ASHRAE Journal - May 2021 - 12

TECHNICAL FEATURE

various types of masks and the importance of proper
fit. We also show that increased ventilation rates
have a diminishing return on reducing the probability of infection via aerosol particles. Although not
explicitly tested during the present work, in-room
portable recirculating HEPA air filtration devices can
be expected to have a similar effect at reducing the
infection probability as increasing room air ventilation rates.

Aerosol Behavior in the Indoor Environment
Estimating the Probability of Infection by Aerosols
In 1974, a measles outbreak occurred in an elementary school in upstate New York. The index case was
a second grader who produced 28 secondary cases in
14 different classrooms within the elementary school,
and two subsequent generations yielded 60 infections.
Riley, et al., analyzed this case and, as part of their
analysis, proposed a mathematical model to predict
the probability of airborne infection based on individual characteristics such as breathing rate and on
building HVAC characteristics such as room ventilation
rate.16 Equation 1 shows the equation that Wells-Riley
used to model the conditional probability of infection,
P, based on a susceptible individual receiving a quantum dose, Dq, sufficient to cause infection (see sidebar
" Relationship Between Infectious Aerosol Particles and
Quantum Dose " ).
P = 1 - exp(-Dq)

(1)

where the infectious quantum dose, Dq, depends on the
average concentration of infectious quanta (i.e., aerosols
uniformly distributed throughout the space and carrying a viral or bacterial payload) within the room. In
Part 2 of this two-part series, we provide further details
on the application of the Wells-Riley model and its
use for predicting the conditional probability of infection in order to evaluate a range of potential protective
measures.
The predictive capability of the Wells-Riley model
depends on establishing accurate values of the various parameters and variables included in the model.
Reported here is a summary of field experiments used
to determine whether the assumption inherent in the
Wells-Riley model, that the indoor space is well-mixed,
is appropriate.
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ASHRAE JOURNAL

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M AY 2021

Relationship Between Infectious Aerosol
Particles and Quantum Dose

Nardell and Nathavitharana note7 that the seminal work in airborne infection and infection control
was conducted by William Wells. Early in the 20th
century, Wells conducted experiments at Harvard
University and the University of Pennsylvania that
produced clear evidence of the airborne route as a
mode of transmission of infection.17 Wells used the
term quantum to represent the minimum dose of
pathogen-in this case, Mycobacterium tuberculosis-
necessary to cause infection in the host.
Understanding that airborne infections inherently
involve low probabilities due to dilution and other
factors, Wells introduced the Poisson distribution in
his definition of quantum dose, which represents
a threshold number of infective particles breathed
that produce infection in 63.2% of occupants.
Unfortunately, there is no simple correspondence
between bioaerosol droplets that may contain viable
virus or bacteria and the quantum dose sufficient to
cause infection. As a result, quantum dose values are
often back-calculated from outbreak events; those
values form a basis for the present analysis.

Classroom Space and Experimental Setup
Classrooms are generally among the highest occupant
density spaces in buildings. Figure 1 shows the actual
classroom space, in its pre-COVID-19 layout, used as a
test bed for the present study. The classroom measures
126 m2 (1,356 ft2) with a ceiling height of 2.87 m (9.42 ft),
yielding a gross room volume of 362 m3 (12,811 ft3). The
room is served by a central station variable air volume
air-handling unit (AHU) equipped with MERV 15 filtration and capable of supplying a maximum total supply
airflow rate of 88 892 m3/h (52,320 cfm), with a minimum supply airflow rate of 28 034 m3/h (16,500 cfm).
The AHU's outdoor airflow rate ranges from 20 261 m3/h
to 88 892 m3/h (11,925 cfm to 52,320 cfm). The AHU
serves multiple spaces, including classrooms, offices,
common areas and lab spaces.
The classroom space in the present study has a single
VAV box that supplies conditioned room air to four,
four-way throw fixed-area diffusers situated overhead
and arranged in a rectangular layout. A single overhead
return is located near a rear corner of the classroom.

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ASHRAE Journal - May 2021

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