 + pc1 * c * Is1
Ig1pos = (1 - d) * Ig1 + pp1 * g * Ic1
S1pos = b + S1 - L1pos
# 3-14 years old
E2pos = L2pos + (1 - e) * E2
Is2pos = (1 - (pc2 * c + (1 - pc2) * r)) * Is2 + e * E2
Ic2pos = (1 - (pp2 * g + (1 - pp2) * r)) * Ic2 + pc2 * c * Is2
Ig2pos = (1 - d) * Ig2 + pp2 * g * Ic2
S2pos = b + S2 - L2pos
# 15-59 years old
E3pos = L3pos + (1 - e) * E3
Is3pos = (1 - (pc3 * c + (1 - pc3) * r)) * Is3 + e * E3
Ic3pos = (1 - (pp3 * g + (1 - pp3) * r)) * Ic3 + pc3 * c * Is3
Ig3pos = (1 - d) * Ig3 + pp3 * g * Ic3
S3pos = b + S3 - L3pos
# >60 years old
E4pos = L4pos + (1 - e) * E4
Is4pos = (1 - (pc4 * c + (1 - pc4) * r)) * Is4 + e * E4
Ic4pos = (1 - (pp4 * g + (1 - pp4) * r)) * Ic4 + pc4 * c * Is4
Ig4pos = (1 - d) * Ig4 + pp4 * g * Ic4
S4pos = b + S4 - L4pos
#Migrating infecctious
migInf = (
Ig1pos + Ig2pos + Ig3pos + Ig4pos + Ic1pos + Ic2pos + Ic3pos + Ic4pos + 0.5 * (Is1pos + Is2pos + Is3pos + Is4pos))
# Return variable values
return [S1pos, E1pos, Is1pos, Ic1pos, Ig1pos, S2pos, E2pos, Is2pos,
Ic2pos, Ig2pos, S3pos, E3pos, Is3pos, Ic3pos, Ig3pos, S4pos,
E4pos, Is4pos, Ic4pos, Ig4pos], Lpos, migInf
def stepSIS(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=()):
"""
calculates the model SIS, and return its values (no demographics)
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
#parameter: beta,alpha,e,r,delta,b,w,p
Lpos = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
# Model
Ipos = (1 - r) * I + Lpos
Spos = S + b - Lpos + r * I
#Migrating infecctious
migInf = (Ipos)
return [0, Ipos, Spos], Lpos, migInf
def stepSIS_s(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=(), dist='poisson'):
"""
Defines an stochastic model SIS:
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
# parameter: beta,alpha,e,r,delta,b,w,p
Lpos_esp = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
if dist == 'poisson':
Lpos = poisson(Lpos_esp)
elif dist == 'negbin':
prob = I / (I + Lpos_esp) #convertin between parameterizations
Lpos = negative_binomial(I, prob)
# Model
Ipos = (1 - r) * I + Lpos
Spos = S + b - Lpos + r * I
#Migrating infecctious
migInf = (Ipos)
return [0, Ipos, Spos], Lpos, migInf
def stepSIR(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=()):
"""
calculates the model SIR, and return its values (no demographics)
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
# parameters: b ,r
Lpos = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
# Model
Ipos = (1 - r) * I + Lpos
Spos = S + b - Lpos
Rpos = N - (Spos + Ipos)
#Migrating infecctious
migInf = Ipos
return [0, Ipos, Spos], Lpos, migInf
def stepSIR_s(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=(), dist='poisson'):
"""
Defines an stochastic model SIR:
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
#parameter: beta,alpha,e,r,delta,b,w,p
Lpos_esp = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
if dist == 'poisson':
Lpos = poisson(Lpos_esp)
elif dist == 'negbin':
prob = I / (I + Lpos_esp) #convertin between parameterizations
Lpos = negative_binomial(I, prob)
# Model
Ipos = (1 - r) * I + Lpos
Spos = S + b - Lpos
Rpos = N - (Spos + Ipos)
#Migrating infecctious
migInf = Ipos
return [0, Ipos, Spos], Lpos, migInf
def stepSEIS(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=()):
"""
Defines the model SEIS:
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
#parameters: b,e,r
Lpos = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
#Model
Epos = (1 - e) * E + Lpos
Ipos = e * E + (1 - r) * I
Spos = S + b - Lpos + r * I
#Migrating infecctious
migInf = Ipos
return [Epos, Ipos, Spos], Lpos, migInf
def stepSEIS_s(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=(), dist='poisson'):
"""
Defines an stochastic model SEIS:
- inits = (E,I,S)
- par = (Beta, alpha, E,r,delta,B,w,p) see docs.
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
#parameters: beta,alpha,e,r,delta,b,w,p
Lpos_esp = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
if dist == 'poisson':
Lpos = poisson(Lpos_esp)
elif dist == 'negbin':
prob = I / (I + Lpos_esp) #converting between parameterizations
Lpos = negative_binomial(I, prob)
Epos = (1 - e) * E + Lpos
Ipos = e * E + (1 - r) * I
Spos = S + b - Lpos + r * I
#Migrating infecctious
migInf = Ipos
return [Epos, Ipos, Spos], Lpos, migInf
def stepSEIR(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=()):
"""
Defines the model SEIR:
- inits = (E,I,S)
- par = (Beta, alpha, E,r,delta,B,w,p) see docs.
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
#parameters: beta,alpha,e,r,delta,B,w,p
Lpos = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
#Model
Epos = (1 - e) * E + Lpos
Ipos = e * E + (1 - r) * I
Spos = S + b - Lpos
Rpos = N - (Spos + Epos + Ipos)
#Migrating infecctious
migInf = Ipos
return [Epos, Ipos, Spos], Lpos, migInf
def stepSEIR_s(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=(), dist='poisson'):
"""
Defines an stochastic model SEIR:
- inits = (E,I,S)
- par = (Beta, alpha, E,r,delta,B,w,p) see docs.
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
#parameters: beta,alpha,e,r,delta,B,w,p
Lpos_esp = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
if dist == 'poisson':
Lpos = poisson(Lpos_esp) #poisson(Lpos_esp)
## if theta == 0 and Lpos_esp == 0 and Lpos > 0:
## print Lpos,Lpos_esp,S,I,theta,N,parentSite.sitename
elif dist == 'negbin':
prob = I / (I + Lpos_esp) #convertin between parameterizations
Lpos = negative_binomial(I, prob)
Epos = (1 - e) * E + Lpos
Ipos = e * E + (1 - r) * I
Spos = S + b - Lpos
Rpos = N - (Spos + Epos + Ipos)
#Migrating infecctious
migInf = Ipos
return [Epos, Ipos, Spos], Lpos, migInf
def stepSIpRpS(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=()):
"""
calculates the model SIpRpS, and return its values (no demographics)
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
# parameter: beta,alpha,e,r,delta,b,w,p
Lpos = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
# Model
Ipos = (1 - r) * I + Lpos
Spos = S + b - Lpos + (1 - delta) * r * I
Rpos = N - (Spos + Ipos) + delta * r * I
#Migrating infecctious
migInf = Ipos
return [0, Ipos, Spos], Lpos, migInf
def stepSIpRpS_s(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=(), dist='poisson'):
"""
Defines an stochastic model SIpRpS:
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
# parameter: beta,alpha,e,r,delta,B,w,p
Lpos_esp = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
if dist == 'poisson':
Lpos = poisson(Lpos_esp)
elif dist == 'negbin':
prob = I / (I + Lpos_esp) #convertin between parameterizations
Lpos = negative_binomial(I, prob)
# Model
Ipos = (1 - r) * I + Lpos
Spos = S + b - Lpos + (1 - delta) * r * I
Rpos = N - (Spos + Ipos) + delta * r * I
#Migrating infecctious
migInf = Ipos
return [0, Ipos, Spos], Lpos, migInf
def stepSEIpRpS(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=()):
"""
Defines the model SEIpRpS:
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
# parameter: beta,alpha,e,r,delta,b,w,p
Lpos = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
Epos = (1 - e) * E + Lpos
Ipos = e * E + (1 - r) * I
Spos = S + b - Lpos + (1 - delta) * r * I
Rpos = N - (Spos + Epos + Ipos) + delta * r * I
#Migrating infecctious
migInf = Ipos
return [Epos, Ipos, Spos], Lpos, migInf
def stepSEIpRpS_s(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=(), dist='poisson'):
"""
Defines an stochastic model SEIpRpS:
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
# parameter: beta,alpha,e,r,delta,b,w,p
Lpos_esp = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
if dist == 'poisson':
Lpos = poisson(Lpos_esp)
elif dist == 'negbin':
prob = I / (I + Lpos_esp) #convertin between parameterizations
Lpos = negative_binomial(I, prob)
Epos = (1 - e) * E + Lpos
Ipos = e * E + (1 - r) * I
Spos = S + b - Lpos + (1 - delta) * r * I
Rpos = N - (Spos + Epos + Ipos) + delta * r * I
#Migrating infecctious
migInf = Ipos
return [Epos, Ipos, Spos], Lpos, migInf
def stepSIpR(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=()):
"""
calculates the model SIpR, and return its values (no demographics)
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
R = N - E - I - S
for k, v in bp.items():
exec ('%s = %s' % (k, v))
#parameter: beta,alpha,e,r,delta,b,w,p
Lpos = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
Lpos2 = p * float(beta) * R * ((I + theta) / (N + npass)) ** alpha #number of secondary Infections
# Model
Ipos = (1 - r) * I + Lpos + Lpos2
Spos = S + b - Lpos
Rpos = N - (Spos + Ipos) - Lpos2
#Migrating infecctious
migInf = Ipos
return [0, Ipos, Spos], Lpos + Lpos2, migInf
def stepSIpR_s(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=(), dist='poisson'):
"""
Defines an stochastic model SIpRs:
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
#parameter: beta,alpha,e,r,delta,b,w,p
R = N - E - I - S
Lpos_esp = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
Lpos2_esp = p * float(beta) * R * ((I + theta) / (N + npass)) ** alpha #number of secondary Infections
if dist == 'poisson':
Lpos = poisson(Lpos_esp)
Lpos2 = poisson(Lpos2_esp)
elif dist == 'negbin':
prob = I / (I + Lpos_esp) #convertin between parameterizations
Lpos = negative_binomial(I, prob)
prob = I / (I + Lpos2_esp) #convertin between parameterizations
Lpos2 = negative_binomial(I, prob)
# Model
Ipos = (1 - r) * I + Lpos + Lpos2
Spos = S + b - Lpos
Rpos = N - (Spos + Ipos) - Lpos2
#Migrating infecctious
migInf = Ipos
return [0, Ipos, Spos], Lpos + Lpos2, migInf
def stepSEIpR(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=()):
"""
calculates the model SEIpR, and return its values (no demographics)
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
R = N - E - I - S
for k, v in bp.items():
exec ('%s = %s' % (k, v))
# parameters: beta,alpha,e,r,delta,b,w,p
Lpos = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
Lpos2 = p * float(beta) * R * ((I + theta) / (N + npass)) ** alpha # secondary infections
# Model
Epos = (1 - e) * E + Lpos + Lpos2
Ipos = e * E + (1 - r) * I
Spos = S + b - Lpos
Rpos = N - (Spos + Ipos) - Lpos2
#Migrating infecctious
migInf = Ipos
return [0, Ipos, Spos], Lpos + Lpos2, migInf
def stepSEIpR_s(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=(), dist='poisson'):
"""
Defines an stochastic model SEIpRs:
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
for k, v in bp.items():
exec ('%s = %s' % (k, v))
# parameter: beta,alpha,e,r,delta,B,w,p
R = N - E - I - S
Lpos_esp = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
Lpos2_esp = p * float(beta) * R * ((I + theta) / (N + npass)) ** alpha # secondary infections
if dist == 'poisson':
Lpos = poisson(Lpos_esp)
Lpos2 = poisson(Lpos2_esp)
elif dist == 'negbin':
prob = I / (I + Lpos_esp) #converting between parameterizations
Lpos = negative_binomial(I, prob)
prob = I / (I + Lpos2_esp) #converting between parameterizations
Lpos2 = negative_binomial(I, prob)
# Model
Epos = (1 - e) * E + Lpos + Lpos2
Ipos = e * E + (1 - r) * I
Spos = S + b - Lpos
Rpos = N - (Spos + Ipos) - Lpos2
#Migrating infecctious
migInf = Ipos
return [0, Ipos, Spos], Lpos + Lpos2, migInf
def stepSIRS(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=()):
"""
calculates the model SIRS, and return its values (no demographics)
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
R = N - E + I + S
for k, v in bp.items():
exec ('%s = %s' % (k, v))
#parameter: beta,alpha,e,r,delta,b,w,p
Lpos = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
# Model
Ipos = (1 - r) * I + Lpos
Spos = S + b - Lpos + w * R
Rpos = N - (Spos + Ipos) - w * R
#Migrating infecctious
migInf = Ipos
return [0, Ipos, Spos], Lpos, migInf
def stepSIRS_s(inits, simstep, totpop, theta=0, npass=0, bi={}, bp={}, values=(), dist='poisson'):
"""
Defines an stochastic model SIR:
- inits = (E,I,S)
- theta = infectious individuals from neighbor sites
"""
if simstep == 1: #get initial values
E, I, S = (bi['e'], bi['i'], bi['s'])
else:
E, I, S = inits
N = totpop
R = N - E + I + S
for k, v in bp.items():
exec ('%s = %s' % (k, v))
# parameter: beta,alpha,e,r,delta,b,w,p
Lpos_esp = float(beta) * S * ((I + theta) / (N + npass)) ** alpha #Number of new cases
if dist == 'poisson':
Lpos = poisson(Lpos_esp)
elif dist == 'negbin':
prob = I / (I + Lpos_esp) #convertin between parameterizations
Lpos = negative_binomial(I, prob)
# Model
Ipos = (1 - r) * I + Lpos
Spos = S + b - Lpos + w * R
Rpos = N - (Spos + Ipos) - w * R
#Migrating infecctious
migInf = Ipos
return [0, Ipos, Spos], Lpos, migInf
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