twinks in the generated scenarios

Squashed commits:
[ad950a9] variable renaming and docstring of host_immunity fix

cara/model_scenarios_paper.py

@@ -0,0 +1,264 @@
+from cara import models, data
+from cara.monte_carlo.data import activity_distributions, symptomatic_vl_frequencies, viable_to_RNA_ratio_distribution, infectious_dose_distribution, expiration_distributions, mask_distributions, virus_distributions
+import cara.monte_carlo as mc
+import numpy as np
+from cara.monte_carlo.sampleable import Normal,LogNormal,LogCustomKernel,CustomKernel,Uniform
+from cara.monte_carlo.data import BLOmodel
+import typing
+from cara.apps.calculator.model_generator import build_expiration
+
+######### 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]
+############# 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]
+
+def cn_expiration_distribution(BLO_factors, cn_values):
+    """
+    Returns an Expiration with an aerosol diameter distribution, defined
+    by the BLO factors (a length-3 tuple).
+    The total concentration of aerosols is computed by integrating
+    the distribution between 0.1 and 30 microns - these boundaries are
+    an historical choice based on previous implementations of the model
+    (it limits the influence of the O-mode).
+    """
+    dscan = np.linspace(0.1, 30. ,3000)
+    return mc.Expiration(CustomKernel(dscan,
+                BLOmodel(BLO_factors, cn_values).distribution(dscan),kernel_bandwidth=0.1),
+                BLOmodel(BLO_factors, cn_values).integrate(0.1, 30.))
+
+expiration_BLO_factors = {
+    'Breathing': (1., 0., 0.),
+    'Talking':   (1., 1., 1.),
+    'Singing':   (1., 5., 5.),
+    'Shouting':  (1., 5., 5.),
+}
+
+######### Standard exposure models ###########
+
+def exposure_module(activity: str, expiration: str, mask: str):
+    if mask == 'No mask':
+        exposure_mask = models.Mask.types['No mask']
+    else:
+        exposure_mask = mask_distributions[mask]
+
+    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=virus_distributions['SARS_CoV_2'],
+                presence=mc.SpecificInterval(((0, 2),)),
+                mask=exposure_mask,
+                activity=activity_distributions[activity],
+                expiration=expiration_distributions[expiration],
+                host_immunity=0.,
+            ),
+        ),
+        exposed=mc.Population(
+            number=14,
+            presence=mc.SpecificInterval(((0, 2),)),
+            activity=activity_distributions[activity],
+            mask=exposure_mask,
+            host_immunity=0.,
+        ),
+    )
+    return exposure_mc
+
+######### Exposure model for specific viral load ###########
+def exposure_vl(activity: str, expiration: str, mask: str, vl: float):
+    if mask == 'No mask':
+        exposure_mask = models.Mask.types['No mask']
+    else:
+        exposure_mask = mask_distributions[mask]
+
+    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=mc.SARSCoV2(
+                    viral_load_in_sputum=10**vl,
+                    infectious_dose=infectious_dose_distribution,
+                    viable_to_RNA_ratio=viable_to_RNA_ratio_distribution,
+                    transmissibility_factor=1.,
+                ),
+                presence=mc.SpecificInterval(((0, 2),)),
+                mask=exposure_mask,
+                activity=activity_distributions[activity],
+                expiration=expiration_distributions[expiration],
+                host_immunity=0.,
+            ),
+        ),
+        exposed=mc.Population(
+            number=14,
+            presence=mc.SpecificInterval(((0, 2),)),
+            activity=activity_distributions[activity],
+            mask=exposure_mask,
+            host_immunity=0.,
+        ),
+    )
+    return exposure_mc
+
+######### Exposure model for specific viral load ###########
+def exposure_vl_cn(activity: str, expiration: str, mask: str, vl: float, cn: typing.Tuple[float, float, float]):
+    if mask == 'No mask':
+        exposure_mask = models.Mask.types['No mask']
+    else:
+        exposure_mask = mask_distributions[mask]
+
+    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=infectious_dose_distribution,
+                    viable_to_RNA_ratio=viable_to_RNA_ratio_distribution,
+                    transmissibility_factor=1.,
+                ),
+                presence=mc.SpecificInterval(((0, 2),)),
+                mask=exposure_mask,
+                activity=activity_distributions[activity],
+                expiration=cn_expiration_distribution(expiration_BLO_factors[expiration], cn),
+                host_immunity=0.,
+            ),
+        ),
+        exposed=mc.Population(
+            number=14,
+            presence=mc.SpecificInterval(((0, 2),)),
+            activity=activity_distributions[activity],
+            mask=exposure_mask,
+            host_immunity=0.,
+        ),
+    )
+    return exposure_mc
+
+########## Concentration curves for specific scenarios ###########
+def office_model_no_mask_windows_closed():
+    office_model_no_vent = mc.ExposureModel(
+        concentration_model=mc.ConcentrationModel(
+            room=models.Room(volume=16, humidity=0.3),
+            ventilation=models.MultipleVentilation(
+                (models.AirChange(active=models.PeriodicInterval(period=120, duration=120), air_exch=0.0), 
+                models.AirChange(active=models.PeriodicInterval(period=120, duration=120), air_exch=0.25))),
+            infected=mc.InfectedPopulation(
+                number=1,
+                presence=mc.SpecificInterval(present_times = ((0, 1.5), (2, 3.5), (4.5, 6), (6.5, 8))),
+                virus=virus_distributions['SARS_CoV_2'],
+                mask=models.Mask.types["No mask"],
+                activity=activity_distributions['Light activity'],
+                expiration=build_expiration({'Talking': 0.33, 'Breathing': 0.67}),
+                host_immunity=0.,
+            )
+        ),
+        exposed=mc.Population(
+            number=18,
+            presence=mc.SpecificInterval(present_times = ((0, 1.5), (2, 3.5), (4.5, 6), (6.5, 8))),
+            activity=activity_distributions['Light activity'],
+            mask=models.Mask.types['No mask'],
+            host_immunity=0.,
+        )
+    )
+    return office_model_no_vent
+
+def office_model_no_mask_windows_open_breaks():
+    office_model_no_vent = mc.ExposureModel(
+        concentration_model=mc.ConcentrationModel(
+            room=models.Room(volume=16, humidity=0.3),
+            ventilation = models.MultipleVentilation(
+                ventilations=(
+                    models.SlidingWindow(
+                        active=models.SpecificInterval(present_times=((1.5, 2), (3.5, 4.5), (6, 6.5))),
+                        inside_temp=models.PiecewiseConstant((0., 24.), (293,)),
+                        outside_temp=data.GenevaTemperatures['Jul'],
+                        window_height=1.6, 
+                        opening_length=0.6,
+                    ),
+                    models.AirChange(active=models.PeriodicInterval(period=120, duration=120), air_exch=0.25),
+                )  
+            ),
+            infected=mc.InfectedPopulation(
+                number=1,
+                presence=mc.SpecificInterval(present_times=((0, 1.5), (2, 3.5), (4.5, 6), (6.5, 8))),
+                virus=virus_distributions['SARS_CoV_2'],
+                mask=models.Mask.types["No mask"],
+                activity=activity_distributions['Light activity'],
+                expiration=build_expiration({'Talking': 0.33, 'Breathing': 0.67}),
+                host_immunity=0.,
+            )
+        ),
+        exposed=mc.Population(
+            number=18,
+            presence=mc.SpecificInterval(present_times=((0, 1.5), (2, 3.5), (4.5, 6), (6.5, 8))),
+            activity=activity_distributions['Light activity'],
+            mask=models.Mask.types['No mask'],
+            host_immunity=0.,
+        )
+    )
+    return office_model_no_vent
+
+def office_model_no_mask_windows_open_alltimes():
+    office_model_no_vent = mc.ExposureModel(
+        concentration_model=mc.ConcentrationModel(
+            room=models.Room(volume=16, humidity=0.3),
+            ventilation=models.MultipleVentilation(
+                ventilations=(
+                    models.SlidingWindow(
+                        active=models.PeriodicInterval(period=120, duration=120),
+                        inside_temp=models.PiecewiseConstant((0., 24.), (293,)),
+                        outside_temp=data.GenevaTemperatures['Jul'],
+                        window_height=1.6, opening_length=0.6,
+                    ),
+                    models.AirChange(active=models.PeriodicInterval(period=120, duration=120), air_exch=0.25),
+                )
+            ),
+            infected=mc.InfectedPopulation(
+                number=1,
+                presence=mc.SpecificInterval(present_times=((0, 1.5), (2, 3.5), (4.5, 6), (6.5, 8))),
+                virus=virus_distributions['SARS_CoV_2'],
+                mask=models.Mask.types["No mask"],
+                activity=activity_distributions['Light activity'],
+                expiration=build_expiration({'Talking': 0.33, 'Breathing': 0.67}),
+                host_immunity=0.,
+            )
+        ),
+        exposed=mc.Population(
+            number=18,
+            presence=mc.SpecificInterval(present_times=((0, 1.5), (2, 3.5), (4.5, 6), (6.5, 8))),
+            activity=activity_distributions['Light activity'],
+            mask=models.Mask.types['No mask'],
+            host_immunity=0.,
+        )
+    )
+    return office_model_no_vent

cara/plot_output.py

@@ -0,0 +1,64 @@
+""" Title: COVID Airborne Risk Assessment
+Author: <author(s) names>
+Date: <date>
+Code version: <code version>
+Availability: <where it's located> """
+
+from cara.models import ExposureModel, InfectedPopulation
+from cara import model_scenarios_paper
+from cara.results_paper import *
+from cara.monte_carlo.data import symptomatic_vl_frequencies
+from itertools import product
+from dataclasses import dataclass
+
+# Exhaled virions while talking, seated #
+#print('\n<<<<<<<<<<< Vlout for Talking, seated >>>>>>>>>>>')
+#exposure_model_from_vl(activity='Seated', expiration='Talking', mask='No mask')
+
+# Exhaled virions while breathing, seated #
+#print('\n<<<<<<<<<<< Vlout for Breathing, seated >>>>>>>>>>>')
+#exposure_model_from_vl(activity='Seated', expiration='Breathing', mask='No mask')
+
+# Exhaled virions while breathing, light activity #
+#print('\n<<<<<<<<<<< Vlout for Shouting, light activity >>>>>>>>>>>')
+#exposure_model_from_vl(activity='Light activity', expiration='Shouting', mask='No mask')
+
+# Exhaled virions while talking according to BLO model, seated #
+#print('\n<<<<<<<<<<< Vlout for Talking, seated with chosen Cn,L >>>>>>>>>>>')
+#exposure_model_from_vl_cn(activity='Seated', expiration='Talking', mask='No mask')
+#print('\n')
+
+# Exhaled virions while breathing according to BLO model, seated #
+#print('\n<<<<<<<<<<< Vlout for Breathing, seated with chosen Cn,B >>>>>>>>>>>')
+#exposure_model_from_vl_cn(activity='Seated', expiration='Breathing', mask='No mask')
+#print('\n')
+
+############ Plots with viral loads and emission rates + statistical data ############
+#present_vl_er_histograms(activity='Seated', mask='No mask')
+#present_vl_er_histograms(activity='Light activity', mask='No mask')
+#present_vl_er_histograms(activity='Heavy exercise', mask='No mask')
+
+############ CDFs for comparing the ER-Values in different scenarios ############
+#generate_cdf_curves()
+
+############ Deposition Fraction Graph ############
+#print('\n<<<<<<<<<<< Deposition Fraction for Breathing, seated >>>>>>>>>>>') 
+#calculate_deposition_factor()
+
+############ Comparison between concentration curves ############ 
+# compare_concentration_curves(models = [office_model_no_mask_windows_closed(), office_model_no_mask_windows_open_breaks(), office_model_no_mask_windows_open_alltimes()],
+#                              labels = ['Windows closed', 'Window open during breaks', 'Window open at all times'])
+
+############ Emission Rate Violin plot ############ 
+#compare_viruses_vr()
+
+############ Probability of infection vs Viral load ############ 
+#plot_pi_vs_viral_load(activity='Seated', expiration='Talking', mask='No mask')
+
+############ Composite plots vs Viral load ############
+# composite_plot_pi_vs_viral_load(models = [office_model_no_mask_windows_closed(), office_model_no_mask_windows_open_breaks(), office_model_no_mask_windows_open_alltimes()],
+#                                 labels = ['Windows closed', 'Window open during breaks', 'Window open at all times'],
+#                                 show_lines = True)
+
+############ Used for testing ############
+plot_hourly_temperatures()

cara/results_paper.py

@@ -0,0 +1,940 @@
+from tqdm import tqdm
+from matplotlib.patches import Rectangle, Patch
+from scipy.spatial import ConvexHull
+from model_scenarios_paper import *
+from cara.monte_carlo.data import symptomatic_vl_frequencies
+import cara.monte_carlo as mc
+import numpy as np
+import matplotlib.pyplot as plt
+import pandas as pd
+import matplotlib.lines as mlines
+import matplotlib.patches as patches
+import matplotlib as mpl
+from scipy.interpolate import make_interp_spline, BSpline
+
+######### Plot material #########
+np.random.seed(2000)
+SAMPLE_SIZE = 250000
+viral_loads = np.linspace(2, 12, 600)
+
+############# Markers (for legend) #############
+markers = [5, 'd', 4]
+
+
+def emission_rate_when_present(exposure_model: mc.ExposureModel):
+    aerosols = exposure_model.concentration_model.infected.expiration.aerosols(
+        exposure_model.concentration_model.infected.mask).mean()
+    exhalation_rate = exposure_model.concentration_model.infected.activity.exhalation_rate
+    viral_load_in_sputum = exposure_model.concentration_model.infected.virus.viral_load_in_sputum
+    return (viral_load_in_sputum * exhalation_rate * 10 ** 6 * aerosols) * exposure_model.concentration_model.infected.number
+
+
+def _normed_exposure_between_bounds(model: mc.ExposureModel, time1: float, time2: float):
+    """The number of virions per meter^3 between any two times, normalized 
+    by the emission rate of the infected population"""
+    for start, stop in model.exposed.presence.boundaries():
+        if start > time2:
+            normed_exposure = 0.
+            break
+        elif time2 <= stop:
+            normed_exposure = model.concentration_model.normed_integrated_concentration(
+                time1, time2)
+            break
+        else:
+            normed_exposure = model.concentration_model.normed_integrated_concentration(
+                time1, time2)
+    return normed_exposure
+
+
+def exposure_between_bounds(model: mc.ExposureModel, time1: float, time2: float):
+    """The number of virions per meter^3 between any two times."""
+    return (_normed_exposure_between_bounds(model, time1, time2) *
+            emission_rate_when_present(model))
+
+######### Exhaled virions from exposure models #########
+
+
+def exposure_model_from_vl(activity, expiration, mask):
+    fig = plt.figure()
+    ax = fig.add_subplot(1, 1, 1)
+
+    er_means = []
+    er_means_1h = []
+    lower_percentiles = []
+    upper_percentiles = []
+
+    for vl in tqdm(viral_loads):
+        exposure_mc = exposure_vl(activity, expiration, mask, vl)
+        exposure_model = exposure_mc.build_model(size=SAMPLE_SIZE)
+
+        if expiration == 'Breathing':
+            # divide by 2 to have in 30min (half an hour)
+            emission_rate = emission_rate_when_present(exposure_model) / 2
+        elif expiration == 'Talking':
+            # divide by 4 to have in 15min (quarter of an hour)
+            emission_rate = emission_rate_when_present(exposure_model) / 4
+        elif expiration == 'Shouting':
+            emission_rate = emission_rate_when_present(exposure_model)
+
+        er_means.append(np.mean(emission_rate))
+        lower_percentiles.append(np.quantile(emission_rate, 0.01))
+        upper_percentiles.append(np.quantile(emission_rate, 0.99))
+        emission_rate_1h = emission_rate_when_present(exposure_model)
+        er_means_1h.append(np.mean(emission_rate_1h))
+
+    if expiration == 'Breathing':
+        # 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]
+
+        ratio = np.mean(10**viral_loads / er_means)
+        ratio_1h = np.mean(10**viral_loads / er_means_1h)
+        print('Mean swab-to-aersol vl ratio in 30min:')
+        print(format(ratio, "5.1e"))
+        print('Mean swab-to-aersol vl ratio emission rate per hour:')
+        print(format(ratio_1h, "5.1e"))
+
+        ############# Coleman #############
+        scatter_coleman_data(coleman_etal_vl_breathing,
+                             coleman_etal_er_breathing_2)
+
+        ############# Milton et al #############
+        scatter_milton_data(milton_vl, milton_er_2)
+
+        ############# Yan et al #############
+        scatter_yann_data(yann_vl, yann_er_2)
+
+        ############ Legend ############
+        build_breathing_legend(fig)
+
+    elif expiration == 'Talking':
+        # 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]
+
+        ratio = np.mean(10**viral_loads / er_means)
+        ratio_1h = np.mean(10**viral_loads / er_means_1h)
+        print('Mean swab-to-aersol vl ratio in 30min:')
+        print(format(ratio, "5.1e"))
+        print('Mean swab-to-aersol vl ratio emission rate per hour:')
+        print(format(ratio_1h, "5.1e"))
+
+        ############# Coleman #############
+        scatter_coleman_data(coleman_etal_vl_talking,
+                             coleman_etal_er_talking_2)
+
+        ############ Legend ############
+        build_talking_legend(fig)
+
+    elif expiration == 'Shouting':
+        ratio_1h = np.mean(10**viral_loads / er_means_1h)
+        print('Mean swab-to-aersol vl ratio emission rate per hour:')
+        print(format(ratio_1h, "5.1e"))
+
+    ax.plot(viral_loads, er_means)
+    ax.fill_between(viral_loads, lower_percentiles,
+                    upper_percentiles, alpha=0.2)
+    ax.set_yscale('log')
+
+    ############ Plot ############
+    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()
+
+
+""" Variation according to the BLO model """
+
+
+def exposure_model_from_vl_cn(activity, expiration, mask):
+    fig = plt.figure()
+    ax = fig.add_subplot(1, 1, 1)
+
+    n_lines = 30
+    cns = np.linspace(0.01, 0.5, n_lines)
+
+    cmap = define_colormap(cns)
+
+    for cn in tqdm(cns):
+        er_means = np.array([])
+        for vl in tqdm(viral_loads):
+            exposure_mc = exposure_vl_cn(
+                activity, expiration, mask, vl, (cn, 0.2, 0.0010008))
+            exposure_model = exposure_mc.build_model(size=SAMPLE_SIZE)
+            # divide by 2 to have in 30min (half an hour)
+            emission_rate = emission_rate_when_present(exposure_model) / 2
+            er_means = np.append(er_means, np.mean(emission_rate))
+        # 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, alpha=0.75), linewidth=0.5)
+
+    # The dashed line for the chosen Cn,B
+    er_means = np.array([])
+    for vl in viral_loads:
+        exposure_mc = exposure_vl_cn(
+            activity, expiration, mask, vl, (0.06, 0.2, 0.0010008))
+        exposure_model = exposure_mc.build_model(size=SAMPLE_SIZE)
+        # divide by 2 to have in 30min (half an hour)
+        emission_rate = emission_rate_when_present(exposure_model) / 2
+        er_means = np.append(er_means, np.mean(emission_rate))
+    ax.plot(viral_loads, er_means, color=cmap.to_rgba(
+        cn, alpha=0.75), linewidth=1, ls='--')
+
+    plt.text(viral_loads[int(len(viral_loads)*0.9)], 10**4.2, r"$\mathbf{c_{n,B}=0.06}$", color=cmap.to_rgba(cn), fontsize=12) if activity == 'Breathing' else plt.text(
+        viral_loads[int(len(viral_loads)*0.93)], 10**5.5, r"$\mathbf{c_{n,L}=0.2}$", color=cmap.to_rgba(cn), fontsize=12)
+
+    cmap = fig.colorbar(cmap, ticks=[0.01, 0.1, 0.25, 0.5])
+    cmap.set_label(
+        label='Particle emission concentration, ${c_{n,B}}$', fontsize=12)
+    ax.set_yscale('log')
+
+    ############# Coleman #############
+    scatter_coleman_data(coleman_etal_vl_breathing,
+                         coleman_etal_er_breathing_2)
+
+    ############# Milton et al #############
+    scatter_milton_data(milton_vl, milton_er_2)
+
+    ############# Yan et al #############
+    scatter_yann_data(yann_vl, yann_er_2)
+
+    ############ Legend ############
+    build_breathing_legend(fig)
+
+    ############ Plot ############
+    plt.title('',
+              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()
+
+
+############ Plots with viral loads and emission rates ############
+############ Statistical Data ############
+
+
+def get_statistical_data(activity: str, mask: str):
+
+    log10_ers = {}
+    for expiration in ('Breathing', 'Talking', 'Shouting'):
+        exposure_mc = exposure_module(activity, expiration, mask)
+        exposure_model = exposure_mc.build_model(size=SAMPLE_SIZE)
+        emission_rate = emission_rate_when_present(exposure_model)
+        log10_ers[expiration] = [np.log10(er) for er in emission_rate]
+        print('\n<<<<<<<<<<< ' + expiration + ' model statistics >>>>>>>>>>>')
+        print_er_info(emission_rate, log10_ers[expiration])
+
+    viral_load_in_sputum = exposure_model.concentration_model.infected.virus.viral_load_in_sputum
+    return viral_load_in_sputum, log10_ers['Breathing'], log10_ers['Talking'], log10_ers['Shouting']
+
+
+def present_vl_er_histograms(activity: str, mask: str):
+    viral_load_in_sputum, breathing_er, speaking_er, shouting_er = get_statistical_data(
+        activity, mask)
+
+    fig, axs = plt.subplots(1, 2, sharex=False, sharey=False)
+    fig.set_figheight(5)
+    fig.set_figwidth(10)
+    plt.tight_layout()
+    plt.subplots_adjust(wspace=0.2)
+    plt.subplots_adjust(top=0.9)
+    plt.subplots_adjust(bottom=0.15)
+
+    viral_loads = [np.log10(vl) for vl in viral_load_in_sputum]
+
+    axs[0].hist(viral_loads, bins=300, color='lightgrey')
+    axs[0].set_xlabel('vl$_{\mathrm{in}}$ (log$_{10}$ RNA copies mL$^{-1}$)')
+
+    mean = np.mean(viral_loads)
+    axs[0].vlines(x=(mean), ymin=0, ymax=axs[0].get_ylim()[
+                  1], colors=('grey'), linestyles=('dashed'))
+
+    breathing_mean_er = np.mean(breathing_er)
+    speaking_mean_er = np.mean(speaking_er)
+    shouting_mean_er = np.mean(shouting_er)
+
+    axs[1].hist(breathing_er, bins=300, color='lightsteelblue')
+    axs[1].hist(speaking_er, bins=300, color='wheat')
+    axs[1].hist(shouting_er, bins=300, color='darkseagreen')
+    axs[1].set_xlabel('vR (log$_{10}$ virions h$^{-1}$)')
+
+    axs[1].vlines(x=(breathing_mean_er, speaking_mean_er, shouting_mean_er), ymin=0, ymax=axs[1].get_ylim()[1], colors=(
+        'cornflowerblue', 'goldenrod', 'olivedrab'), alpha=(0.75, 0.75, 0.75), linestyles=('dashed', 'dashed', 'dashed'))
+
+    labels = [Patch([], [], color=color, label=label)
+              for color, label in zip(['lightgrey', 'lightsteelblue', 'wheat', 'darkseagreen'],
+                                      ['Viral Load', 'Breathing', 'Speaking', 'Shouting'])]
+    labels.append(mlines.Line2D([], [], color='black',
+                                marker='', linestyle='dashed', label='Mean'))
+
+    for x in (0, 1):
+        axs[x].set_yticklabels([])
+        axs[x].set_yticks([])
+
+    plt.legend(handles=labels, loc='upper left', bbox_to_anchor=(1, 1))
+    plt.tight_layout()
+    plt.show()
+
+############ CDFs for comparing the QR-Values in different scenarios ############
+
+
+def generate_cdf_curves():
+    fig, axs = plt.subplots(3, 1, sharex='all')
+
+    ############ Breathing models ############
+    br_seated = exposure_module('Seated', 'Breathing', 'No mask')
+    br_seated_model = br_seated.build_model(size=SAMPLE_SIZE)
+
+    br_light_activity = exposure_module(
+        'Light activity', 'Breathing', 'No mask')
+    br_light_activity_model = br_light_activity.build_model(size=SAMPLE_SIZE)
+
+    br_heavy_exercise = exposure_module(
+        'Heavy exercise', 'Breathing', 'No mask')
+    br_heavy_exercise_model = br_heavy_exercise.build_model(size=SAMPLE_SIZE)
+
+    ############ Speaking models ############
+    sp_seated = exposure_module('Seated', 'Talking', 'No mask')
+    sp_seated_model = sp_seated.build_model(size=SAMPLE_SIZE)
+
+    sp_light_activity = exposure_module('Light activity', 'Talking', 'No mask')
+    sp_light_activity_model = sp_light_activity.build_model(size=SAMPLE_SIZE)
+
+    sp_heavy_exercise = exposure_module('Heavy exercise', 'Talking', 'No mask')
+    sp_heavy_exercise_model = sp_heavy_exercise.build_model(size=SAMPLE_SIZE)
+
+    ############ Shouting models ############
+    sh_seated = exposure_module('Seated', 'Shouting', 'No mask')
+    sh_seated_model = sh_seated.build_model(size=SAMPLE_SIZE)
+
+    sh_light_activity = exposure_module(
+        'Light activity', 'Shouting', 'No mask')
+    sh_light_activity_model = sh_light_activity.build_model(size=SAMPLE_SIZE)
+
+    sh_heavy_exercise = exposure_module(
+        'Heavy exercise', 'Shouting', 'No mask')
+    sh_heavy_exercise_model = sh_heavy_exercise.build_model(size=SAMPLE_SIZE)
+
+    er_values = [np.log10(emission_rate_when_present(scenario)) for scenario in (br_seated_model, br_light_activity_model,
+                                                                                 br_heavy_exercise_model, sp_seated_model,
+                                                                                 sp_light_activity_model, sp_heavy_exercise_model,
+                                                                                 sh_seated_model, sh_light_activity_model,
+                                                                                 sh_heavy_exercise_model)]
+
+    # Colors can be changed here
+    colors_breathing = ['lightsteelblue', 'cornflowerblue', 'royalblue']
+    colors_speaking = ['wheat', 'tan', 'orange']
+    colors_shouting = ['palegreen', 'darkseagreen', 'forestgreen']
+    colors = [colors_breathing, colors_speaking, colors_shouting]
+
+    breathing_rates = ['Seated', 'Light activity', 'Heavy activity']
+    activities = ['Breathing', 'Speaking', 'Shouting']
+    lines_breathing = [mlines.Line2D([], [], color=color, markersize=15, label=label)
+                       for color, label in zip(colors_breathing, breathing_rates)]
+    lines_speaking = [mlines.Line2D([], [], color=color, markersize=15, label=label)
+                      for color, label in zip(colors_speaking, breathing_rates)]
+    lines_shouting = [mlines.Line2D([], [], color=color, markersize=15, label=label)
+                      for color, label in zip(colors_shouting, breathing_rates)]
+    lines = [lines_breathing, lines_speaking, lines_shouting]
+
+    for i in range(3):
+        axs[i].hist(er_values[3 * i:3 * (i + 1)], bins=2000,
+                    histtype='step', cumulative=True, range=(-7, 6), color=colors[i])
+        axs[i].set_xlim(-6, 6)
+        axs[i].set_yticks([0, SAMPLE_SIZE / 2, SAMPLE_SIZE])
+        axs[i].set_yticklabels(['0.0', '0.5', '1.0'])
+        axs[i].yaxis.set_label_position("right")
+        axs[i].set_ylabel(activities[i], fontsize=14)
+        axs[i].grid(linestyle='--')
+        axs[i].legend(handles=lines[i], loc='upper left')
+
+    plt.xlabel('$\mathrm{vR}$', fontsize=16)
+    tick_positions = np.arange(-6, 6, 2)
+    plt.xticks(ticks=tick_positions, labels=[
+               '$\;10^{' + str(i) + '}$' for i in tick_positions])
+
+    fig.text(0.02, 0.5, 'Cumulative Distribution Function',
+             va='center', rotation='vertical', fontsize=14)
+    fig.set_figheight(8)
+    fig.set_figwidth(5)
+    plt.show()
+
+############ Deposition Fraction Graph #############
+
+
+def calculate_deposition_factor():
+
+    fig = plt.figure()
+    ax = fig.add_subplot(1, 1, 1)
+
+    diameters = np.linspace(0.001, 0.01, 1000)  # particle diameter (μm)
+    diameters = np.append(diameters, np.linspace(0.01, 0.1, 1000))
+    diameters = np.append(diameters, np.linspace(0.1, 1., 1000))
+    diameters = np.append(diameters, np.linspace(1., 10., 1000))
+    diameters = np.append(diameters, np.linspace(10, 100, 1000))
+
+    fractions_et = []
+    fractions_tb = []
+    fractions_al = []
+    fractions_df = []
+    for d in diameters:
+
+        IF = 1 - 0.5 * (1 - (1 / (1 + (0.00076*(d**2.8)))))
+        DF_et = IF * (
+            (1 / (1 + np.exp(6.84 + 1.183 * np.log(d)))) +
+            (1 / (1 + np.exp(0.924 - 1.885 * np.log(d))))
+        )
+        fractions_et.append(DF_et)
+
+        DF_tb = (0.00352/d) * (np.exp(-0.234*((np.log(d) + 3.40)**2)
+                                      ) + (63.9 * np.exp(-0.819*((np.log(d) - 1.61)**2))))
+        fractions_tb.append(DF_tb)
+
+        DF_al = (0.0155/d) * (np.exp(-0.416*((np.log(d) + 2.84)**2)) +
+                              (19.11*np.exp(-0.482 * ((np.log(d) - 1.362)**2))))
+        fractions_al.append(DF_al)
+
+        DF = IF * (0.0587 + (0.911/(1 + np.exp(4.77 + 1.485 * np.log(d)))
+                             ) + (0.943/(1 + np.exp(0.508 - 2.58 * np.log(d)))))
+        fractions_df.append(DF)
+
+    ax.plot(diameters, fractions_df, label='Total Deposition', color='k')
+    ax.plot(diameters, fractions_et, label='Extrathoracic',
+            ls='-.', lw=0.9, color='grey')
+    ax.plot(diameters, fractions_tb, label='Tracheobronchial',
+            ls='--', lw=0.9, color='darkgray')
+    ax.plot(diameters, fractions_al, label='Alveolar',
+            ls=(0, (1, 1)), lw=0.9, color='darkgray')
+
+    ax.grid(linestyle='--')
+    ax.set_xscale('log')
+    ax.margins(x=0, y=0)
+    plt.legend(bbox_to_anchor=(1.04, 1), loc="upper left")
+
+    y_ticks = [0., 0.2, 0.4, 0.6, 0.8, 1]
+    x_ticks = [0.001, 0.01, 0.1, 1, 10, 100]
+    plt.yticks(ticks=y_ticks, labels=[
+               str(i) for i in y_ticks])
+    plt.xticks(ticks=x_ticks, labels=[
+               str(i) for i in x_ticks])
+    plt.xlabel('Particle diameter (μm)', fontsize=14)
+    plt.ylabel('Deposition fraction\nf$_{dep}$', fontsize=14)
+
+    fig.set_figwidth(10)
+    plt.tight_layout()
+    plt.show()
+
+############ Compare concentration curves ############
+
+
+def compare_concentration_curves(models, labels):
+
+    exp_models = [model.build_model(size=SAMPLE_SIZE) for model in models]
+
+    colors = ['tomato', 'lightskyblue', 'limegreen',
+              '#1f77b4', 'seagreen', 'lightskyblue', 'deepskyblue']
+
+    start = min(min(model.concentration_model.infected.presence.transition_times())
+                for model in exp_models)
+    stop = max(max(model.concentration_model.infected.presence.transition_times())
+               for model in exp_models)
+
+    TIMESTEP = 0.01
+    times = np.arange(start, stop, TIMESTEP)
+
+    concentrations = [[np.mean(model.concentration_model.concentration(
+        t)) for t in times] for model in exp_models]
+    fig, ax = plt.subplots()
+    for c, label, color in zip(concentrations, labels, colors):
+        ax.plot(times, c, label=label, color=color)
+
+    ax.legend(loc='upper left')
+    ax.set_ylim(ax.get_ylim()[0], ax.get_ylim()[1] * 1.2)
+    ax.spines["right"].set_visible(False)
+
+    cumulative_doses = [np.cumsum([
+        np.array(exposure_between_bounds(model,
+            float(time1), float(time2))).mean()
+        for time1, time2 in zip(times[:-1], times[1:])
+    ]) for model in exp_models]
+
+    plt.xlabel("Exposure time ($h$)", fontsize=14)
+    plt.ylabel("Mean concentration (virions m$^{-3}$)", fontsize=14)
+
+    ax1 = ax.twinx()
+    for qd, label, color in zip(cumulative_doses, labels, colors):
+        ax1.plot(times[:-1], qd, label='qD - ' + label,
+                 color=color, linestyle='dotted')
+    ax1.spines["right"].set_linestyle("--")
+    ax1.spines["right"].set_linestyle((0, (1, 5)))
+    ax1.set_ylabel('Mean cumulative dose (virions)', fontsize=14)
+    ax1.set_ylim(ax1.get_ylim()[0], ax1.get_ylim()[1] * 1.2)
+
+    plt.show()
+
+
+def compare_viruses_vr():
+
+    # Represented as tuples of three numbers on the interval [0, 1] (e.g. (1, 0, 0)) (R, G, B)
+    colors = [(0., 0.5, 0.5), (0, 0, 0.5), (0.5, 0, 0), (0., 0.78, 0.)]
+    colors_violin=['lightsteelblue', 'wheat', 'darkseagreen']
+    colors_violin_lines = ['royalblue', 'orange', 'forestgreen']
+
+    # The colors of the borders surrounding the violin plots
+    border_colors = [(0, 0, 0), (0, 0, 0), (0, 0, 0)]
+    
+    whisker_width = 0.8
+    positions = [1, 2, 3, 12]
+
+    exposure_modules = [exposure_module('Light activity', expiration, 'No mask').build_model(size=SAMPLE_SIZE) for expiration in ('Breathing', 'Talking', 'Shouting')]
+    
+    vrs = [np.log10(emission_rate_when_present(module)) for module in exposure_modules]
+
+    fig, ax = plt.subplots()
+    ax.set_xlim((0, 11))
+
+    parts = ax.violinplot(vrs, quantiles=[(0.05, 0.95) for _ in vrs], showextrema=False)
+    means = [np.log10(np.mean(10 ** vr)) for vr in vrs]
+    ax.hlines(y=means,
+                xmin=[pos - whisker_width / 2 for pos in positions[:3]],
+                xmax=[pos + whisker_width / 2 for pos in positions[:3]],
+                colors=colors_violin_lines,
+                alpha=0.8)
+
+
+    for pc, color, bc in zip(parts['bodies'], colors_violin, border_colors):
+        pc.set_facecolor(color)
+        pc.set_edgecolor(bc)
+        pc.set_alpha(0.5)
+    parts['cquantiles'].set_color([c for c in colors_violin_lines[:3] for _ in range(2)])
+    parts['cquantiles'].set_alpha(1)
+
+    positions=np.linspace(4.5, 11.5, 20)
+
+    ######### SARS-CoV #########
+    lower_bound = [418]
+    higher_bound = [4176]
+
+    for i in range(len(lower_bound)):
+        data = np.random.uniform(lower_bound[i], higher_bound[i], size=200000)
+        ax.boxplot(np.log10(data), positions=[positions[i]], medianprops=dict(color=colors[3] + (0.5,)),
+                   whiskerprops=dict(color=colors[3] + (0.5,)), boxprops=dict(color=colors[3] + (0.5,)))
+
+    ######### SARS-CoV-2 #########
+    lower_bound = [216, 216, 518, 648, 878, 893, 1670, 1872, 1915, 2002, 2002, 2189, 3341, 9835, 13968, 60667]
+    higher_bound = [2160, 2160, 5184, 6480, 8784, 8928, 16704, 18720, 19152, 20016, 20016, 21888, 33408, 98352, 139680, 606672]
+    
+    for i in range(len(lower_bound)):
+        data = np.random.uniform(lower_bound[i], higher_bound[i], size=200000)
+        ax.boxplot(np.log10(data), positions=[positions[i+1]], medianprops=dict(color=colors[0]+ (0.5,)),
+                   whiskerprops=dict(color=colors[0]+ (0.5,)), boxprops=dict(color=colors[0]+ (0.5,)))
+
+    ######### Measles #########
+    lower_bound = [259, 8640, 39816, 124416]
+    higher_bound = [2592, 86400, 398160, 1244160]
+    
+    for i in range(len(lower_bound)):
+        data = np.random.uniform(lower_bound[i], higher_bound[i], size=200000)
+        ax.boxplot(np.log10(data), positions=[positions[i+5]], medianprops=dict(color=colors[1]+ (0.5,)),
+                   whiskerprops=dict(color=colors[1]+ (0.5,)), boxprops=dict(color=colors[1]+ (0.5,)))
+
+    ######### Influenza #########
+    lower_bound = [2, 114, 1138]
+    higher_bound = [16, 1145, 11376]
+    
+    for i in range(len(lower_bound)):
+        data = np.random.uniform(lower_bound[i], higher_bound[i], size=200000)
+        ax.boxplot(np.log10(data), positions=[positions[i+12]], medianprops=dict(color=colors[2]+ (0.5,)),
+                   whiskerprops=dict(color=colors[2]+ (0.5,)), boxprops=dict(color=colors[2]+ (0.5,)))
+
+    ######### Rhinovirus #########
+    lower_bound = [45]
+    higher_bound = [446]
+    
+    for i in range(len(lower_bound)):
+        data = np.random.uniform(lower_bound[i], higher_bound[i], size=200000)
+        ax.boxplot(np.log10(data), positions=[positions[i+8]], medianprops=dict(color=(0.5, 0.5, 0.5, 0.5, )),
+                   whiskerprops=dict(color=(0.5, 0.5, 0.5, 0.5,)), boxprops=dict(color=(0.5, 0.5, 0.5, 0.5,)))
+    
+    handles = [patches.Patch(edgecolor=c, facecolor='none', label=l)
+               for c, l in zip([p + (0.5,) for p in [(0., 0.78, 0.), (0., 0.5, 0.5), (0, 0, 0.5), (0.5, 0, 0), (0.5, 0.5, 0.5)]],
+                               ('SARS-CoV', 'SARS-CoV-2', 'Measles', 'Influenza', 'Rhinovirus'))]
+    boxplot_legend = plt.legend(handles=handles, loc='lower right')
+
+    ax.annotate("Bus ride", xy=(6, np.log10(5500)), color='k', fontsize=8,
+                xycoords='data',
+                xytext=(-50, 50), textcoords='offset points',
+                arrowprops=dict(arrowstyle="->",
+                                connectionstyle="arc3,rad=-0.2", color='lightgrey'))
+
+    ax.annotate("S V Chorale", xy=(10, np.log10(110000)), color='k', fontsize=8,
+                xycoords='data',
+                xytext=(-50, 40), textcoords='offset points',
+                arrowprops=dict(arrowstyle="->",
+                                connectionstyle="arc3,rad=-0.2", color='lightgrey'))
+    
+    handles = [patches.Patch(color=c, label=l) for c, l in zip([p  for p in colors_violin], ('Breathing', 'Speaking', 'Shouting'))]
+    plt.legend(handles=handles, loc='lower left', bbox_to_anchor=(0.12, 0.))
+    plt.gca().add_artist(boxplot_legend)
+
+    ax.hlines(y=[-2, 0, 2, 4, 6], xmin=ax.get_xlim()[0], xmax=ax.get_xlim()[1], colors=(0.8, 0.8, 0.8), linestyles='--', alpha=0.3)
+    ax.vlines(x=4, ymin=ax.get_ylim()[0], ymax=ax.get_ylim()[1], colors=(0.8, 0.8, 0.8))
+    ax.set_yticks([i for i in range(-4, 7, 2)])
+    ax.set_yticklabels(['$10^{' + str(i) + '}$' for i in range(-4, 7, 2)])
+    ax.set_xticks([2, 7])
+    ax.set_xticklabels(['SARS-CoV-2\n(model)', 'Literature Data\n(recorded outbreaks) '])
+    ax.set_ylabel('Emission rate (virions h$^{-1}$)', fontsize=12)
+
+    plt.tight_layout()
+    plt.show()
+
+
+######### Probability of infection vs Viral load #########
+def plot_pi_vs_viral_load(activity, expiration, mask):
+    fig = plt.figure()
+    ax = fig.add_subplot(1, 1, 1)
+
+    pi_means = []
+    lower_percentiles = []
+    upper_percentiles = []
+
+    for vl in tqdm(viral_loads):
+        exposure_mc = exposure_vl(activity, expiration, mask, vl)
+        exposure_model = exposure_mc.build_model(size=SAMPLE_SIZE)
+
+        pi = exposure_model.infection_probability()/100
+        
+        pi_means.append(np.mean(pi))
+        lower_percentiles.append(np.quantile(pi, 0.01))
+        upper_percentiles.append(np.quantile(pi, 0.99))
+
+    ax.plot(viral_loads, pi_means, label='Baseline')
+    ax.fill_between(viral_loads, lower_percentiles,
+                    upper_percentiles, alpha=0.2)
+
+    ############ Plot ############
+    plt.ylabel('Probability of infection', 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)
+
+    # add vertical lines for the critical viral loads for which pi= 5 or 95
+    left_index, right_index = 0, 0
+    for i, pi in enumerate(pi_means):
+        if pi > 0.05:
+            left_index = i
+            break
+
+    for i, pi in enumerate(pi_means[::-1]):
+        if pi < 0.95:
+            right_index = len(viral_loads) - i
+            break
+
+    left, right = viral_loads[left_index], viral_loads[right_index]
+    print('Vl_0.05 = 10^', np.round(left, 1), '\n')
+    print('Vl_0.95 = 10^', np.round(right, 1), '\n')
+
+    plt.vlines(x=(left, right), ymin=0, ymax=1,
+              colors=('grey', 'grey'), linestyles='dotted')
+    plt.text(left - 1.1, 0.80, '$vl_{0.05}$', fontsize=14,color='black')
+    plt.text(right + 0.1, 0.80, '$vl_{0.95}$', fontsize=14,color='black')
+    # add 3 shaded areas
+    plt.axvspan(2, left, alpha=0.1, color='limegreen')
+    plt.axvspan(left, right, alpha=0.1, color='orange')
+    plt.axvspan(right, 12, alpha=0.1, color='tomato')
+
+    plt.legend()
+    plt.show()
+
+######### Composite plot P(I) vs Vl #########
+def composite_plot_pi_vs_viral_load(models, labels, show_lines):
+    
+    colors = ['tomato', 'lightskyblue', 'limegreen']
+
+    lines, lowers, uppers = [], [], []
+    for exposure_mc in models:
+        infected = exposure_mc.concentration_model.infected
+        pi_means = []
+        lower_percentiles = []
+        upper_percentiles = []
+
+        for vl in tqdm(viral_loads):
+            model = mc.ExposureModel(
+                concentration_model=mc.ConcentrationModel(
+                    room=exposure_mc.concentration_model.room,
+                    ventilation=exposure_mc.concentration_model.ventilation,
+                    infected=mc.InfectedPopulation(
+                        number=infected.number,
+                        virus=mc.SARSCoV2(
+                            viral_load_in_sputum=10**vl,
+                            infectious_dose=infectious_dose_distribution,
+                            viable_to_RNA_ratio=viable_to_RNA_ratio_distribution,
+                            transmissibility_factor=1.,
+                        ),
+                        presence=infected.presence,
+                        mask=infected.mask,
+                        activity=infected.activity,
+                        expiration=infected.expiration,
+                        host_immunity=0.,
+                    ),
+                ), 
+            exposed=exposure_mc.exposed)
+            
+            pi = model.build_model(size=SAMPLE_SIZE).infection_probability()/100
+            pi_means.append(np.mean(pi))
+            lower_percentiles.append(np.quantile(pi, 0.01))
+            upper_percentiles.append(np.quantile(pi, 0.99))
+
+        lines.append(pi_means)
+        uppers.append(upper_percentiles)
+        lowers.append(lower_percentiles)
+
+    histogram_data = [model.build_model(size=SAMPLE_SIZE).infection_probability() / 100 for model in models]
+
+    fig, axs = plt.subplots(2, 2 + len(models), gridspec_kw={'width_ratios': [5, 0.5] + [1] * len(models),
+                                                                'height_ratios': [3, 1], 'wspace': 0},
+                            sharey='row', sharex='col')
+
+    for y, x in [(0, 1)] + [(1, i + 1) for i in range(len(models) + 1)]:
+        axs[y, x].axis('off')
+
+    for x in range(len(models) - 1):
+        axs[0, x + 3].tick_params(axis='y', which='both', left='off')
+
+    axs[0, 1].set_visible(False)
+    
+    for line, upper, lower, label, color in zip(lines, uppers, lowers, labels, colors):
+        axs[0, 0].plot(viral_loads, line, label=label, color=color)
+        axs[0, 0].fill_between(viral_loads, lower, upper, alpha=0.2, color=color)
+
+    for i, (data, color) in enumerate(zip(histogram_data, colors)):
+        axs[0, i + 2].hist(data, bins=30, orientation='horizontal', color=color)
+        axs[0, i + 2].set_xticks([])
+        axs[0, i + 2].set_xticklabels([])
+        # axs[0, i + 2].set_xlabel(f"{np.round(np.mean(data) * 100, 1)}%")
+        axs[0, i + 2].set_facecolor("lightgrey")
+
+    highest_bar = max(axs[0, i + 2].get_xlim()[1] for i in range(len(histogram_data)))
+    for i in range(len(histogram_data)):
+        axs[0, i + 2].set_xlim(0, highest_bar)
+
+        axs[0, i + 2].text(highest_bar * 0.5, 0.5,
+                           "$P(I)=$\n" + rf"$\bf{np.round(np.mean(histogram_data[i]) * 100, 1)}$%",
+                           color=colors[i], ha='center', va='center')
+
+    axs[1, 0].hist([np.log10(vl) for vl in models[0].build_model(size=SAMPLE_SIZE).concentration_model.infected.virus.viral_load_in_sputum],
+                    bins=150, range=(2, 12), color='grey')
+    axs[1, 0].set_facecolor("lightgrey")
+    axs[1, 0].set_yticks([])
+    axs[1, 0].set_yticklabels([])
+    axs[1, 0].set_xticks([i for i in range(2, 13, 2)])
+    axs[1, 0].set_xticklabels(['$10^{' + str(i) + '}$' for i in range(2, 13, 2)])
+    axs[1, 0].set_xlim(2, 12)
+    axs[1, 0].set_xlabel('NP viral load, $\mathrm{vl_{in}}$\n(RNA copies)', fontsize=12)
+    axs[0, 0].set_ylabel('Probability of infection\n$P(\,\mathtt{I}\,|\,\mathrm{vl}\,)$', fontsize=12)
+ 
+    axs[0, 0].text(11, -0.01, '$(i)$')
+    axs[1, 0].text(11, axs[1, 0].get_ylim()[1] * 0.8, '$(ii)$')
+    #axs[0, 2].text(axs[0, 2].get_xlim()[1] * 0.1, -0.05, '$(iii)$')
+    axs[0, 2].set_title('$(iii)$', fontsize=10)
+
+    crits = []
+    for line in lines:
+        for i, point in enumerate(line):
+            if point >= 0.05:
+                crits.append(viral_loads[i])
+                break
+
+    for i, (crit, color) in enumerate(zip(crits, colors)):
+        axs[0, 0].text(2.5, 0.40 - i * 0.1, f'x $vl_{"{0.05}"}=' + '10^{' + str(np.round(crits[i], 1)) + '}$', fontsize=10, color=color)
+        axs[0, 0].plot(crits[i], 0.05, 'x', color=color)
+
+    if show_lines:
+        axs[0, 0].hlines([0.5], colors=['lightgrey'], linestyles=['dashed'], xmin=2, xmax=12)
+        axs[0, 0].text(9.7, 0.52, "$P(I|vl) = 0.5$", color='grey')
+        middle_positions = []
+        for line in lines:
+            for i, point in enumerate(line):
+                if point >= 0.5:
+                    middle_positions.append(viral_loads[i])
+                    break
+
+        for mpos, color in zip(middle_positions, colors):
+            axs[0, 0].plot(mpos, 0.5, '.', color=color)
+
+        axs[0, 0].vlines(middle_positions, colors=colors, linestyles=['dotted']*2, ymin=axs[0, 0].get_ylim()[0],
+                         ymax=0.5*1.3)
+        axs[1, 0].vlines(middle_positions, colors=colors, linestyles=['dotted']*2, ymin=0, ymax=axs[1, 0].get_ylim()[1])
+
+    axs[0, 0].legend()
+    plt.show()
+
+
+
+######### 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
+
+
+def define_colormap(cns):
+    min_val, max_val = 0.25, 0.85
+    n = 10
+    orig_cmap = plt.cm.Blues
+    colors = orig_cmap(np.linspace(min_val, max_val, n))
+
+    norm = mpl.colors.Normalize(vmin=cns.min(), vmax=cns.max())
+    cmap = mpl.cm.ScalarMappable(
+        norm=norm, cmap=mpl.colors.LinearSegmentedColormap.from_list("mycmap", colors))
+    cmap.set_array([])
+
+    return cmap
+
+
+def scatter_coleman_data(coleman_etal_vl_breathing, coleman_etal_er_breathing):
+    plt.scatter(coleman_etal_vl_breathing,
+                coleman_etal_er_breathing, marker='x', c='orange')
+    x_hull, y_hull = get_enclosure_points(
+        coleman_etal_vl_breathing, coleman_etal_er_breathing)
+    # plot shape
+    plt.fill(x_hull, y_hull, '--', c='orange', alpha=0.2)
+
+
+def scatter_milton_data(milton_vl, milton_er):
+    try:
+        for index, m in enumerate(markers):
+            plt.scatter(milton_vl[index], milton_er[index],
+                        marker=m, color='red')
+        x_hull, y_hull = get_enclosure_points(milton_vl, milton_er)
+        # plot shape
+        plt.fill(x_hull, y_hull, '--', c='red', alpha=0.2)
+    except:
+        print("No data for Milton et al")
+
+
+def scatter_yann_data(yann_vl, yann_er):
+    try:
+        plt.scatter(yann_vl[0], yann_er[0], marker=markers[0], color='green')
+        plt.scatter(yann_vl[1], yann_er[1],
+                    marker=markers[1], color='green', s=50)
+        plt.scatter(yann_vl[2], yann_er[2], marker=markers[2], color='green')
+
+        x_hull, y_hull = get_enclosure_points(yann_vl, yann_er)
+        # plot shape
+        plt.fill(x_hull, y_hull, '--', c='green', alpha=0.2)
+    except:
+        print("No data for Yan et al")
+
+
+def build_talking_legend(fig):
+    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], "Results 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))
+
+
+def build_breathing_legend(fig):
+    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], "Results 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))
+
+
+def print_er_info(er: np.array, log_er: np.array):
+    """
+    Prints statistical parameters of a given distribution of ER-values
+    """
+    print(f"MEAN of ER = {np.mean(er)}\n"
+          f"MEAN of log ER = {np.mean(log_er)}\n"
+          f"SD of ER = {np.std(er)}\n"
+          f"SD of log ER = {np.std(log_er)}\n"
+          f"Median of ER = {np.quantile(er, 0.5)}\n")
+
+    print(f"Percentiles of ER:")
+    for quantile in (0.01, 0.05, 0.25, 0.50, 0.55, 0.65, 0.75, 0.95, 0.99):
+        print(f"ER_{quantile} = {np.quantile(er, quantile)}")
+
+    return
+
+def plot_hourly_temperatures():
+
+    fig = plt.figure()
+    ax = fig.add_subplot(1, 1, 1)
+
+    hours = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23])
+    march = data.Geneva_hourly_temperatures_celsius_per_hour['Mar']
+    june = data.Geneva_hourly_temperatures_celsius_per_hour['Jun']
+    september = data.Geneva_hourly_temperatures_celsius_per_hour['Sep']
+    december = data.Geneva_hourly_temperatures_celsius_per_hour['Dec']
+
+    labels = ['March', 'June', 'September', 'December']
+
+    xnew = np.linspace(hours.min(), hours.max(),300) #300 represents number of points to make between hours.min and hours.max
+
+    for i, month in enumerate([march, june, september, december]):
+        spl = make_interp_spline(hours, month, k=3) #BSpline object
+        power_smooth = spl(xnew)
+        ax.plot(xnew, power_smooth, label=labels[i])
+        ax.scatter(hours, month)
+        
+    ax.set_xticks([0, 6, 12, 18, 23])
+    ax.set_xlabel('Hour of the day', fontsize=12)
+    ax.set_ylabel('Temperature (°C)', fontsize=12)
+
+    plt.legend()
+    plt.show()