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cara/cara/model_scenarios.py
Luis Aleixo 32a2a75bc9 Changed color value
2021-09-02 10:43:45 +02:00

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from numpy.core.function_base import linspace
from cara import models
from cara.monte_carlo.data import activity_distributions
from tqdm import tqdm
import cara.monte_carlo as mc
import numpy as np
import matplotlib.pyplot as plt
from scipy.spatial import ConvexHull
import pandas as pd
import matplotlib.lines as mlines
from matplotlib.patches import Rectangle
import matplotlib as mpl
######### Plot material #########
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
SAMPLE_SIZE = 50000
er_means = []
er_medians = []
lower_percentiles = []
upper_percentiles = []
######### Scatter points (data taken: copies per hour) #########
############# Coleman #############
############# Coleman - Breathing #############
coleman_etal_vl_breathing = [np.log10(821065925.4), np.log10(1382131207), np.log10(81801735.96), np.log10(
487760677.4), np.log10(2326593535), np.log10(1488879159), np.log10(884480386.5)]
coleman_etal_er_breathing = [127, 455.2, 281.8, 884.2, 448.4, 1100.6, 621]
############# Coleman - Talking #############
coleman_etal_vl_talking = [np.log10(70492378.55), np.log10(7565486.029), np.log10(7101877592), np.log10(1382131207),
np.log10(821065925.4), np.log10(1382131207), np.log10(81801735.96), np.log10(487760677.4),
np.log10(2326593535), np.log10(1488879159), np.log10(884480386.5)]
coleman_etal_er_talking = [1668, 938, 319.6, 3632.8, 1243.6,
17344, 2932, 5426, 5493.2, 1911.6, 9714.8]
############# Milton et al #############
milton_vl = [np.log10(8.30E+04), np.log10(4.20E+05), np.log10(1.80E+06)]
milton_er = [22, 220, 1120] # removed first and last due to its dimensions
############# Milton et al #############
yann_vl = [np.log10(7.86E+07), np.log10(2.23E+09), np.log10(1.51E+10)]
yann_er = [8396.78166, 45324.55964, 400054.0827]
######### Standard exposure models ###########
def exposure_model_from_vl_talking_new_points(viral_loads):
for vl in tqdm(viral_loads):
exposure_mc = mc.ExposureModel(
concentration_model=mc.ConcentrationModel(
room=models.Room(volume=100, humidity=0.5),
ventilation=models.AirChange(
active=models.SpecificInterval(((0, 24),)),
air_exch=0.25,
),
infected=mc.InfectedPopulation(
number=1,
virus=models.Virus(
viral_load_in_sputum=10**vl,
infectious_dose=50.,
),
presence=mc.SpecificInterval(((0, 2),)),
mask=models.Mask.types["No mask"],
activity=activity_distributions['Seated'],
expiration=models.Expiration.types['Talking'],
),
),
exposed=mc.Population(
number=14,
presence=mc.SpecificInterval(((0, 2),)),
activity=models.Activity.types['Seated'],
mask=models.Mask.types["No mask"],
),
)
exposure_model = exposure_mc.build_model(size=SAMPLE_SIZE)
# divide by 4 to have in 15min (quarter of an hour)
emission_rate = exposure_model.concentration_model.infected.emission_rate_when_present(1.0)/4
er_means.append((10**vl) / np.mean(emission_rate))
er_medians.append(np.median(emission_rate))
lower_percentiles.append(np.quantile(emission_rate, 0.01))
upper_percentiles.append(np.quantile(emission_rate, 0.99))
# divide by 4 to have in 15min (quarter of an hour)
coleman_etal_er_talking_2 = [x/4 for x in coleman_etal_er_talking]
ax.plot(viral_loads, er_means)
ax.set_yscale('log')
new_datapoints = [10**(a) / b for a, b in zip(coleman_etal_vl_talking, coleman_etal_er_talking_2)]
print(new_datapoints)
############# Coleman #############
plt.scatter(coleman_etal_vl_talking, new_datapoints, marker='x')
############# Markers #############
markers = [5, 'd', 4]
############ Legend ############
result_from_model = mlines.Line2D(
[], [], color='blue', marker='_', linestyle='None')
coleman = mlines.Line2D([], [], color='orange',
marker='x', linestyle='None')
title_proxy = Rectangle((0, 0), 0, 0, color='w')
titles = ["$\\bf{CARA \, \\it{(SARS-CoV-2)}:}$", "$\\bf{Coleman \, et \, al. \, \\it{(SARS-CoV-2)}:}$"]
leg = plt.legend([title_proxy, result_from_model, title_proxy, coleman],
[titles[0], "Result from model", titles[1], "Dataset"])
# Move titles to the left
for item, label in zip(leg.legendHandles, leg.texts):
if label._text in titles:
width = item.get_window_extent(fig.canvas.get_renderer()).width
label.set_ha('left')
label.set_position((-3*width, 0))
############ Plot ############
plt.title('Exhaled virions while talking for 15min',
fontsize=16, fontweight="bold")
plt.ylabel(
'Aerosol viral load, $\mathrm{vl_{out}}$\n(RNA copies)', fontsize=14)
plt.xticks(ticks=[i for i in range(2, 13)], labels=[
'$10^{' + str(i) + '}$' for i in range(2, 13)])
plt.xlabel('NP viral load, $\mathrm{vl_{in}}$\n(RNA copies)', fontsize=14)
plt.ylim([10**0, 10**10])
plt.show()
return er_means
def exposure_model_from_vl_talking(viral_loads):
for vl in tqdm(viral_loads):
exposure_mc = mc.ExposureModel(
concentration_model=mc.ConcentrationModel(
room=models.Room(volume=100, humidity=0.5),
ventilation=models.AirChange(
active=models.SpecificInterval(((0, 24),)),
air_exch=0.25,
),
infected=mc.InfectedPopulation(
number=1,
virus=models.Virus(
viral_load_in_sputum=10**vl,
infectious_dose=50.,
),
presence=mc.SpecificInterval(((0, 2),)),
mask=models.Mask.types["No mask"],
activity=activity_distributions['Seated'],
expiration=models.Expiration.types['Talking'],
),
),
exposed=mc.Population(
number=14,
presence=mc.SpecificInterval(((0, 2),)),
activity=models.Activity.types['Seated'],
mask=models.Mask.types["No mask"],
),
)
exposure_model = exposure_mc.build_model(size=SAMPLE_SIZE)
# divide by 4 to have in 15min (quarter of an hour)
emission_rate = exposure_model.concentration_model.infected.emission_rate_when_present(1.0)/4
er_means.append(np.mean(emission_rate))
er_medians.append(np.median(emission_rate))
lower_percentiles.append(np.quantile(emission_rate, 0.01))
upper_percentiles.append(np.quantile(emission_rate, 0.99))
# divide by 4 to have in 15min (quarter of an hour)
coleman_etal_er_talking_2 = [x/4 for x in coleman_etal_er_talking]
ax.plot(viral_loads, er_means)
ax.fill_between(viral_loads, lower_percentiles,
upper_percentiles, alpha=0.2)
ax.set_yscale('log')
############# Coleman #############
plt.scatter(coleman_etal_vl_talking, coleman_etal_er_talking_2, marker='x')
x_hull, y_hull = get_enclosure_points(
coleman_etal_vl_talking, coleman_etal_er_talking_2)
# plot shape
plt.fill(x_hull, y_hull, '--', c='orange', alpha=0.2)
############# Markers #############
markers = [5, 'd', 4]
############ Legend ############
result_from_model = mlines.Line2D(
[], [], color='blue', marker='_', linestyle='None')
coleman = mlines.Line2D([], [], color='orange',
marker='x', linestyle='None')
title_proxy = Rectangle((0, 0), 0, 0, color='w')
titles = ["$\\bf{CARA \, \\it{(SARS-CoV-2)}:}$", "$\\bf{Coleman \, et \, al. \, \\it{(SARS-CoV-2)}:}$"]
leg = plt.legend([title_proxy, result_from_model, title_proxy, coleman],
[titles[0], "Result from model", titles[1], "Dataset"])
# Move titles to the left
for item, label in zip(leg.legendHandles, leg.texts):
if label._text in titles:
width = item.get_window_extent(fig.canvas.get_renderer()).width
label.set_ha('left')
label.set_position((-3*width, 0))
############ Plot ############
plt.title('Exhaled virions while talking for 15min',
fontsize=16, fontweight="bold")
plt.ylabel(
'Aerosol viral load, $\mathrm{vl_{out}}$\n(RNA copies)', fontsize=14)
plt.xticks(ticks=[i for i in range(2, 13)], labels=[
'$10^{' + str(i) + '}$' for i in range(2, 13)])
plt.xlabel('NP viral load, $\mathrm{vl_{in}}$\n(RNA copies)', fontsize=14)
plt.show()
return er_means
def exposure_model_from_vl_talking_cn(viral_loads):
n_lines = 5
cns = np.linspace(0.1, 1, n_lines)
norm = mpl.colors.Normalize(vmin=cns.min(), vmax=cns.max())
cmap = mpl.cm.ScalarMappable(norm=norm, cmap=mpl.cm.jet)
cmap.set_array([])
for cn in tqdm(cns):
er_means = []
er_medians = []
lower_percentiles = []
upper_percentiles = []
for vl in viral_loads:
exposure_mc = mc.ExposureModel(
concentration_model=mc.ConcentrationModel(
room=models.Room(volume=100, humidity=0.5),
ventilation=models.AirChange(
active=models.SpecificInterval(((0, 24),)),
air_exch=0.25,
),
infected=mc.InfectedPopulation(
number=1,
virus=models.Virus(
viral_load_in_sputum=10**vl,
infectious_dose=50.,
),
presence=mc.SpecificInterval(((0, 2),)),
mask=models.Mask.types["No mask"],
activity=activity_distributions['Seated'],
expiration=models.Expiration.types['Talking'],
),
),
exposed=mc.Population(
number=14,
presence=mc.SpecificInterval(((0, 2),)),
activity=models.Activity.types['Seated'],
mask=models.Mask.types["No mask"],
),
)
exposure_model = exposure_mc.build_model(size=SAMPLE_SIZE)
# divide by 4 to have in 15min (quarter of an hour)
emission_rate = exposure_model.concentration_model.infected.emission_rate_when_present(cn)/4
er_means.append(np.mean(emission_rate))
er_medians.append(np.median(emission_rate))
lower_percentiles.append(np.quantile(emission_rate, 0.01))
upper_percentiles.append(np.quantile(emission_rate, 0.99))
# divide by 4 to have in 15min (quarter of an hour)
coleman_etal_er_talking_2 = [x/4 for x in coleman_etal_er_talking]
ax.plot(viral_loads, er_means, color=cmap.to_rgba(cn))
#ax.fill_between(viral_loads, lower_percentiles,
# upper_percentiles, alpha=0.2, color=cmap.to_rgba(cn))
fig.colorbar(cmap, ticks=cns)
ax.set_yscale('log')
############# Coleman #############
plt.scatter(coleman_etal_vl_talking, coleman_etal_er_talking_2, marker='x')
x_hull, y_hull = get_enclosure_points(
coleman_etal_vl_talking, coleman_etal_er_talking_2)
# plot shape
plt.fill(x_hull, y_hull, '--', c='orange', alpha=0.2)
############# Markers #############
markers = [5, 'd', 4]
############ Legend ############
result_from_model = mlines.Line2D(
[], [], color='blue', marker='_', linestyle='None')
coleman = mlines.Line2D([], [], color='orange',
marker='x', linestyle='None')
title_proxy = Rectangle((0, 0), 0, 0, color='w')
titles = ["$\\bf{CARA \, \\it{(SARS-CoV-2)}:}$", "$\\bf{Coleman \, et \, al. \, \\it{(SARS-CoV-2)}:}$"]
leg = plt.legend([title_proxy, result_from_model, title_proxy, coleman],
[titles[0], "Result from model", titles[1], "Dataset"])
# Move titles to the left
for item, label in zip(leg.legendHandles, leg.texts):
if label._text in titles:
width = item.get_window_extent(fig.canvas.get_renderer()).width
label.set_ha('left')
label.set_position((-3*width, 0))
############ Plot ############
plt.title('Exhaled virions while talking for 15min',
fontsize=16, fontweight="bold")
plt.ylabel(
'Aerosol viral load, $\mathrm{vl_{out}}$\n(RNA copies)', fontsize=14)
plt.xticks(ticks=[i for i in range(2, 13)], labels=[
'$10^{' + str(i) + '}$' for i in range(2, 13)])
plt.xlabel('NP viral load, $\mathrm{vl_{in}}$\n(RNA copies)', fontsize=14)
plt.show()
return er_means
def exposure_model_from_vl_breathing(viral_loads):
for vl in tqdm(viral_loads):
exposure_mc = mc.ExposureModel(
concentration_model=mc.ConcentrationModel(
room=models.Room(volume=100, humidity=0.5),
ventilation=models.AirChange(
active=models.SpecificInterval(((0, 24),)),
air_exch=0.25,
),
infected=mc.InfectedPopulation(
number=1,
virus=models.Virus(
viral_load_in_sputum=10**vl,
infectious_dose=50.,
),
presence=mc.SpecificInterval(((0, 2),)),
mask=models.Mask.types["No mask"],
activity=activity_distributions['Seated'],
expiration=models.Expiration.types['Breathing'],
),
),
exposed=mc.Population(
number=14,
presence=mc.SpecificInterval(((0, 2),)),
activity=models.Activity.types['Seated'],
mask=models.Mask.types["No mask"],
),
)
exposure_model = exposure_mc.build_model(size=SAMPLE_SIZE)
# divide by 2 to have in 30min (half an hour)
emission_rate = exposure_model.concentration_model.infected.emission_rate_when_present(1.0) / 2
er_means.append(np.mean(emission_rate))
er_medians.append(np.median(emission_rate))
lower_percentiles.append(np.quantile(emission_rate, 0.01))
upper_percentiles.append(np.quantile(emission_rate, 0.99))
# divide by 2 to have in 30min (half an hour)
coleman_etal_er_breathing_2 = [x/2 for x in coleman_etal_er_breathing]
milton_er_2 = [x/2 for x in milton_er]
yann_er_2 = [x/2 for x in yann_er]
ax.plot(viral_loads, er_means)
ax.fill_between(viral_loads, lower_percentiles,
upper_percentiles, alpha=0.2)
ax.set_yscale('log')
############# Coleman #############
plt.scatter(coleman_etal_vl_breathing,
coleman_etal_er_breathing_2, marker='x')
x_hull, y_hull = get_enclosure_points(
coleman_etal_vl_breathing, coleman_etal_er_breathing_2)
# plot shape
plt.fill(x_hull, y_hull, '--', c='orange', alpha=0.2)
############# Markers #############
markers = [5, 'd', 4]
############# Milton et al #############
try:
for index, m in enumerate(markers):
plt.scatter(milton_vl[index], milton_er_2[index],
marker=m, color='red')
x_hull, y_hull = get_enclosure_points(milton_vl, milton_er_2)
# plot shape
plt.fill(x_hull, y_hull, '--', c='red', alpha=0.2)
except:
print("No data for Milton et al")
############# Yan et al #############
try:
plt.scatter(yann_vl[0], yann_er_2[0], marker=markers[0], color='green')
plt.scatter(yann_vl[1], yann_er_2[1],
marker=markers[1], color='green', s=50)
plt.scatter(yann_vl[2], yann_er_2[2], marker=markers[2], color='green')
x_hull, y_hull = get_enclosure_points(yann_vl, yann_er_2)
# plot shape
plt.fill(x_hull, y_hull, '--', c='green', alpha=0.2)
except:
print("No data for Yan et al")
############ Legend ############
result_from_model = mlines.Line2D(
[], [], color='blue', marker='_', linestyle='None')
coleman = mlines.Line2D([], [], color='orange',
marker='x', linestyle='None')
milton_mean = mlines.Line2D(
[], [], color='red', marker='d', linestyle='None') # mean
milton_25 = mlines.Line2D(
[], [], color='red', marker=5, linestyle='None') # 25
milton_75 = mlines.Line2D(
[], [], color='red', marker=4, linestyle='None') # 75
yann_mean = mlines.Line2D([], [], color='green',
marker='d', linestyle='None') # mean
yann_25 = mlines.Line2D([], [], color='green',
marker=5, linestyle='None') # 25
yann_75 = mlines.Line2D([], [], color='green',
marker=4, linestyle='None') # 75
title_proxy = Rectangle((0, 0), 0, 0, color='w')
titles = ["$\\bf{CARA \, \\it{(SARS-CoV-2)}:}$", "$\\bf{Coleman \, et \, al. \, \\it{(SARS-CoV-2)}:}$",
"$\\bf{Milton \, et \, al. \,\\it{(Influenza)}:}$", "$\\bf{Yann \, et \, al. \,\\it{(Influenza)}:}$"]
leg = plt.legend([title_proxy, result_from_model, title_proxy, coleman, title_proxy, milton_mean, milton_25, milton_75, title_proxy, yann_mean, yann_25, yann_75],
[titles[0], "Result from model", titles[1], "Dataset", titles[2], "Mean", "25th per.", "75th per.", titles[3], "Mean", "25th per.", "75th per."])
# Move titles to the left
for item, label in zip(leg.legendHandles, leg.texts):
if label._text in titles:
width = item.get_window_extent(fig.canvas.get_renderer()).width
label.set_ha('left')
label.set_position((-3*width, 0))
############ Plot ############
plt.title('Exhaled virions while breathing for 30 min',
fontsize=16, fontweight="bold")
plt.ylabel(
'Aerosol viral load, $\mathrm{vl_{out}}$\n(RNA copies)', fontsize=14)
plt.xticks(ticks=[i for i in range(2, 13)], labels=[
'$10^{' + str(i) + '}$' for i in range(2, 13)])
plt.xlabel('NP viral load, $\mathrm{vl_{in}}$\n(RNA copies)', fontsize=14)
plt.show()
return er_means
def exposure_model_from_vl_breathing_cn(viral_loads):
n_lines = 5
cns = np.linspace(0.01, 0.5, n_lines)
norm = mpl.colors.Normalize(vmin=cns.min(), vmax=cns.max())
cmap = mpl.cm.ScalarMappable(norm=norm, cmap=mpl.cm.Blues)
cmap.set_array([])
for cn in tqdm(cns):
er_means = []
er_medians = []
lower_percentiles = []
upper_percentiles = []
for vl in viral_loads:
exposure_mc = mc.ExposureModel(
concentration_model=mc.ConcentrationModel(
room=models.Room(volume=100, humidity=0.5),
ventilation=models.AirChange(
active=models.SpecificInterval(((0, 24),)),
air_exch=0.25,
),
infected=mc.InfectedPopulation(
number=1,
virus=models.Virus(
viral_load_in_sputum=10**vl,
infectious_dose=50.,
),
presence=mc.SpecificInterval(((0, 2),)),
mask=models.Mask.types["No mask"],
activity=activity_distributions['Seated'],
expiration=models.Expiration.types['Breathing'],
),
),
exposed=mc.Population(
number=14,
presence=mc.SpecificInterval(((0, 2),)),
activity=models.Activity.types['Seated'],
mask=models.Mask.types["No mask"],
),
)
exposure_model = exposure_mc.build_model(size=SAMPLE_SIZE)
# divide by 2 to have in 30min (half an hour)
emission_rate = exposure_model.concentration_model.infected.emission_rate_when_present(cn_B = cn, cn_L = 1.0) / 2
er_means.append(np.mean(emission_rate))
er_medians.append(np.median(emission_rate))
lower_percentiles.append(np.quantile(emission_rate, 0.01))
upper_percentiles.append(np.quantile(emission_rate, 0.99))
# divide by 2 to have in 30min (half an hour)
coleman_etal_er_breathing_2 = [x/2 for x in coleman_etal_er_breathing]
milton_er_2 = [x/2 for x in milton_er]
yann_er_2 = [x/2 for x in yann_er]
ax.plot(viral_loads, er_means, color=cmap.to_rgba(cn), linewidth=1)
#ax.fill_between(viral_loads, lower_percentiles,
# upper_percentiles, alpha=0.2)
fig.colorbar(cmap, ticks=cns)
ax.set_yscale('log')
############# Coleman #############
plt.scatter(coleman_etal_vl_breathing,
coleman_etal_er_breathing_2, marker='x')
x_hull, y_hull = get_enclosure_points(
coleman_etal_vl_breathing, coleman_etal_er_breathing_2)
# plot shape
plt.fill(x_hull, y_hull, '--', c='orange', alpha=0.2)
############# Markers #############
markers = [5, 'd', 4]
############# Milton et al #############
try:
for index, m in enumerate(markers):
plt.scatter(milton_vl[index], milton_er_2[index],
marker=m, color='red')
x_hull, y_hull = get_enclosure_points(milton_vl, milton_er_2)
# plot shape
plt.fill(x_hull, y_hull, '--', c='red', alpha=0.2)
except:
print("No data for Milton et al")
############# Yan et al #############
try:
plt.scatter(yann_vl[0], yann_er_2[0], marker=markers[0], color='green')
plt.scatter(yann_vl[1], yann_er_2[1],
marker=markers[1], color='green', s=50)
plt.scatter(yann_vl[2], yann_er_2[2], marker=markers[2], color='green')
x_hull, y_hull = get_enclosure_points(yann_vl, yann_er_2)
# plot shape
plt.fill(x_hull, y_hull, '--', c='green', alpha=0.2)
except:
print("No data for Yan et al")
############ Legend ############
result_from_model = mlines.Line2D(
[], [], color='blue', marker='_', linestyle='None')
coleman = mlines.Line2D([], [], color='orange',
marker='x', linestyle='None')
milton_mean = mlines.Line2D(
[], [], color='red', marker='d', linestyle='None') # mean
milton_25 = mlines.Line2D(
[], [], color='red', marker=5, linestyle='None') # 25
milton_75 = mlines.Line2D(
[], [], color='red', marker=4, linestyle='None') # 75
yann_mean = mlines.Line2D([], [], color='green',
marker='d', linestyle='None') # mean
yann_25 = mlines.Line2D([], [], color='green',
marker=5, linestyle='None') # 25
yann_75 = mlines.Line2D([], [], color='green',
marker=4, linestyle='None') # 75
title_proxy = Rectangle((0, 0), 0, 0, color='w')
titles = ["$\\bf{CARA \, \\it{(SARS-CoV-2)}:}$", "$\\bf{Coleman \, et \, al. \, \\it{(SARS-CoV-2)}:}$",
"$\\bf{Milton \, et \, al. \,\\it{(Influenza)}:}$", "$\\bf{Yann \, et \, al. \,\\it{(Influenza)}:}$"]
leg = plt.legend([title_proxy, result_from_model, title_proxy, coleman, title_proxy, milton_mean, milton_25, milton_75, title_proxy, yann_mean, yann_25, yann_75],
[titles[0], "Result from model", titles[1], "Dataset", titles[2], "Mean", "25th per.", "75th per.", titles[3], "Mean", "25th per.", "75th per."])
# Move titles to the left
for item, label in zip(leg.legendHandles, leg.texts):
if label._text in titles:
width = item.get_window_extent(fig.canvas.get_renderer()).width
label.set_ha('left')
label.set_position((-3*width, 0))
############ Plot ############
plt.title('Exhaled virions while breathing for 30 min',
fontsize=16, fontweight="bold")
plt.ylabel(
'Aerosol viral load, $\mathrm{vl_{out}}$\n(RNA copies)', fontsize=14)
plt.xticks(ticks=[i for i in range(2, 13)], labels=[
'$10^{' + str(i) + '}$' for i in range(2, 13)])
plt.xlabel('NP viral load, $\mathrm{vl_{in}}$\n(RNA copies)', fontsize=14)
plt.show()
return er_means
######### Auxiliar functions #########
def get_enclosure_points(x_coordinates, y_coordinates):
df = pd.DataFrame({'x': x_coordinates, 'y': y_coordinates})
points = df[['x', 'y']].values
# get convex hull
hull = ConvexHull(points)
# get x and y coordinates
# repeat last point to close the polygon
x_hull = np.append(points[hull.vertices, 0],
points[hull.vertices, 0][0])
y_hull = np.append(points[hull.vertices, 1],
points[hull.vertices, 1][0])
return x_hull, y_hull
# # Milton
# boxes = [
# {
# 'label': "Milton data",
# 'whislo': 0, # Bottom whisker position
# 'q1': 22, # First quartile (25th percentile)
# 'med': 220, # Median (50th percentile)
# 'q3': 1120, # Third quartile (75th percentile)
# 'whishi': 260000, # Top whisker position
# 'fliers': [] # Outliers
# }
# ]
# # `box plot aligned with the viral load value of 5.62325
# ax.bxp(boxes, showfliers=False, positions=[5.62324929])
# # Yan
# boxes = [
# {
# 'whislo': 1424.81, # Bottom whisker position
# 'q1': 8396.78, # First quartile (25th percentile)
# 'med': 45324.6, # Median (50th percentile)
# 'q3': 400054, # Third quartile (75th percentile)
# 'whishi': 88616200, # Top whisker position
# 'fliers': [] # Outliers
# }
# ]
# ax.bxp(boxes, showfliers=False, positions=[9.34786])
# box plot aligned with the viral load value of 9.34786
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