In the published article, there were several errors made in the text:

Two definitions were not properly spaced.

A correction has been made to Inhalation equations, Paragraph 3. The definition sentences previously stated:

“N _T = number of occupants in the space t = occupancy time after the exposed group including the infector enter the space”

The corrected definition sentences appear below:

“N _T = number of occupants in the space

t = occupancy time after the exposed group including the infector enter the space”

The definitions of r _o and P are not provided.

A correction has been made to the Infection Equations following Equation 14.

r o = 1 − P P 1 − e − D Q D 50 H I D 50

The definitions to be added after Equation 14 appear below: r o = 1 − P P 1 − e − D Q D 50 H I D 50 (14) where

r o = reproduction rate, the average number of secondary transmissions per infectious person

P = disease prevalence, the fraction of the population that is shedding infectious aerosols at the rate used in calculating dose, D

Missing words, small p and wrong equation number.

A correction has been made to Designing HVAC Systems, Paragraph 1, missing phrase introducing the equation; variable p should be cap P; Equation 14 should be Equation 15. This sentence and the following equation previously stated:

… for the average infectious period of the index.

p = 1 / NT

The corrected variable name and equation number appear below:

“for the average infectious period of the index, the disease prevalence at the beginning then is”

P = 1 / N T

A variable definition missing.

A correction has been made to Designing HVAC systems, Paragraph 5. This sentence previously stated:

“…maximum reproduction number either in the setting…”

The corrected sentence appears below:

“…maximum reproduction number r _o either in the setting…”

The caption of Table 2 requires more information. The caption previously was: Table 2 Outdoor air exposure estimates”

The corrected Table 2 caption appears below:

“Table 2 Occupancy experience example input data for four settings”

There was an error in the below factor, which originally stated: “then by a factor (i.e. 1.127) to obtain.” The corrected factor appears below

“then by a factor (i.e. 0.898) to obtain.”

The below sub-section name should have been a higher level:

A correction has been made to Design of HVAC systems, Equal reproduction and Equal reproduction and local prevalence.

The equation number in text is incorrect

A correction has been made to Designing HVAC systems, Equal reproduction, Paragraph 8. This sentence previously stated:

“…using Equation 15 where n _o = 1.”

The corrected sentence appears below:

“…using Equation 14 where: n o = P N T r o = n n o ∼   ( 1 − ⅇ − D Q D 50 H I D 50   ) P D = D G   N S ∼ Q B P q G V E Q p t + v o V E Q p e − V E Q p v o t − 1

The equation number and lack of capitalization for p is incorrect.

A correction has been made to Designing HVAC systems Occupancy experience example. The equation number previously and variable P was: r o ∼ 1 − e − Q B P q n t Q p + Q f / p (15)

The corrected equation number and variable P appears below: r o ∼ 1 − e − Q B P q n t Q p + Q f / P (16)

The sub-sub-section title for Recirculation and filter flow was place on too high a level and should have been downsized.

The equation number was incorrect:

A correction has been made to Occupancy experience example. The equation number previously was:

Q R = Q f η  cfm / person

The corrected equation number appears below: Q R = Q f η  cfm / person (17)

The caption for Table 3 needed clarification. The caption for Table 3 as published was: “Determining the filter efficiency and the flow required”

The Table 3 caption as corrected appears below:

“Table 3 Occupancy experience example recirculation flow requirements using Merv 13 filters η = 0.62 to achieve a combined reproduction rate r_o of 2.5 for the four settings.”

Table 3 had too many decimal places and had to be expanded to include the metabolic and breathing rates that were used in the Occupancy experience example. The corrected Table 3 and it’s caption appear below:

The caption of Table 4 needed more information, and some figure were incorrect. The corrected table caption appears below:

The caption of Table 5 required clarification and some values in the Filter Eff column were incorrect. The corrected table caption appears below:

A variable name was incorrect and the equation number is missing.

A correction has been made to Designing HVAC systems, Equal reproduction example , r o = 1 − e − D Q D 50 H I D 50 / p ∼ D G 1.443 H I D 50

The denominator variable should be cap P and the equation number is (19). The corrected equation appears below: r o = 1 − e − D Q D 50 H I D 50 / P ∼ D G 1.443 H I D 50 (19)

There was an error missing equation number.

A correction has been made to Designing HVAC systems, Equal reproduction and local prevalence example

The equation as it now stands r o = N S 1 − ⅇ − D Q D 50 H I D 50  

The equation corrected r o = N S 1 − ⅇ − D Q D 50 H I D 50     (20)

The caption of Table 6 needed more information, and some of the figures presented were inaccurate. The corrected table caption appears below:

The caption of Figure 5, 6 and 7 required additional detail. The corrected titles appear below:

Figure 5 Equal reproduction example using Equation 18 and national prevalence P = 0.03 for ventilation designed for r _o = 2.5.

Figure 6 Equal reproduction example using the Wells-Riley approximation Equation 19 and national prevalence P = 0.03 for ventilation designed for reproduction r _o = 2.5.

Figure 7 Equal reproduction example ventilation requirements for various settings to achieve r_o = 2.5 using Equation 20, the data in Table 6 and local prevalence P = 1/N _T (Equation 15).

The references to Tables 4, 5, Figure 5 and Figure 6 were missing. A corrections have been made to

The missing sentence below has been added to Designing HVAC systems, Equal reproduction example . :

“Equation 18 is used in calculating the recirculation flow requirements shown in Table 4 and Figure 5 for the various settings.”

And a correction has been made to the section Occupancy experience example. The figure and table reference previously was:

Figure 5; Table 4

The corrected reference appears below:

Figure 6; Table 5

The paragraph heading Occupancy Experience was incorrectly located.

A correction has been made to Occupancy Experience. The heading was previously before “This procedure sets a national….” and has been move to before “During COVID-19 Linka et al.

The derivation of Equation 20 was not fully explained.

A correction has been made to missing equations to explain the derivation of Equation 20.

r o = N s 1 − ⅇ − D Q D 50 H I D 50

The missing equations follow.

The possibility of zero infection follows a Poisson distribution: P o i s s o n = ⅇ − λ λ x x !

For zero infection, x = 0 λ x = λ 0 = 1 x ! = 0 ! = 1

Probability of zero infections P o i s s o n = ⅇ − λ

Probability of infection for susceptible individual: r = 1 − ⅇ − λ

Risk for occupant i: r i = 1 − ⅇ − λ i

Total risk for all occupants: n = ∑ i = 1 N s 1 − ⅇ − λ i

Total risk for all occupants assuming a perfectly mixed volume: n = N s 1 − ⅇ − λ

Lambda is the quantity of the statistical unit inhaled for i ^th individual over time: λ i = ∫ 0 t Q B C i t ∂ t

Q B = cfh  b r e a t h i n g   c o u l d   v a r y   w i t h   t i m e   a n d  individual

C i t = concentration  o f   q u a n t a   i n   a i r   c o u l d   v a r y   w i t h   t i m e   a n d   l o c a t i o n   q u a n t a / f t 3 t = hours

λ i = quanta  i n h a l e d   b y   o c c u p a n t   i   o v e r   t i m e   p e r i o n   t   a t   l o c a t i o n   i C i t = C V , i Q D 50 H I D 50

C V , i = concentration  o f   v i r u s   i n   a i r   c o u l d   v a r y   w i t h   t i m e   a n d   l o c a t i o n   v i r u s / f t 3

Q D 50 = quanta  d o s e   t h e   c a u s e s   d i s e a s e   i n   50 %   o f   t h e   g r o u p , 0.693   q u a n t a : n N s = 0.5 = 1 − ⅇ − λ = 1 − ⅇ − 0.693 H I D 50 = virus  d o s e   t h a t   c a u s e s   d i s e a s e   i n   50 %   o f   t h e   g r o u p λ i = ∫ 0 t Q B C i t ∂ t = ∫ 0 t Q B C V , i Q D 50 H I D 50 ∂ t ∫ 0 t Q B C V , i ∂ t = D

For the transient case, the virus dose is: D = Q B n o q n Q T t + 1 A C H ⅇ − A C H t − 1

The reproduction number shows the number of infections from an infector, no = 1: D = Q B q n Q T t + 1 A C H ⅇ − A C H t − 1 q n = v i r u s h r f r o m   i n f e c t o r N s = number  o f   s u s c e p t i b l e s n = r o = N s 1 − ⅇ − λ = N s 1 − ⅇ − D Q D 50 H I D 50

For steady state case t > 5 air changes: D = Q B q n Q T t + 1 A C H ⅇ − A C H t − 1 = Q B q n Q T t r o = N s 1 − ⅇ − Q B q n Q T t Q D 50 H I D 50 r o = N s 1 − ⅇ − D Q D 50 H I D 50

In terms of quanta: q G = Q D 50 q n H I D 50

You get the Wells-Riley equation:

r o = N s ( 1 − ⅇ − Q B q G t Q T ) (20)

Extra clarification was need in the section Occupancy experience, following “…in that setting.

The additional sentence is: “Steady state occupancies only are considered ”

Clarification was needed in the section Equal reproduction, following “and transient”

The below was added: “(leaving or entering)”.