def transition_probabilities(mortality_multiplier):
"""2b. Construct transition probabilities between disease severities
There are three disease states: mild, severe and critical.
- Mild represents sub-hospitalization.
- Severe is hospitalization.
- Critical is ICU.
The key results of this section are:
- p_mild_severe: N_AGES x 2 x 2 matrix. For each age and comorbidity state
(length two bool vector indicating whether the individual has diabetes and/or
hypertension), what is the probability of the individual transitioning from
the mild to severe state.
- p_severe_critical, p_critical_death are the same for the other state transitions.
All of these probabilities are proportional to the base progression rate
for an (age, diabetes, hypertension) state which is stored in p_death_target
and estimated via logistic regression.
"""
# N_AGES vector: The probability of transitioning from the mild to
# severe state for a patient of age i is p_mild_severe_cdc[i]. We will match
# these overall probabilities.
# Source: https://www.cdc.gov/mmwr/volumes/69/wr/mm6912e2.htm?s_cid=mm6912e2_w#T1_down
# Using the lower bounds for probability of hospitalization, since that's more
# consistent with frequency of severe infection reported in
# https://www.nejm.org/doi/full/10.1056/NEJMoa2002032 (at a lower level of age granularity).
p_mild_severe_cdc = np.zeros(N_AGES)
p_mild_severe_cdc[0:20] = 0.016
p_mild_severe_cdc[20:45] = 0.143
p_mild_severe_cdc[45:55] = 0.212
p_mild_severe_cdc[55:65] = 0.205
p_mild_severe_cdc[65:75] = 0.286
p_mild_severe_cdc[75:85] = 0.305
p_mild_severe_cdc[85:] = 0.313
# overall probability of progression from critical to severe
# https://www.ecdc.europa.eu/sites/default/files/documents/RRA-sixth-update-Outbreak-of-novel-coronavirus-disease-2019-COVID-19.pdf
# taking midpoint of the intervals
overall_p_severe_critical = (0.15 + 0.2) / 2
# overall mortality, which is set separately, but rather how many individuals
# end up in critical state. 0.49 is from
# http://weekly.chinacdc.cn/en/article/id/e53946e2-c6c4-41e9-9a9b-fea8db1a8f51
overall_p_critical_death = 0.49
# go back to using CDC hospitalization rates as mild->severe
severe_critical_multiplier = overall_p_severe_critical / p_mild_severe_cdc
critical_death_multiplier = overall_p_critical_death / p_mild_severe_cdc
# get the overall CFR for each age/comorbidity combination by running the logistic model
"""
Mortality model. We fit a logistic regression to estimate p_mild_death from
(age, diabetes, hypertension) to match the marginal mortality rates from TODO.
The results of the logistic regression are used to set the disease severity
transition probabilities.
"""
c_age = np.loadtxt(resource_filename(__package__,
'comorbidities/c_age.txt'),
delimiter=',').mean(axis=0)
"""float vector: Logistic regression weights for each age bracket."""
c_diabetes = np.loadtxt(resource_filename(__package__,
'comorbidities/c_diabetes.txt'),
delimiter=',').mean(axis=0)
"""float: Logistic regression weight for diabetes."""
c_hyper = np.loadtxt(resource_filename(__package__,
'comorbidities/c_hypertension.txt'),
delimiter=',').mean(axis=0)
"""float: Logistic regression weight for hypertension."""
intervals = np.loadtxt(resource_filename(
__package__, 'comorbidities/comorbidity_age_intervals.txt'),
delimiter=',')
def age_to_interval(i):
"""Return the corresponding comorbidity age interval for a specific age.
Args:
i (int): age.
Returns:
int: index of interval containing i in intervals.
"""
for idx, a in enumerate(intervals):
if i >= a[0] and i < a[1]:
return idx
return idx
p_death_target = np.zeros((N_AGES, 2, 2))
for i in range(N_AGES):
for diabetes_state in [0, 1]:
for hyper_state in [0, 1]:
if i < intervals[0][0]:
p_death_target[i, diabetes_state, hyper_state] = 0
else:
p_death_target[i, diabetes_state,
hyper_state] = sp.special.expit(
c_age[age_to_interval(i)] +
diabetes_state * c_diabetes +
hyper_state * c_hyper)
# p_death_target *= params['mortality_multiplier']
# p_death_target[p_death_target > 1] = 1
#calibrate the probability of the severe -> critical transition to match the
#overall CFR for each age/comorbidity combination
#age group, diabetes (0/1), hypertension (0/1)
progression_rate = np.zeros((N_AGES, 2, 2))
p_mild_severe = np.zeros((N_AGES, 2, 2))
"""float N_AGES x 2 x 2 vector: Probability a patient with a particular age combordity
profile transitions from mild to severe state."""
p_severe_critical = np.zeros((N_AGES, 2, 2))
"""float N_AGES x 2 x 2 vector: Probability a patient with a particular age combordity
profile transitions from severe to critical state."""
p_critical_death = np.zeros((N_AGES, 2, 2))
"""float N_AGES x 2 x 2 vector: Probability a patient with a particular age combordity
profile transitions from critical to dead state."""
for i in range(N_AGES):
for diabetes_state in [0, 1]:
for hyper_state in [0, 1]:
progression_rate[i, diabetes_state, hyper_state] = (
p_death_target[i, diabetes_state, hyper_state] /
(severe_critical_multiplier[i] *
critical_death_multiplier[i]))**(1. / 3)
p_mild_severe[i, diabetes_state,
hyper_state] = progression_rate[i,
diabetes_state,
hyper_state]
p_severe_critical[i, diabetes_state,
hyper_state] = severe_critical_multiplier[
i] * progression_rate[i, diabetes_state,
hyper_state]
p_critical_death[i, diabetes_state,
hyper_state] = critical_death_multiplier[
i] * progression_rate[i, diabetes_state,
hyper_state]
#no critical cases under 20 (CDC)
p_critical_death[:20] = 0
p_severe_critical[:20] = 0
#for now, just cap 80+yos with diabetes and hypertension
p_critical_death[p_critical_death > 1] = 1
p_mild_severe *= mortality_multiplier**(1 / 3)
p_severe_critical *= mortality_multiplier**(1 / 3)
p_critical_death *= mortality_multiplier**(1 / 3)
p_mild_severe[p_mild_severe > 1] = 1
p_severe_critical[p_severe_critical > 1] = 1
p_critical_death[p_critical_death > 1] = 1
return aljpy.dotdict(
p_mild_severe=p_mild_severe,
p_severe_critical=p_severe_critical,
p_critical_death=p_critical_death,
)
# If lockdown, by how much do divide contact matrix?
LOCKDOWN_FACTOR = 2.
# How infectious are asymptomatic cases relative to symptomatic ones
# https://science.sciencemag.org/content/early/2020/03/13/science.abb3221
ASYMPTOMATIC_TRANSMISSIBILITY = 0.55
# DON'T CHANGE: we don't want p infect household to recalibrate for different policy what ifs on mean time to isolate
MEAN_TIME_TO_ISOLATE = 4.6 # DON'T CHANGE
TUNED = aljpy.dotdict(Italy=aljpy.dotdict(
# increase probability of death for all ages and comorbidities by this amount
mortality_multiplier=4,
# Probability of infection given contact between two individuals
# This is currently set arbitrarily and will be calibrated to match the empirical r0
pigc=.029,
population=int(1e4),
n_infected_start=5.,
start_date=date(2020, 1, 22),
stay_home_date=date(2020, 3, 8),
lockdown_date=date(2022, 12, 31))) # no lockdown
AGE_GROUPS = {
'infected_1': '0-4',
'contact_1': '0-4',
'infected_2': '5-9',
'contact_2': '5-9',
'infected_3': '10-14',
'contact_3': '10-14',
'infected_4': '15-19',
'contact_4': '15-19',
