%matplotlib inline
import pandas as pd
import numpy as np
import numpy.ma as ma
from datetime import datetime
import matplotlib.pyplot as plt
import seaborn as sb
sb.set()
import pdb
from IPython.core.display import HTML
def css_styling():
styles = open("styles/custom.css", "r").read()
return HTML(styles)
css_styling()
/usr/local/lib/python3.4/dist-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter. warnings.warn(self.msg_depr % (key, alt_key))
data_dir = "data/"
Import outbreak data
measles_data = pd.read_csv(data_dir+"measles.csv", index_col=0)
measles_data.NOTIFICATION = pd.to_datetime(measles_data.NOTIFICATION)
measles_data.BIRTH = pd.to_datetime(measles_data.BIRTH)
measles_data.ONSET = pd.to_datetime(measles_data.ONSET)
measles_data = measles_data.replace({'DISTRICT': {'BRASILANDIA':'BRAZILANDIA'}})
Sao Paulo population by district
sp_pop = pd.read_csv(data_dir+'sp_pop.csv', index_col=0)
_names = sp_pop.index.values
_names[_names=='BRASILANDIA'] = 'BRAZILANDIA'
sp_pop.set_index(_names, inplace = True)
sp_pop.head()
0 a 4 anos | 5 a 9 anos | 10 a 14 anos | 15 a 19 anos | 20 a 24 anos | 25 a 29 anos | 30 a 34 anos | 35 a 39 anos | 40 a 44 anos | 45 a 49 anos | 50 a 54 anos | 55 a 59 anos | 60 a 64 anos | 65 a 69 anos | 70 a 74 anos | 75 anos e + | Total | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
AGUA RASA | 5411 | 5750 | 6450 | 7122 | 7621 | 7340 | 6999 | 6984 | 6346 | 5608 | 4987 | 4212 | 4152 | 3595 | 2937 | 3637 | 89151 |
ALTO DE PINHEIROS | 2070 | 2369 | 2953 | 3661 | 4612 | 4190 | 3539 | 3633 | 3448 | 3289 | 3040 | 2533 | 2298 | 1732 | 1305 | 1823 | 46495 |
ANHANGUERA | 3068 | 3006 | 2755 | 2431 | 2426 | 2636 | 2695 | 2308 | 1653 | 1107 | 753 | 509 | 352 | 217 | 162 | 171 | 26249 |
ARICANDUVA | 7732 | 7730 | 8373 | 8956 | 9182 | 8531 | 7813 | 7365 | 6551 | 5554 | 4887 | 3858 | 3320 | 2449 | 1611 | 1723 | 95635 |
ARTUR ALVIM | 9031 | 9078 | 10000 | 11058 | 11387 | 10347 | 9125 | 8658 | 7830 | 7055 | 5919 | 4612 | 3756 | 2633 | 1727 | 1724 | 113940 |
Plot of cumulative cases by district
measles_onset_dist = measles_data.groupby(['DISTRICT','ONSET']).size().unstack(level=0).fillna(0)
measles_onset_dist.cumsum().plot(legend=False, grid=False)
<matplotlib.axes._subplots.AxesSubplot at 0x7f465cc31358>
total_district_cases = measles_onset_dist.sum()
Top 5 districts by number of cases
totals = measles_onset_dist.sum()
totals.sort(ascending=False)
totals[:5]
/usr/local/lib/python3.4/dist-packages/ipykernel/__main__.py:2: FutureWarning: sort is deprecated, use sort_values(inplace=True) for for INPLACE sorting from ipykernel import kernelapp as app
DISTRICT GRAJAU 1074 JARDIM ANGELA 944 CAPAO REDONDO 849 JARDIM SAO LUIZ 778 CAMPO LIMPO 692 dtype: float64
Age distribution of cases, by confirmation status
by_conclusion = measles_data.groupby(["YEAR_AGE", "CONCLUSION"])
counts_by_cause = by_conclusion.size().unstack().fillna(0)
ax = counts_by_cause.plot(kind='bar', stacked=True, xlim=(0,50), figsize=(15,5))
vaccination_data = pd.read_csv('data/BrazilVaxRecords.csv', index_col=0)
vaccination_data.head()
BIRTHS | VAX | POP | SIA | |
---|---|---|---|---|
YEAR | ||||
1980 | 3896442 | 0.57 | 121740438 | 0 |
1981 | 3933136 | 0.73 | 124610790 | 0 |
1982 | 3952137 | 0.66 | 127525420 | 0 |
1983 | 3952735 | 0.68 | 130455659 | 0 |
1984 | 3935224 | 0.73 | 133364277 | 0 |
vax_97 = np.r_[[0]*(1979-1921+1), vaccination_data.VAX[:17]]
n = len(vax_97)
FOI_mat = np.resize((1 - vax_97*0.9), (n,n)).T
vacc_susc = (1 - vax_97*0.9)[::-1]
vacc_susc[0] = 0.5
sia_susc = np.ones(len(vax_97))
birth_year = np.arange(1922, 1998)[::-1]
by_mask = (birth_year > 1983) & (birth_year < 1992)
sia_susc[by_mask] *= 0.2
As a baseline for comparison, we can fit a model to all the clinically-confirmed cases, regardless of lab confirmation status. For this, we will use a simple SIR disease model, which will be fit using MCMC.
This model fits the series of 2-week infection totals in each district $i$ as a set of Poisson models:
$$Pr(I(t)_{i} | \lambda(t)_i) = \text{Poisson}(\lambda(t)_i) $$Where the outbreak intensity is modeled as:
$$\lambda(t)_i = \beta [I^{(w)}(t-1)_i]^{\alpha} S(t-1)_i$$$$\alpha \sim \text{Exp}(1)$$We will assume here that the transmission rate is constant over time (and across districts):
$$\beta \sim \text{Gamma}(1, 0.1)$$To account for the influence of infected individuals from neighboring districts on new infections, the outbreak intensity was modeled using a spatial-weighted average of infecteds across districts, where populations were weighted as an exponential function of the distance between district centroids:
$$w_{d} = \text{exp}(-\theta d)$$$$\theta \sim \text{Exp}(1)$$Rather than assume all clinical cases are true cases, we can adjust the model to account for lab confirmation probability. This is done by including a sub-model that estimates age group-specific probabilities of confirmation, and using these probabilities to estimate the number of lab-confirmed cases. These estimates are then plugged into the model in place of the clinically-confirmed cases.
We specified a structured confirmation model to retrospectively determine the age group-specific probabilities of lab confirmation for measles, conditional on clinical diagnosis. Individual lab confirmation events $c_i$ were modeled as Bernoulli random variables, with the probability of confirmation being allowed to vary by age group:
$$c_i \sim \text{Bernoulli}(p_{a(i)})$$where $a(i)$ denotes the appropriate age group for the individual indexed by i. There were 16 age groups, the first 15 of which were 5-year age intervals $[0,5), [5, 10), \ldots , [70, 75)$, with the 16th interval including all individuals 75 years and older.
Since the age interval choices were arbitrary, and the confirmation probabilities of adjacent groups likely correlated, we modeled the correlation structure directly, using a multivariate logit-normal model. Specifically, we allowed first-order autocorrelation among the age groups, whereby the variance-covariance matrix retained a tridiagonal structure.
$$\begin{aligned} \Sigma = \left[{ \begin{array}{c} {\sigma^2} & {\sigma^2 \rho} & 0& \ldots & {0} & {0} \\ {\sigma^2 \rho} & {\sigma^2} & \sigma^2 \rho & \ldots & {0} & {0} \\ {0} & \sigma^2 \rho & {\sigma^2} & \ldots & {0} & {0} \\ \vdots & \vdots & \vdots & & \vdots & \vdots\\ {0} & {0} & 0 & \ldots & {\sigma^2} & \sigma^2 \rho \\ {0} & {0} & 0 & \ldots & \sigma^2 \rho & {\sigma^2} \end{array} }\right] \end{aligned}$$From this, the confirmation probabilities were specified as multivariate normal on the inverse-logit scale.
$$ \text{logit}(p_a) = \{a\} \sim N(\mu, \Sigma)$$Priors for the confirmation sub-model were specified by:
$$\begin{aligned} \mu_i &\sim N(0, 100) \\ \sigma &\sim \text{HalfCauchy}(25) \\ \rho &\sim U(-1, 1) \end{aligned}$$Age classes are defined in 5-year intervals.
age_classes = [0,5,10,15,20,25,30,35,40,100]
measles_data.dropna(subset=['YEAR_AGE'], inplace=True)
measles_data['YEAR_AGE'] = measles_data.YEAR_AGE.astype(int)
measles_data['AGE_GROUP'] = pd.cut(measles_data.AGE, age_classes, right=False)
Lab-checked observations are extracted for use in estimating lab confirmation probability.
CONFIRMED = measles_data.CONCLUSION == 'CONFIRMED'
CLINICAL = measles_data.CONCLUSION == 'CLINICAL'
DISCARDED = measles_data.CONCLUSION == 'DISCARDED'
Extract confirmed and clinical subset, with no missing county information.
lab_subset = measles_data[(CONFIRMED | CLINICAL) & measles_data.COUNTY.notnull()].copy()
age = lab_subset.YEAR_AGE.values
ages = lab_subset.YEAR_AGE.unique()
counties = lab_subset.COUNTY.unique()
y = (lab_subset.CONCLUSION=='CONFIRMED').values
_lab_subset = lab_subset.replace({"CONCLUSION": {"CLINICAL": "UNCONFIRMED"}})
by_conclusion = _lab_subset.groupby(["YEAR_AGE", "CONCLUSION"])
counts_by_cause = by_conclusion.size().unstack().fillna(0)
ax = counts_by_cause.plot(kind='bar', stacked=True, xlim=(0,50), figsize=(15,5), grid=False)
lab_subset.shape
(39982, 16)
y.sum()
22097
Proportion of lab-confirmed cases older than 20 years
(measles_data[CONFIRMED].YEAR_AGE>20).mean()
0.60257048468117846
age_classes
[0, 5, 10, 15, 20, 25, 30, 35, 40, 100]
age_group = pd.cut(age, age_classes, right=False)
age_index = np.array([age_group.categories.tolist().index(i) for i in age_group])
age_groups = age_group.categories
age_groups
Index(['[0, 5)', '[5, 10)', '[10, 15)', '[15, 20)', '[20, 25)', '[25, 30)', '[30, 35)', '[35, 40)', '[40, 100)'], dtype='object')
#Extract cases by age and time.
age_group = pd.cut(age, age_classes, right=False)
age_index = np.array([age_group.categories.tolist().index(i) for i in age_group])
age_group.categories
Index(['[0, 5)', '[5, 10)', '[10, 15)', '[15, 20)', '[20, 25)', '[25, 30)', '[30, 35)', '[35, 40)', '[40, 100)'], dtype='object')
age_slice_endpoints = [g[1:-1].split(',') for g in age_groups]
age_slices = [slice(int(i[0]), int(i[1])) for i in age_slice_endpoints]
# Get index from full crosstabulation to use as index for each district
dates_index = measles_data.groupby(
['ONSET', 'AGE_GROUP']).size().unstack().index
unique_districts = measles_data.DISTRICT.dropna().unique()
excludes = ['BOM RETIRO']
N = sp_pop.ix[unique_districts, 'Total'].dropna()
N = N.drop(excludes).sum()
N
9727688.0
Compile bi-weekly confirmed and unconfirmed data by Sao Paulo district
sp_counts_2w = lab_subset.groupby(
['ONSET', 'AGE_GROUP']).size().unstack().reindex(dates_index).fillna(0).resample('2W', how='sum')
# All confirmed cases, by district
confirmed_data = lab_subset[lab_subset.CONCLUSION=='CONFIRMED']
confirmed_counts = confirmed_data.groupby(
['ONSET', 'AGE_GROUP']).size().unstack().reindex(dates_index).fillna(0).sum()
all_confirmed_cases = confirmed_counts.reindex_axis(measles_data['AGE_GROUP'].unique()).fillna(0)
# Ensure the age groups are ordered
I_obs = sp_counts_2w.reindex_axis(measles_data['AGE_GROUP'].unique(),
axis=1).fillna(0).values.astype(int)
I_obs.max()
1442
I_obs.sum()
38502
age_groups = np.sort(measles_data['AGE_GROUP'].unique())
age_groups
array(['[0, 5)', '[10, 15)', '[15, 20)', '[20, 25)', '[25, 30)', '[30, 35)', '[35, 40)', '[40, 100)', '[5, 10)'], dtype=object)
Check shape of data frame
assert I_obs.shape == (28, len(age_groups))
Prior distribution on susceptible proportion:
$$p_s \sim \text{Beta}(2, 100)$$from pymc import rbeta
plt.hist(rbeta(2, 100, 10000))
(array([ 3.91700000e+03, 3.57900000e+03, 1.63300000e+03, 6.18000000e+02, 1.70000000e+02, 5.40000000e+01, 2.20000000e+01, 5.00000000e+00, 1.00000000e+00, 1.00000000e+00]), array([ 0.00014776, 0.0133144 , 0.02648105, 0.03964769, 0.05281434, 0.06598098, 0.07914763, 0.09231428, 0.10548092, 0.11864757, 0.13181421]), <a list of 10 Patch objects>)
I_obs
array([[ 1, 3, 0, 1, 0, 0, 0, 0, 1], [ 4, 13, 7, 18, 1, 2, 0, 1, 4], [ 3, 12, 2, 14, 0, 1, 1, 2, 5], [ 4, 10, 2, 17, 0, 2, 2, 2, 2], [ 6, 15, 7, 19, 1, 3, 1, 7, 6], [ 19, 27, 20, 34, 0, 7, 2, 13, 8], [ 9, 27, 6, 26, 1, 1, 1, 6, 8], [ 13, 27, 13, 20, 1, 4, 2, 5, 2], [ 28, 32, 16, 21, 2, 6, 1, 9, 9], [ 42, 39, 46, 31, 6, 17, 2, 13, 18], [ 93, 69, 72, 40, 4, 18, 6, 19, 26], [ 157, 95, 153, 64, 12, 47, 5, 31, 42], [ 359, 183, 315, 169, 26, 95, 18, 76, 68], [ 807, 363, 622, 282, 65, 234, 34, 162, 136], [1168, 660, 1035, 388, 87, 398, 63, 257, 166], [1442, 913, 1193, 536, 137, 430, 48, 318, 292], [1350, 1051, 1255, 643, 116, 476, 68, 366, 339], [1314, 933, 1261, 525, 160, 474, 91, 448, 339], [1218, 773, 1061, 444, 146, 458, 75, 424, 320], [ 712, 485, 629, 292, 80, 262, 67, 267, 214], [ 368, 295, 382, 187, 47, 163, 26, 122, 92], [ 181, 162, 192, 130, 27, 97, 10, 43, 65], [ 122, 151, 88, 102, 14, 43, 10, 27, 36], [ 72, 95, 63, 64, 6, 36, 2, 15, 18], [ 32, 46, 39, 52, 7, 15, 2, 20, 14], [ 20, 42, 30, 42, 2, 9, 2, 8, 17], [ 7, 23, 5, 15, 1, 4, 3, 3, 7], [ 1, 1, 2, 1, 0, 1, 0, 0, 0]])
obs_date = '1997-06-15'
obs_index = sp_counts_2w.index <= obs_date
I_obs_t = I_obs[obs_index]
np.sum(I_obs_t, (0)) / float(I_obs_t.sum())
array([ 0.21114206, 0.20557103, 0.19164345, 0.16991643, 0.01559889, 0.06016713, 0.01281337, 0.06016713, 0.0729805 ])
I_obs_t
array([[ 1, 3, 0, 1, 0, 0, 0, 0, 1], [ 4, 13, 7, 18, 1, 2, 0, 1, 4], [ 3, 12, 2, 14, 0, 1, 1, 2, 5], [ 4, 10, 2, 17, 0, 2, 2, 2, 2], [ 6, 15, 7, 19, 1, 3, 1, 7, 6], [ 19, 27, 20, 34, 0, 7, 2, 13, 8], [ 9, 27, 6, 26, 1, 1, 1, 6, 8], [ 13, 27, 13, 20, 1, 4, 2, 5, 2], [ 28, 32, 16, 21, 2, 6, 1, 9, 9], [ 42, 39, 46, 31, 6, 17, 2, 13, 18], [ 93, 69, 72, 40, 4, 18, 6, 19, 26], [157, 95, 153, 64, 12, 47, 5, 31, 42]])
I_obs_t.sum((0,1))
1795
I_obs_t.sum(1).cumsum()
array([ 6, 56, 96, 137, 202, 332, 417, 504, 628, 842, 1189, 1795])
from pymc import MCMC, Matplot, AdaptiveMetropolis
from pymc import (Uniform, DiscreteUniform, Beta, Binomial, Normal,
CompletedDirichlet,
Poisson, NegativeBinomial, negative_binomial_like, poisson_like,
Lognormal, Exponential, binomial_like,
TruncatedNormal, Binomial, Gamma, HalfCauchy, normal_like,
MvNormalCov, Bernoulli, Uninformative,
Multinomial, rmultinomial, rbinomial,
Dirichlet, multinomial_like)
from pymc import (Lambda, observed, invlogit, deterministic, potential, stochastic,)
def measles_model(obs_date, confirmation=True, spatial_weighting=False,
all_traces=False):
n_periods, n_age_groups = I_obs.shape
### Confirmation sub-model
if confirmation:
# Specify priors on age-specific means
age_classes = np.unique(age_index)
mu = Normal("mu", mu=0, tau=0.0001, value=[0]*len(age_classes))
sig = HalfCauchy('sig', 0, 25, value=1)
var = sig**2
cor = Uniform('cor', -1, 1, value=0)
# Build variance-covariance matrix with first-order correlation
# among age classes
@deterministic
def Sigma(var=var, cor=cor):
I = np.eye(len(age_classes))*var
E = np.diag(np.ones(len(age_classes)-1), k=-1)*var*cor
return I + E + E.T
# Age-specific probabilities of confirmation as multivariate normal
# random variables
beta_age = MvNormalCov("beta_age", mu=mu, C=Sigma,
value=[1]*len(age_classes))
p_age = Lambda('p_age', lambda t=beta_age: invlogit(t))
@deterministic(trace=False)
def p_confirm(beta=beta_age):
return invlogit(beta[age_index])
# Confirmation likelihood
lab_confirmed = Bernoulli('lab_confirmed', p=p_confirm, value=y,
observed=True)
'''
Truncate data at observation period
'''
obs_index = sp_counts_2w.index <= obs_date
I_obs_t = I_obs[obs_index]
# Index for observation date, used to index out values of interest
# from the model.
t_obs = obs_index.sum() - 1
if confirmation:
@stochastic(trace=all_traces, dtype=int)
def I(value=(I_obs_t*0.5).astype(int), n=I_obs_t, p=p_age):
# Binomial confirmation process
return np.sum([binomial_like(xi, ni, p) for xi,ni in zip(value,n)])
age_dist_init = np.sum(I.value, 0)/ float(I.value.sum())
else:
I = I_obs_t
age_dist_init = np.sum(I, 0) / float(I.sum())
assert I.shape == (t_obs +1, n_age_groups)
# Calcuate age distribution from observed distribution of infecteds to date
_age_dist = Dirichlet('_age_dist', np.ones(n_age_groups),
value=age_dist_init[:-1]/age_dist_init.sum())
age_dist = CompletedDirichlet('age_dist', _age_dist)
@potential
def age_dist_like(p=age_dist, I=I):
return multinomial_like(I.sum(0), I.sum(), p)
# age_dist = age_dist_init
# Transmission parameter
beta = Uniform('beta', 1, 100, value=10)
# Downsample annual series to observed age groups
downsample = lambda x: np.array([x[s].mean() for s in age_slices])
# Weakly-informative prior on proportion susceptible being
# between 0 and 0.07
p_susceptible = Beta('p_susceptible', 2, 100)
# Estimated total initial susceptibles
S_0 = Binomial('S_0', n=int(N), p=p_susceptible)
S = Lambda('S', lambda I=I, S_0=S_0: S_0 - I.cumsum(axis=0))
# Check shape
assert S.value.shape == (t_obs+1., n_age_groups)
S_t = Lambda('S_t', lambda S=S: S[-1])
# Susceptibles at time t, by age
S_age = Multinomial('S_age', S_t, age_dist)
# Force of infection
@deterministic
def lam(beta=beta, I=I, S=S, N=N):
return beta * I.sum(axis=1) * S.sum(axis=1) / N
# Check shape
assert lam.value.shape == (t_obs+1,) # n_age_groups)
# FOI in observation period
lam_t = Lambda('lam_t', lambda lam=lam: lam[-1])
# Poisson likelihood for observed cases
@potential
def new_cases(I=I, lam=lam):
# return negative_binomial_like(I[1:].sum(1), lam[:-1], I[:-1].sum(1))
return poisson_like(I.sum(axis=1), lam)
'''
Vaccination targets
'''
@deterministic
def vacc_5(S=S_age):
# Vaccination of 5 and under
p = [0.95] + [0]*(n_age_groups - 1)
return rbinomial(S, p)
# Proportion of susceptibles vaccinated
pct_5 = Lambda('pct_5',
lambda V=vacc_5, S=S_age: V.sum()/S.sum())
@deterministic
def vacc_15(S=S_age):
# Vaccination of 15 and under
p = [0.95]*3 + [0]*(n_age_groups - 3)
return rbinomial(S, p)
# Proportion of susceptibles vaccinated
pct_15 = Lambda('pct_15',
lambda V=vacc_15, S=S_age: V.sum()/S.sum())
@deterministic
def vacc_30(S=S_age):
# Vaccination of 30 and under
p = [0.95]*6 + [0]*(n_age_groups - 6)
return rbinomial(S, p)
# Proportion of 30 and under susceptibles vaccinated
pct_30 = Lambda('pct_30',
lambda V=vacc_30, S=S_age: V.sum()/S.sum())
@deterministic
def vacc_adult(S=S_age):
# Vaccination of adults under 30 (and young kids)
p = [0.95, 0, 0, 0, 0.95, 0.95] + [0]*(n_age_groups - 6)
return rbinomial(S, p)
# Proportion of adults under 30 (and young kids)
pct_adult = Lambda('pct_adult',
lambda V=vacc_adult, S=S_age: V.sum()/S.sum())
return locals()
Run models for June 15 and July 15 observation points, both with and without clinical confirmation.
db = 'ram'
n_iterations = 100000
n_burn = 50000
June 15, with lab confirmation
model = measles_model
model_june = MCMC(model('1997-06-15'), db=db, dbname='model_june')
# model_june.use_step_method(AdaptiveMetropolis, model_june._age_dist)
# model_june.use_step_method(AdaptiveMetropolis, [model_june.beta,
# model_june.p_susceptible])
model_june.sample(n_iterations, n_burn)
[-----------------100%-----------------] 100000 of 100000 complete in 425.0 sec
July 15, with lab confirmation
model_july = MCMC(model('1997-07-15'), db=db, dbname='model_july')
# model_july.use_step_method(AdaptiveMetropolis, model_july.age_dist)
# model_july.use_step_method(AdaptiveMetropolis, [model_july.beta, model_july.p_susceptible])
model_july.sample(n_iterations, n_burn)
[-----------------100%-----------------] 100000 of 100000 complete in 428.3 sec
June 15, no lab confirmation
model_june_noconf = MCMC(model('1997-06-15',
confirmation=False),
db=db, dbname='model_june_noconf')
# model_june_noconf.use_step_method(AdaptiveMetropolis, [model_june_noconf.β, model_june_noconf.p_susceptible])
# model_june_noconf.use_step_method(AdaptiveMetropolis, model_june_noconf.age_dist)
model_june_noconf.sample(n_iterations, n_burn)
[-----------------100%-----------------] 100000 of 100000 complete in 76.3 sec
July 15, no lab confirmation
model_july_noconf = MCMC(model('1997-07-15',
confirmation=False),
db=db, dbname='model_july_noconf')
model_july_noconf.sample(n_iterations, n_burn)
[-----------------100%-----------------] 100000 of 100000 complete in 81.0 sec
Distance weighting parameter for june model with confirmation
Matplot.plot(model_june.p_susceptible)
Plotting p_susceptible
Matplot.plot(model_june.beta)
Plotting beta
Lab confirmation rates, June model
p_age = pd.DataFrame(model_june.p_age.trace(), columns=age_groups)
f, axes = plt.subplots(figsize=(14,6))
sb.boxplot(data=p_age, linewidth=0.3, fliersize=0, ax=axes,
color=sb.color_palette("coolwarm", 5)[0],
order=age_group.categories)
axes.set_ylabel('Confirmation rate')
axes.set_xlabel('Age group')
<matplotlib.text.Text at 0x7f64b1c63278>
Proportion of population susceptible, June model.
Matplot.plot(model_july.beta)
Plotting beta
Proportion of population susceptible, June model with no confirmation correction
Matplot.plot(model_june_noconf.p_susceptible)
Plotting p_susceptible
Epidemic intensity estimates at June and July, per district.
Matplot.plot(model_june.lam_t)
Plotting lam_t
Matplot.plot(model_july.lam_t)
Plotting lam_t
Epidemic intensity for lab- versus clinical-confirmation models
lam_june = model_june.lam.stats()
fig, axes = plt.subplots(2, 1, sharey=True)
axes[0].plot(lam_june['quantiles'][50].T, 'b-', alpha=0.4)
axes[0].set_ylabel('Epidemic intensity')
axes[0].set_xlabel('time (2-week periods)')
axes[0].set_title('Lab confirmation')
lam_june_noconf = model_june_noconf.lam.stats()
axes[1].plot(lam_june_noconf['quantiles'][50].T, 'b-', alpha=0.4)
axes[1].set_ylabel('Epidemic intensity')
axes[1].set_xlabel('time (2-week periods)')
axes[1].set_title('Clinical confirmation')
plt.tight_layout()
model_june.S_age.trace()[0]
array([[27135, 25373, 23611, 25416, 2677, 11117, 2516, 8950, 10866]])
S_age_june = pd.DataFrame(model_june.S_age.trace().squeeze(), columns=age_groups).unstack().reset_index()
S_age_june.columns = 'Age', 'Iteration', 'S'
S_age_june['Confirmation'] = 'Lab'
S_age_june = pd.DataFrame(model_june.S_age.trace().squeeze(), columns=age_groups).unstack().reset_index()
S_age_june.columns = 'Age', 'Iteration', 'S'
S_age_june['Confirmation'] = 'Lab'
S_age_june_noconf = pd.DataFrame(model_june_noconf.S_age.trace().squeeze(), columns=age_groups).unstack().reset_index()
S_age_june_noconf.columns = 'Age', 'Iteration', 'S'
S_age_june_noconf['Confirmation'] = 'Clinical'
S_age_june = pd.concat([S_age_june, S_age_june_noconf], ignore_index=True)
S_age_july = pd.DataFrame(model_july.S_age.trace().squeeze(), columns=age_groups).unstack().reset_index()
S_age_july.columns = 'Age', 'Iteration', 'S'
S_age_july['Confirmation'] = 'Lab'
S_age_july_noconf = pd.DataFrame(model_july_noconf.S_age.trace().squeeze(), columns=age_groups).unstack().reset_index()
S_age_july_noconf.columns = 'Age', 'Iteration', 'S'
S_age_july_noconf['Confirmation'] = 'Clinical'
S_age_july = pd.concat([S_age_july, S_age_july_noconf], ignore_index=True)
Numbers of suscepibles in each age group, under lab vs clinical confirmation
g = sb.factorplot("Age", "S", "Confirmation", S_age_june, kind="box",
palette="hls", size=6, aspect=2, linewidth=0.3, fliersize=0,
order=age_group.categories)
g.despine(offset=10, trim=True)
g.set_axis_labels("Age Group", "Susceptibles");
/usr/local/lib/python3.4/dist-packages/matplotlib/__init__.py:892: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter. warnings.warn(self.msg_depr % (key, alt_key))
june_lam = pd.DataFrame(model_june.lam_t.trace()).unstack().reset_index()
june_lam.columns = ('district', 'iteration', 'λ')
june_lam['month'] = 'June'
june_lam_noconf = pd.DataFrame(model_june_noconf.lam_t.trace()).unstack().reset_index()
june_lam_noconf.columns = ('district', 'iteration', 'λ')
june_lam_noconf['month'] = 'June'
july_lam = pd.DataFrame(model_july.lam_t.trace()).unstack().reset_index()
july_lam.columns = ('district', 'iteration', 'λ')
july_lam['month'] = 'July'
july_lam_noconf = pd.DataFrame(model_july_noconf.lam_t.trace()).unstack().reset_index()
july_lam_noconf.columns = ('district', 'iteration', 'λ')
july_lam_noconf['month'] = 'July'
confirmed_lam = june_lam.append(july_lam, ignore_index=True)
june_means = june_lam.groupby('district')['λ'].mean()
june_means.sort(ascending=False)
/usr/local/lib/python3.4/dist-packages/ipykernel/__main__.py:2: FutureWarning: sort is deprecated, use sort_values(inplace=True) for for INPLACE sorting from ipykernel import kernelapp as app
july_means = july_lam.groupby('district')['λ'].mean()
july_means.sort(ascending=False)
/usr/local/lib/python3.4/dist-packages/ipykernel/__main__.py:2: FutureWarning: sort is deprecated, use sort_values(inplace=True) for for INPLACE sorting from ipykernel import kernelapp as app
sorted_districts = june_means.index.values
Epidemic intensity by district in June and July (with lab confirmation), sorted by June means.
sb.set_context("talk", font_scale=0.8)
f, (ax_1, ax_2) = plt.subplots(2, 1, figsize=(12,6), sharey=True, sharex=True)
sb.boxplot('district', 'λ', data=june_lam, ax=ax_1, linewidth=0.5,
fliersize=0, color='r', order=sorted_districts)
# ax_1.hlines(1, xmin=0, xmax=93, linestyles='dashed', linewidth=0.2)
ax_1.set_xticks([])
ax_1.set_xlabel('')
ax_1.set_ylabel('June')
ax_1.set_title(r'Epidemic intensity (λ) estimates, ordered by June means')
sb.boxplot('district', 'λ', data=july_lam, ax=ax_2, linewidth=0.5,
fliersize=0, color='r', order=sorted_districts)
# ax_2.hlines(1, xmin=0, xmax=93, linestyles='dashed', linewidth=0.2)
ax_2.set_xticks([])
ax_2.set_ylabel('July')
f.tight_layout()
Epidemic intensity by district in June for lab-confirmed and clinical-confirmed, sorted by lab-confirmed means.
f, (ax_1, ax_2) = plt.subplots(2, 1, figsize=(12,6), sharey=True, sharex=True)
sb.boxplot('district', 'λ', data=june_lam, ax=ax_1, linewidth=0.5,
fliersize=0, color='r', order=june_means.index.values)
# ax_1.hlines(1, xmin=0, xmax=93, linestyles='dotted', linewidth=0.75)
ax_1.set_xticks([])
ax_1.set_xlabel('')
ax_1.set_ylabel('Lab')
ax_1.set_title(r'June epidemic intensity (λ) estimates, ordered by lab-confirmed means')
sb.boxplot('district', 'λ', data=june_lam_noconf, ax=ax_2, linewidth=0.5,
fliersize=0, color='r', order=june_means.index.values)
# ax_2.hlines(1, xmin=0, xmax=93, linestyles='dotted', linewidth=0.75)
ax_2.set_xticks([])
ax_2.set_ylabel('Clinical')
f.tight_layout()
Epidemic intensity by district in July for lab-confirmed and clinical-confirmed, sorted by lab-confirmed means.
july_means = july_lam.groupby('district')['λ'].mean()
july_means.sort(ascending=False)
f, (ax_1, ax_2) = plt.subplots(2, 1, figsize=(12,6), sharey=True, sharex=True)
sb.boxplot('district', 'λ', data=july_lam, ax=ax_1, linewidth=0.5,
fliersize=0, color='r', order=july_means.index.values)
# ax_1.hlines(1, xmin=0, xmax=93, linestyles='dotted', linewidth=0.75)
ax_1.set_xticks([])
ax_1.set_xlabel('')
ax_1.set_ylabel('Lab')
# ax_1.set_yticks(np.arange(13, step=2))
ax_1.set_title(r'July epidemic intensity (λ) estimates, ordered by lab-confirmed means')
sb.boxplot('district', 'λ', data=july_lam_noconf, ax=ax_2, linewidth=0.5,
fliersize=0, color='r', order=sorted_districts)
# ax_2.hlines(1, xmin=0, xmax=93, linestyles='dotted', linewidth=0.75)
ax_2.set_xticks([])
ax_2.set_ylabel('Clinical')
f.tight_layout()
model_june.summary(['pct_5', 'pct_15', 'pct_30', 'pct_adult'])
pct_5: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.207 0.013 0.001 [ 0.185 0.232] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.184 0.197 0.207 0.217 0.231 pct_15: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.546 0.02 0.002 [ 0.513 0.584] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.509 0.53 0.544 0.563 0.581 pct_30: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.793 0.014 0.001 [ 0.768 0.818] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.764 0.782 0.793 0.804 0.816 pct_adult: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.305 0.012 0.001 [ 0.281 0.325] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.282 0.295 0.306 0.314 0.326
june_coverage = pd.DataFrame({name: model_june.trace(name)[:] for name in ['pct_5', 'pct_15', 'pct_30', 'pct_adult']})
june_coverage['Month'] = 'June'
june_coverage['Confirmation'] = 'Lab'
june_noconf_coverage = pd.DataFrame({name: model_june_noconf.trace(name)[:] for name in ['pct_5', 'pct_15', 'pct_30', 'pct_adult']})
june_noconf_coverage['Month'] = 'June'
june_noconf_coverage['Confirmation'] = 'Clinical'
july_coverage = pd.DataFrame({name: model_july.trace(name)[:] for name in ['pct_5', 'pct_15', 'pct_30', 'pct_adult']})
july_coverage['Month'] = 'July'
july_coverage['Confirmation'] = 'Lab'
july_noconf_coverage = pd.DataFrame({name: model_july_noconf.trace(name)[:] for name in ['pct_5', 'pct_15', 'pct_30', 'pct_adult']})
july_noconf_coverage['Month'] = 'July'
july_noconf_coverage['Confirmation'] = 'Clinical'
coverage = pd.concat([june_coverage, june_noconf_coverage, july_coverage, july_noconf_coverage],
ignore_index=True)
sb.factorplot(row="Month", col="Confirmation", data=coverage, kind='box',
row_order=['June', 'July'],
order=['pct_5', 'pct_15', 'pct_30', 'pct_adult'],
palette="YlGnBu_d", linewidth=0.7, fliersize=0, aspect=1.25).despine(left=True)
/usr/local/lib/python3.4/dist-packages/matplotlib/__init__.py:892: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter. warnings.warn(self.msg_depr % (key, alt_key))
<seaborn.axisgrid.FacetGrid at 0x7f464480c2e8>
sb.factorplot(row="Month", col="Confirmation", data=coverage, kind='box',
row_order=['June', 'July'],
order=['pct_5', 'pct_15', 'pct_30', 'pct_adult'],
palette="YlGnBu_d", linewidth=0.7, fliersize=0, aspect=1.25).despine(left=True)
/usr/local/lib/python3.4/dist-packages/matplotlib/__init__.py:892: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter. warnings.warn(self.msg_depr % (key, alt_key))
<seaborn.axisgrid.FacetGrid at 0x7f64990997b8>
axes = sb.boxplot(data=june_coverage, order=['pct_5', 'pct_15', 'pct_30', 'pct_adult'],
color=sb.color_palette("coolwarm", 5)[0])
axes.set_xticklabels(['Under 5', 'Under 15', 'Under 30', 'Under 5 + 20-30'])
axes.set_ylabel('% susceptibles vaccinated')
sb.despine(offset=10, trim=True)
model_june_noconf.summary(['pct_5', 'pct_15', 'pct_30', 'pct_adult'])
pct_5: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.199 0.01 0.001 [ 0.181 0.221] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.179 0.194 0.199 0.205 0.22 pct_15: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.573 0.01 0.001 [ 0.554 0.593] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.553 0.565 0.573 0.581 0.592 pct_30: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.807 0.009 0.001 [ 0.79 0.824] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.789 0.801 0.807 0.813 0.823 pct_adult: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.275 0.013 0.001 [ 0.249 0.301] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.247 0.266 0.274 0.284 0.3
model_july.summary(['pct_5', 'pct_15', 'pct_30', 'pct_adult'])
pct_5: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.255 0.007 0.001 [ 0.243 0.27 ] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.24 0.251 0.255 0.26 0.269 pct_15: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.584 0.009 0.001 [ 0.568 0.6 ] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.567 0.578 0.584 0.59 0.599 pct_30: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.815 0.006 0.001 [ 0.803 0.827] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.803 0.811 0.816 0.819 0.827 pct_adult: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.365 0.01 0.001 [ 0.346 0.385] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.343 0.358 0.365 0.372 0.384
model_july_noconf.summary(['pct_5', 'pct_15', 'pct_30', 'pct_adult'])
pct_5: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.252 0.006 0.001 [ 0.239 0.264] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.239 0.248 0.252 0.256 0.264 pct_15: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.613 0.007 0.001 [ 0.602 0.626] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.602 0.608 0.612 0.617 0.627 pct_30: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.827 0.004 0.0 [ 0.821 0.835] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.821 0.825 0.827 0.83 0.835 pct_adult: Mean SD MC Error 95% HPD interval ------------------------------------------------------------------ 0.342 0.006 0.001 [ 0.331 0.355] Posterior quantiles: 2.5 25 50 75 97.5 |---------------|===============|===============|---------------| 0.33 0.338 0.342 0.346 0.354
Matplot.summary_plot(model_june.p_age)
Could not calculate Gelman-Rubin statistics. Requires multiple chains of equal length.
from mpl_toolkits.basemap import Basemap
import geopandas as gpd
lllat=-24
urlat=-23.3
lllon=-47
urlon=-46.3
SP_base = Basemap(ax=None, lon_0=(urlon + lllon) / 2, lat_0=(urlat + lllat) / 2,
llcrnrlat=lllat, urcrnrlat=urlat, llcrnrlon=lllon, urcrnrlon=urlon,
resolution='i',
epsg='4326')
SP_dist = gpd.GeoDataFrame.from_file('Sao Paulo/Brazil_full/BRA_adm3.shp').to_crs({'proj': 'longlat',
'ellps': 'WGS84',
'datum': 'WGS84'})
SP_dist['DIST_NAME'] = [trans.trans(_).upper() for _ in SP_dist.NAME_3]
λ_june = pd.Series(model_june.λ_t.stats()['mean'], index=sp_districts)
λ_june
SP_dist_merged = SP_dist.merge(pd.DataFrame(λ_june, columns=['λ']), left_on='DIST_NAME', right_index=True)
measles_onset_conf = measles_data[CONFIRMED].groupby(['DISTRICT','ONSET']).size().unstack(level=0).fillna(0).sum()
measles_onset_conf
_rates = measles_onset_conf/sp_pop.sum(1)
SP_dist_conf = SP_dist.merge(pd.DataFrame(_rates, columns=['rate']), left_on='DIST_NAME', right_index=True)
Estimated expected value for infecteds, by district
from matplotlib.pyplot import cm
map_fig = plt.figure(figsize=(16,12))
map_ax = plt.gca()
SP_base.drawcoastlines()
SP_base.drawrivers()
SP_dist_merged.plot(column='λ', colormap=cm.Reds, axes=map_ax)
Observed confirmed cases, by district
map_fig = plt.figure(figsize=(16,12))
map_ax = plt.gca()
SP_base.drawcoastlines()
SP_base.drawrivers()
SP_dist_conf.plot(column='rate', colormap=cm.Reds, axes=map_ax)