224 lines
No EOL
9.4 KiB
Python
224 lines
No EOL
9.4 KiB
Python
from dataclasses import dataclass
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import typing
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import numpy as np
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from scipy import special as sp
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from scipy.stats import weibull_min
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import caimira.monte_carlo as mc
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from caimira.monte_carlo.sampleable import LogCustom, LogNormal,LogCustomKernel,CustomKernel,Uniform, Custom
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sqrt2pi = np.sqrt(2.*np.pi)
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sqrt2 = np.sqrt(2.)
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@dataclass(frozen=True)
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class BLOmodel:
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"""
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Represents the probability distribution from the BLO model.
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It is a sum of three lognormal distributions, each of the form
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A * cn * (1 / d) * (1 / (np.sqrt(2 * np.pi) * sigma)) *
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np.exp(-(np.log(d)-mu) ** 2 / (2 * sigma ** 2))
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with A the factor in front of the B, L or O mode.
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From G. Johnson et al., Modality of human
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expired aerosol size distributions, Journal of Aerosol Science,
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vol. 42, no. 12, pp. 839 – 851, 2011,
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https://doi.org/10.1016/j.jaerosci.2011.07.009).
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"""
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#: Factors assigned to resp. the B, L and O modes. They are
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# charateristics of the kind of expiratory activity (e.g. breathing,
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# speaking, singing, or shouting). These are applied on top of the
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# cn concentrations (see below), and depend on the kind of activity
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# (breathing, speaking, singing/shouting)
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BLO_factors: typing.Tuple[float, float, float]
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#: cn (cm^-3) for resp. the B, L and O modes. Corresponds to the
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# total concentration of aerosols for each mode.
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cn: typing.Tuple[float, float, float] = (0.06, 0.2, 0.0010008)
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# Mean of the underlying normal distributions (represents the log of a
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# diameter in microns), for resp. the B, L and O modes.
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mu: typing.Tuple[float, float, float] = (0.989541, 1.38629, 4.97673)
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# Std deviation of the underlying normal distribution, for resp.
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# the B, L and O modes.
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sigma: typing.Tuple[float, float, float] = (0.262364, 0.506818, 0.585005)
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def distribution(self, d):
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"""
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Returns the raw value of the probability distribution for a
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given diameter d (microns).
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"""
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return sum( (1 / d) * (A * cn / (sqrt2pi * sigma)) *
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np.exp(-(np.log(d) - mu) ** 2 / (2 * sigma ** 2))
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for A,cn,mu,sigma in zip(self.BLO_factors, self.cn,
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self.mu, self.sigma) )
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def integrate(self, dmin, dmax):
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"""
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Returns the integral between dmin and dmax (in microns) of the
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probability distribution.
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"""
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result = 0.
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for A,cn,mu,sigma in zip(self.BLO_factors, self.cn, self.mu, self.sigma):
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ymin = (np.log(dmin)-mu)/(sqrt2*sigma)
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ymax = (np.log(dmax)-mu)/(sqrt2*sigma)
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result += A * cn * (sp.erf(ymax)-sp.erf(ymin)) / 2.
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return result
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# From https://doi.org/10.1101/2021.10.14.21264988 and references therein
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activity_distributions = {
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'Seated': mc.Activity(LogNormal(-0.6872121723362303, 0.10498338229297108),
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LogNormal(-0.6872121723362303, 0.10498338229297108)),
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'Standing': mc.Activity(LogNormal(-0.5742377578494785, 0.09373162411398223),
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LogNormal(-0.5742377578494785, 0.09373162411398223)),
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'Light activity': mc.Activity(LogNormal(0.21380242785625422,0.09435378091059601),
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LogNormal(0.21380242785625422,0.09435378091059601)),
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'Moderate activity': mc.Activity(LogNormal(0.551771330362601, 0.1894616357138137),
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LogNormal(0.551771330362601, 0.1894616357138137)),
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'Heavy exercise': mc.Activity(LogNormal(1.1644665696723049, 0.21744554768657565),
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LogNormal(1.1644665696723049, 0.21744554768657565)),
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}
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# From https://doi.org/10.1101/2021.10.14.21264988 and references therein
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symptomatic_vl_frequencies = LogCustomKernel(
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np.array((2.46032, 2.67431, 2.85434, 3.06155, 3.25856, 3.47256, 3.66957, 3.85979, 4.09927, 4.27081,
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4.47631, 4.66653, 4.87204, 5.10302, 5.27456, 5.46478, 5.6533, 5.88428, 6.07281, 6.30549,
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6.48552, 6.64856, 6.85407, 7.10373, 7.30075, 7.47229, 7.66081, 7.85782, 8.05653, 8.27053,
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8.48453, 8.65607, 8.90573, 9.06878, 9.27429, 9.473, 9.66152, 9.87552)),
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np.array((0.001206885, 0.007851618, 0.008078144, 0.01502491, 0.013258014, 0.018528495, 0.020053765,
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0.021896167, 0.022047184, 0.018604005, 0.01547796, 0.018075445, 0.021503523, 0.022349217,
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0.025097721, 0.032875078, 0.030594727, 0.032573045, 0.034717482, 0.034792991,
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0.033267721, 0.042887485, 0.036846816, 0.03876473, 0.045016819, 0.040063473, 0.04883754,
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0.043944602, 0.048142864, 0.041588741, 0.048762031, 0.027921732, 0.033871788,
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0.022122693, 0.016927718, 0.008833228, 0.00478598, 0.002807662)),
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kernel_bandwidth=0.1
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)
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# Weibull distribution with a shape factor of 3.47 and a scale factor of 7.01.
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# From https://elifesciences.org/articles/65774 and first line of the figure in
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# https://iiif.elifesciences.org/lax:65774%2Felife-65774-fig4-figsupp3-v2.tif/full/1500,/0/default.jpg
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viral_load = np.linspace(weibull_min.ppf(0.01, c=3.47, scale=7.01),
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weibull_min.ppf(0.99, c=3.47, scale=7.01), 30)
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frequencies_pdf = weibull_min.pdf(viral_load, c=3.47, scale=7.01)
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covid_overal_vl_data = LogCustom(bounds=(2, 10),
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function=lambda d: np.interp(d, viral_load, frequencies_pdf, left=0., right=0.),
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max_function=0.2)
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# Derived from data in doi.org/10.1016/j.ijid.2020.09.025 and
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# https://iosh.com/media/8432/aerosol-infection-risk-hospital-patient-care-full-report.pdf (page 60)
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viable_to_RNA_ratio_distribution = Uniform(0.01, 0.6)
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# From discussion with virologists
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infectious_dose_distribution = Uniform(10., 100.)
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# From https://doi.org/10.1101/2021.10.14.21264988 and refererences therein
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virus_distributions = {
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'SARS_CoV_2': mc.SARSCoV2(
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viral_load_in_sputum=covid_overal_vl_data,
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infectious_dose=infectious_dose_distribution,
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viable_to_RNA_ratio=viable_to_RNA_ratio_distribution,
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transmissibility_factor=1.,
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),
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'SARS_CoV_2_ALPHA': mc.SARSCoV2(
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viral_load_in_sputum=covid_overal_vl_data,
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infectious_dose=infectious_dose_distribution,
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viable_to_RNA_ratio=viable_to_RNA_ratio_distribution,
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transmissibility_factor=0.78,
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),
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'SARS_CoV_2_BETA': mc.SARSCoV2(
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viral_load_in_sputum=covid_overal_vl_data,
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infectious_dose=infectious_dose_distribution,
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viable_to_RNA_ratio=viable_to_RNA_ratio_distribution,
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transmissibility_factor=0.8,
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),
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'SARS_CoV_2_GAMMA': mc.SARSCoV2(
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viral_load_in_sputum=covid_overal_vl_data,
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infectious_dose=infectious_dose_distribution,
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viable_to_RNA_ratio=viable_to_RNA_ratio_distribution,
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transmissibility_factor=0.72,
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),
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'SARS_CoV_2_DELTA': mc.SARSCoV2(
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viral_load_in_sputum=covid_overal_vl_data,
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infectious_dose=infectious_dose_distribution,
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viable_to_RNA_ratio=viable_to_RNA_ratio_distribution,
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transmissibility_factor=0.51,
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),
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'SARS_CoV_2_OMICRON': mc.SARSCoV2(
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viral_load_in_sputum=covid_overal_vl_data,
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infectious_dose=infectious_dose_distribution,
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viable_to_RNA_ratio=viable_to_RNA_ratio_distribution,
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transmissibility_factor=0.2,
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),
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}
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# From:
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# https://doi.org/10.1080/02786826.2021.1890687
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# https://doi.org/10.1016/j.jhin.2013.02.007
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# https://doi.org/10.4209/aaqr.2020.08.0531
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mask_distributions = {
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'Type I': mc.Mask(Uniform(0.25, 0.80)),
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'FFP2': mc.Mask(Uniform(0.83, 0.91)),
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}
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def expiration_distribution(
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BLO_factors,
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d_max=30.,
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) -> mc.Expiration:
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"""
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Returns an Expiration with an aerosol diameter distribution, defined
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by the BLO factors (a length-3 tuple).
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The total concentration of aerosols, cn, is computed by integrating
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the distribution between 0.1 and 30 microns - these boundaries are
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an historical choice based on previous implementations of the model
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(it limits the influence of the O-mode).
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"""
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dscan = np.linspace(0.1, d_max, 3000)
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return mc.Expiration(
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CustomKernel(
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dscan,
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BLOmodel(BLO_factors).distribution(dscan),
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kernel_bandwidth=0.1,
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),
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cn=BLOmodel(BLO_factors).integrate(0.1, d_max),
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)
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expiration_BLO_factors = {
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'Breathing': (1., 0., 0.),
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'Speaking': (1., 1., 1.),
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'Singing': (1., 5., 5.),
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'Shouting': (1., 5., 5.),
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}
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expiration_distributions = {
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exp_type: expiration_distribution(BLO_factors)
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for exp_type, BLO_factors in expiration_BLO_factors.items()
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}
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short_range_expiration_distributions = {
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exp_type: expiration_distribution(BLO_factors, d_max=100)
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for exp_type, BLO_factors in expiration_BLO_factors.items()
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}
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# Derived from Fig 8 a) "stand-stand" in https://www.mdpi.com/1660-4601/17/4/1445/htm
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distances = np.array((0.5,0.6,0.7,0.8,0.9,1,1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2))
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frequencies = np.array((0.0598036,0.0946154,0.1299152,0.1064905,0.1099066,0.0998209, 0.0845298,0.0479286,0.0406084,0.039795,0.0205997,0.0152316,0.0118155,0.0118155,0.018485,0.0205997))
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short_range_distances = Custom(bounds=(0.5,2.),
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function=lambda x: np.interp(x,distances,frequencies,left=0.,right=0.),
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max_function=0.13) |