Given for engineering students/faculty at AFIT. Welcome to use all or part for other educational endeavors.

1. Basic Engineering Information
Related to Infectious Disease
Transmission
Andrew Hoisington, PhD, PE
andyhois@yahoo.com or Andrew.Hoisington@afit.edu
Department of Systems Engineering & Management, Air Force Institute of Technology, Wright-Patterson AFB, OH, USA
Rocky Mountain Mental Illness Research Education and Clinical Center (MIRECC), Rocky Mountain Regional VA Medical Center
(RMRVAMC), Aurora, CO, USA
Department of Physical Medicine & Rehabilitation, University of Colorado Anschutz Medical Campus, Aurora, CO, USA
Military and Veteran Microbiome: Consortium for Research and Education, Aurora, CO, USA

2. Official Disclaimer: The views expressed in this study are those of the authors and do not
reflect the official policy or position of the United States Air Force, Department of
Defense, Department of Veteran Affairs, or the United States Government. This material
is declared a work of the United States Government and is not subject to copyright
protection in the United States of America.
Unofficial Disclaimer: I am an avid building scientist and have been studying the
microbiome of the built environment for the past 10 years. I am not a virologist or
epidemiologist. The talk from these slides is in reaction to my engineering students and
peers asking me last week about the connection between the built environment and
infectious disease. However, if anyone else finds this useful you are welcome to use the
slides.
“Life moves pretty fast. If you don't stop and look around once in a while, you could miss it.”
- Ferris Bueller

3. https://systems.jhu.edu

4. Liu et al. (2010). “Viral architecture of SARS-CoV-2 with post-fusion spike
revealed by cryo-EM”, bioRxiv
Image from Khan Academy

5. Basics – Buildings
Ventilation/
Outdoor Pollutants
Penetration
Ventilation/
Outdoor Pollutants
HVAC
Filtration
Outdoor Air ?
Indoor
Chemistry
Biology
Indoor
Emissions
Adsorption
Desorption
Deposition
Resuspension
Many function of occupant behavior, building
characteristics, environmental parameters

6. • Exchange of indoor and outdoor air ( =
𝑄
𝑉
)
• Entry of outdoor pollutants, removal of indoor emitted pollutants
• Leakage, natural ventilation, mechanical ventilation
Additional Reading: Breen et al. (2014). “A review of air exchange rate models for air pollution exposure assessments”, Journal of Exp. Science & Env. Epi
Yamamoto et al. (2010). “Residential air exchange rates in three major US
metropolitan areas…”, Indoor Air
Mean = 0.71/hr (n=509)
Steady-State CO2 measures
 =
𝑛𝐸
𝑉(𝐶 − 𝐶 𝑜𝑢𝑡)
n = # people in room
C = CO2 in room (g/m3)
Cout = CO2 outdoors (g/m3)
E = Emission CO2 per person (g/hr)
V = Volume (m3)
Steady-State CO2 example (office meeting)
 =
(20 𝑝𝑒𝑟𝑠𝑜𝑛)(30
𝑔
ℎ𝑟 − 𝑝𝑒𝑟𝑠𝑜𝑛
)
(100 𝑚3)(2.76
𝑔
𝑚3 − 0.7
𝑔
𝑚3)
 = 2.9 1/hr
Basics – Air Exchange Rate (, 1/hr)

7. • Fraction of pollutant emitted into air by one course inhaled by others
• 𝐼𝐹 =
𝑚𝑎𝑠𝑠 𝑖𝑛ℎ𝑎𝑙𝑒𝑑
𝑚𝑎𝑠𝑠 𝑒𝑚𝑖𝑡𝑡𝑒𝑑
=
𝐶(𝑡)𝑄 𝑏 𝑑𝑡
𝐸 𝑡 𝑑𝑡
Additional Reading: Bennett et al. (2002). “Defining Intake Fraction”, ES&T
Steady-State
𝐼𝐹 =
𝑄 𝑏
𝑄
=
𝑄 𝑏
𝑉
3 adult in house:
𝐼𝐹 =
0.78
𝑚3
ℎ𝑟
∗ 2
60 𝑚3 ∗ 0.71ℎ𝑟−1 = .0036
- 3.6% of air third adult is breathing is from
other two adults
Non Steady-State
𝐼𝐹 =
𝑄 𝑏
𝑉
(1 − 𝑒− 𝑡)𝑑𝑡
𝐸 𝑡 𝑑𝑡
Basics – Intake Fraction (IF)

8. • Probability (P) = # disease/ # susceptible = (1 – e-)
•  = avg # quanta breathed by person
• Quanta = # infectious droplets to initiate infection
• Depends upon organism
• Higher infection, higher 
• =𝑄 𝑏 𝑡𝑁 (Qb breathing rate, t = time exposure, N = average quanta conc.)
𝑃 = 1 − 𝑒
𝐼𝑞𝑄 𝑏 𝑡
𝑄
1 −
1
𝑡
1 − 𝑒− 𝑡
Where: I = #infected individuals, q = quanta emissions (quanta/hr)
P

Assumptions: Well mixed, no infections from outdoors, no reduction in viability, no filtration loss, no settling
Wells-Riley Equation (1/2)

9. Wells-Riley Equation (2/2)
Where do we find q (quanta emissions rate)?
Stephens (2012), “HVAC filtration and the Wells-Riley approach to assessing risk of infectious airborne diseases”, Final report for NAFA

10. Rudnick-Milton Equation
• Modification of Wells-Riley
• For other modifications, see summary by Sze To and Chao (2010), “Review
and comparison between the Wells-Riley dose-response approaches to risk
assessment of respiratory diseases”, Indoor Air
Additional Reading: Rudnick & Milton (2003). “Risk of indoor airborne infection transmission estimated from carbon dioxide concentration”, Indoor Air
Rebreathed Fraction
𝑓 =
𝐶 − 𝐶 𝑜
𝐶 𝑎
Ca=38000 ppm
C-Co = 700 ppm
f = 0.018 = 1.8%
Rudnick-Milton Equation
𝑃 = 1 − 𝑒
−𝑓𝐼𝑞𝑡
𝑛
f = rebreath fraction
I = number infections
N = number people
q = quanta emissions
t = exposure time
Rudnick-Milton Reproductive #
𝑅 𝑎𝑜 = 𝑛 − 1 ∗ (1 − 𝑒
−𝑓𝑞𝑡
𝑛
)
Rudnick-Milton Critical Rebreath Fraction
𝑓𝑐 =
1
𝑞𝑡
𝑛 − 1
𝑛 − 2
𝑛
When n>30
𝑓𝑐 ≈
1
𝑞𝑡

11. SARS-CoV-2
Is it airborne?
• WHO Director General – No
• But depends upon what you call airborne
Picture from The Guardian article
https://www.theguardian.com/science/2018/jan/15/achoo-why-letting-out-an-
explosive-sneeze-is-safer-than-stifling-it
Recommended Reading - https://www.wired.com/story/they-say-coronavirus-isnt-airborne-but-its-definitely-borne-by-air/
Liu et al. (2020). “Aerodynamic characteristics and RNA concentrations of SARS-CoV-2
aerosol in Wuhan hospital during COVID-19 outbreak”, bioRxiv

12. SARS-CoV-2
Can it “survive” on surfaces in build environment?
• Yes!
• Actual, likely multiple days on common surfaces
• Kampf et al. (2020). “Persistence of coronavirus on inanimate surfaces and their inactivation with biocidal agents”,
Journal of Hosp. Infect.
Van Doremalen et al. (2020). “Aerosol and surface stability of HCoV-19 (SARS-CoV-2) compared to SARS-CoV-1”, medRxiv
Persistence
in aerosols
as well

13. SARS-CoV-2
Reproductive number
Study Ro
Bedford et al. (2020) 1.5-3.5
Imai et al. (2020) 2.5 (1.5-3.5)
Liu et al. (2020) 2.92 (95% CI: 2.28-3.67)
Read et al. (2020) 3.8 (95% CI: 3.6-4.0)
Riou and Althaus (2020) 2.2 (90% CI: 1.4-3.8)
Zhau et al. (2020) 5.47 (95% CI: 4.16-7.1)
Majumder and Mandl (2020) 2.0-3.1
Modified from Park et al. (2020). “Reconciling early-outbreak estimates of the basic
reproductive number and its uncertainty: framework and applications to the novel
coronavirus (SARS-CoV-2) outbreak”, medRxiv.
Biggerstaff et al. (2014). “Estimates of the reproductive
number for seasonal, pandemic, and zoonotic influenza: a
systematic review of the literature”, MBC Infect Disease.

14. Hypothetic Situation 1
Class with 30 students for 1 hour, 1 person sick
• Assume  = 2/hr, q = 100 quanta/hr (influenza), 270 m3 room
𝑃 = 1 − 𝑒
𝐼𝑞𝑄 𝑏 𝑡
𝑄
1 −
1
𝑡
1 − 𝑒− 𝑡
Wells-Riley
P= 7.9% of infection
Rudnick-Milton Equation (f = 2%)
𝑃 = 1 − 𝑒
−𝑓𝐼𝑞𝑡
𝑛
P= 6.5 % of infection
𝑅 𝑎𝑜 = 𝑛 − 1 ∗ (1 − 𝑒
−𝑓𝑞𝑡
𝑛
)
Rao= 1.87
𝑓𝑐 ≈
1
𝑞𝑡
fc= 1.05
To get to that fc you would need to see only ~400 ppm
increase CO2 from outdoors, ASHRAE Std is 700 ppm

15. Hypothetic Situation 2
Class with 100 people in restaurant for 1 hour, 1 person sick
• Assume  = 3/hr, q = 100 quanta/hr (influenza), 2287 m3 restaurant
𝑃 = 1 − 𝑒
𝐼𝑞𝑄 𝑏 𝑡
𝑄
1 −
1
𝑡
1 − 𝑒− 𝑡
Wells-Riley
P= 6.37% of infection
Rudnick-Milton Equation (f = 2%)
𝑃 = 1 − 𝑒
−𝑓𝐼𝑞𝑡
𝑛
P= 6.45% of infection
𝑅 𝑎𝑜 = 𝑛 − 1 ∗ (1 − 𝑒
−𝑓𝑞𝑡
𝑛
)
Rao= 1.87
𝑓𝑐 ≈
1
𝑞𝑡
fc= 1.05
To get to that fc you would need to see only ~400 ppm
increase CO2 from outdoors, ASHRAE Std is 700 ppm

16. Hypothetic Situation 3
My house with me and my son, for 24 hours, 1 person sick
• Assume  = 0.7/hr, q = 100 quanta/hr (influenza), 411 m3 house
𝑃 = 1 − 𝑒
𝐼𝑞𝑄 𝑏 𝑡
𝑄
1 −
1
𝑡
1 − 𝑒− 𝑡
Wells-Riley
P= 99.7% of infection
Rudnick-Milton Equation (f = 2%)
𝑃 = 1 − 𝑒
−𝑓𝐼𝑞𝑡
𝑛
P= 99.8 % of infection
CDC Guidance if sick: separate into different room/bathroom, limit contact with anyone
Andy additions: open window if can, bleach everything…a lot

17. SARS-CoV-2 – What to do for Buildings (1/5)
1. Open windows
• In depth study of residential home in VA and CA
• Opening one window increased  by as much as 0.8/hr (CA), 1.3/hr (VA)
• Multiple window opening increased  0.1-2.8/hr (CA), 0.49-1.49/hr (VA)
• Hypothetical situation 3: = 0.7/hr P= 99.8% while = 3/hr P= 77.6%,
• Added bonus, UV from sunlight MAY assist inactivating virus
MS2 ssRNA
Tseng and Li (2007). “Inactivation of viruses on surfaces by untraviolet
germicidal irradiation”, Jour. Occup. & Envr Hygiene.
- Not a recommendation to UV your house
- Although from mental health
perspective, lots of indications opening
windows (and even blinds) very helpful

18. SARS-CoV-2 – What to do for Buildings (2/5)
2. Install higher efficient filters in HVAC system, if possible
• Not all air going through HVAC filter
(runtime 4-54%)
• Newer home likely less leaky, more air
through filters
• Removal dependent upon run conditions
of HVAC
• Removal dependent upon outdoor
conditions
• Increasing MERV likely increases energy,
mainly through less airflow and longer
runtime
Adapted from Alavy and Siegel (2019). “IAQ and energy
implications of high efficiency filters in residential buildings: A
review (RP-1696)”, Science and Technology of the Built
Environment
(Azimi et al (2014). “Estimates of HVAC filter efficiency for fine
and ultrafine particles of outdoor origin”, Atmospheric Env.

19. SARS-CoV-2 – What to do for Buildings (3/5)
3. Increase humidity
• Most due this through portable
humidifiers – make sure they are clean
• If cool area and still heating, dropping
RH
• Don’t over compensate and get water
droplets on surfaces
• Not sure your indoor RH? Can get
cheap for ~$10 at hardware store
20% RH
50% RH
80% RH
Two surrogate of
SARS-CoV (not
SAR-CoV-2)
Casanova et al. (2010). “Effects of air temperature and relative humidity on Coronavirus survival on surfaces”, App. and Envr. Micro
Additional reading from Joseph Allen:
https://www.nytimes.com/2020/03/04/opinion/coronavirus-buildings.html
Temp and RH (not in buildings but SARS-CoV-2): Wang et al. (2020), “High
temperature and high humidity reduce transmission of COVID-19”, SSRN

20. SARS-CoV-2 – What to do for Buildings (4/5)
4. Use portable air filters (if available)
• Not for everyone
• Competes with , tighter house works better
• Think room, not whole house
• Efficiency important, but not only measure to
consider
• Higher CADR is better (although this is applied to
particles of select size)
• Want more info? Good read - Siegel (2014), “Primary
and secondary consequences of indoor air cleaners”,
Indoor Air
https://www.epa.gov/sites/
production/files/2018-
07/documents/guide_to_ai
r_cleaners_in_the_home_2
nd_edition.pdf

21. SARS-CoV-2 – What to do for Buildings (5/5)
5. Clean/disinfect surfaces
• CDC guidance
• Regularly disinfect frequently touched surfaces with household cleaners
• Diluted bleach (4 teaspoons per quart)
• Launder items (towels, bedding) at warmest possible level
• Don’t shake dirty laundry
• Also see Kampf et al. (2020). “Persistence of coronavirus on inanimate surfaces
and their inactivation with biocidal agents”, Journal of Hosp. Infect.
CDC Website - (https://www.cdc.gov/coronavirus/2019-ncov/prepare/cleaning-
disinfection.html?CDC_AA_refVal=https%3A%2F%2Fwww.cdc.gov%2Fcoronavirus%
2F2019-ncov%2Fcommunity%2Fhome%2Fcleaning-disinfection.html)

22. SARS-CoV-2 People to Follow (mostly building folks)
Jonathan Eisen (UC Davis)
Lindsay Marr (Virginia Tech)
Richard Corsi (Portland State)
Shelly Miller (Colorado)
Joseph Allen (Harvard)
Marina Vance (Colorado)
Van Den Wymelenberg (Oregon)
Faye McNeill (Columbia)
Paula Olsiewski (Sloan Foundation)
Catherine Noakes (Leeds)
Don Milton (Maryland)
* Not exhaustive list but I have known most of these folks for many years (or have been reading their
papers for years) and would feel comfortable having my own mom get scientific advice from them. You can
find them on twitter providing lots of information and guidance

23. https://warriorcanineconnection.org
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