ASHRAE Journal - March 2021 - 25

TECHNICAL FEATURE

from one person to another) can act to passively carry a
pathogen;
* Vectors: mosquitoes, ﬂeas and ticks can transfer
the pathogen; and
* Short-range and long-range airborne transmission.6,7,8
Viruses are not usually speciﬁc to one mode of transfer
and are often transmitted by multiple modes of transmission.6 Direct contact and indirect transmission through
vehicles and vectors are not directly affected by the HVAC
system, so for the purposes of these articles we will focus
on airborne transmission modes. Additionally, transmission routes such as through aerosol-generating procedures like intubation, cardiopulmonary resuscitation,
surgery and others are not common in a classroom situation and also will not be addressed. Designers working in
health-care occupancies should consider all transmission
routes and the unique challenges that may be present.
" Infections are a result of the interaction between susceptibility factors in the exposed host, the concentration
and virulence of the pathogen in the environment and the
extent and nature of the exposure. " 6 Evidence also exists
that where a respiratory virus is deposited (for example,
either as small particles in the lungs or as large particles
in the upper respiratory tract) may alter the infection risk
and illness severity. Particles deposited in the lungs are
thought to carry a greater risk and severity of infection.9
As mentioned above, one of the risk factors for infection is the concentration of the pathogen in the environment. Large droplets can contain more virions
and, therefore, have a higher potential contagiousness
(assuming equal exposure) than smaller droplets.10
While the smaller droplets have less chance of containing a virus, they can remain suspended in the air for a
longer amount of time, increasing the exposure time
and the possibility of infection.10 The probability that a
droplet contains one or more virions is proportional to
the cube of the initial hydrated droplet's diameter (d3).11

Droplets and Droplet Nuclei
In 1934 Wells carried out experiments showing that
droplets greater than 100 microns would fall to the
ground in a couple of seconds, while droplets smaller
than 100 microns would evaporate before they reach the
ground and form droplet nuclei, which could remain
airborne for hours or even days.5 Wells' calculations
were based on pure water and didn't account for salinity

FIGURE 1 Wells-Riley equation.17

P1 =

 Iqpt 
C
= 1 − exp  −
 Q 
S

where
PI = Probability of infection
C = Number of infection cases
S = Number of susceptible
persons
I = Number of infectors
p = Pulmonary ventilation
rate of a person

q = Quanta generation rate
t = Exposure time interval
Q = Room ventilation rate
with clean air

concentration, surrounding air movement, respiratory
jets and other factors,12 but his work became the foundation for our understanding of droplet transition to droplet nuclei. Much of the early research was concentrated
on bacteria, but many of these principles of droplet
movement would later be applied to viruses.
Studies showing the size and duration of droplet aircarriage by using high speed photography were carried
out, and Stokes Law was applied to droplets to calculate
the settling velocity.13 In 1942 Theodore Hatch described
dispersion of particulate matter in the air through
dynamic projection for large particles and by air carriage
for small particles. Large particles, 1.0 mm (0.04 in.) in
size, if projected at 46 m/s (152 fps), could travel 4.6 m
(15 ft) before reaching the ﬂoor if discharged from head
height. Smaller particles, less than 0.1 mm (0.004 in.),
would not be projected any appreciable distance by
their own kinetic energy and must depend on air movement for transport beyond the immediate vicinity of
the source. Hatch also noted that particles larger than
5 microns would be primarily removed in the upper
respiratory tract, while smaller particles would be
deposited by settlement in the alveoli.14
In 1978 Edward C. Riley developed an airborne infection
model using an epidemiological study of a measles outbreak.15 Riley worked with Wells at Harvard in the early
1930s, but left to attend medical school. He didn't return
to the study of airborne contagion until he retired in 1970,
after the death of Wells in 1963.16 Prior to Riley's model,
the Soper equation or Reed-Frost modiﬁcation was used
to model the spread of contagious disease, but what would
become known as the Wells-Riley equation (Figure 1) would
provide a simple and quick calculation to determine the
infection risk of airborne transmissible diseases.
Many epidemic modeling studies have used the WellsRiley equation as part of their mathematical models.
Newer research has modiﬁed the Wells-Riley equation,
MARCH 2021

ashrae.org

ASHRAE JOURNAL

25
http://www.ashrae.org
ASHRAE Journal - March 2021

Table of Contents for the Digital Edition of ASHRAE Journal - March 2021
