Research

Cost-Effectiveness of MultifacetedBuilt Environment Interventionsfor Reducing Transmissionof Pathogenic Bacteria inHealthcare Facilities

Marietta M. Squire, MS1, Takeru Igusa, PhD1,Sauleh Siddiqui, PhD1, Gareth K. Sessel, BM BCh, MSc2,and Edward N. Squire Jr., MD, MPH3

AbstractObjectives: The objective of this study is to determine the optimal allocation of budgets for pairs ofalterations that reduce pathogenic bacterial transmission. Three alterations of the built environmentare examined: handwashing stations (HW), relative humidity control (RH), and negatively pressuredtreatment rooms (NP). These interventions were evaluated to minimize total cost of healthcare-associated infections (HAIs), including medical and litigation costs. Background: HAIs are largelypreventable but are difficult to control because of their multiple mechanisms of transmission. More-over, the costs of HAIs and resulting mortality are increasing with the latest estimates at US$9.8 billionannually. Method: Using 6 years of longitudinal multidrug-resistant infection data, we simulated thetransmission of pathogenic bacteria and the infection control efforts of the three alterations usingChamchod and Ruan’s model. We determined the optimal budget allocations among the alterations byrepresenting them under Karush–Kuhn–Tucker conditions for this nonlinear optimization problem.Results: We examined 24 scenarios using three virulence levels across three facility sizes with varyingbudget levels. We found that in general, most of the budget is allocated to the NP or RH alterations ineach intervention. At lower budgets, however, it was necessary to use the lower cost alterations, HWor RH. Conclusions: Mathematical optimization offers healthcare enterprise executives and engi-neers a tool to assist with the design of safer healthcare facilities within a fiscally constrained envi-ronment. Herein, models were developed for the optimal allocation of funds between HW, RH, andnegatively pressured treatment rooms (NP) to best reduce HAIs. Specific strategies vary by facility sizeand virulence.

1 Department of Civil Engineering, Johns Hopkins University, Baltimore, MD, USA2 Outreach Engineering NPC (non-profit company), Johannesburg, South Africa.3 Moss Clinic, Fredericksburg, VA, USA

Corresponding Author:

Marietta M. Squire, MS, Department of Civil Engineering, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218,

USA.

Email: marietta.squire@gmail.com

Health Environments Research& Design Journal

2019, Vol. 12(2) 147-161ª The Author(s) 2019

Article reuse guidelines:sagepub.com/journals-permissionsDOI: 10.1177/1937586719833360

journals.sagepub.com/home/her

Keywordsinfection control, MRSA, patient safety, airborne transmission, design, hospital hygiene, healthcare-associated infections, hospital, VRE, CRE

Literature Review

Healthcare-Associated Infections

Healthcare-associated infections (HAIs) severely

threaten hospitalized patients who are often

highly susceptible to infection. The numbers are

extremely high. On any given day, 1 in 25 (4%) of

pediatric and adult hospitalized patients will have

at least 1 HAI (Magill et al., 2014). Among those,

1 in 17 will die as a result (Klevens, 2007). Esti-

mates of the annual number of HAIs in U.S. hos-

pitals vary between 400,000 (Zadeh, Sadatsafavi,

& Xue, 2015) and 1.7 million (Klevens et al.,

2007). The estimated annual mortality in the

United States ranges from 75,000 (Lee, 2014) to

99,000 (Klevens et al., 2007).

In 2013, the direct cost of these infections was

US$9.8 billion (US$10.47 billion in 2017; Zim-

lichman et al., 2013). These HAIs had multiple

causes: 33.7% from surgical site infections,

31.6% due to ventilator-associated pneumonia,

18.9% from central line–associated bloodstream

infections, and the remaining 15.8% from Clos-

tridium difficile and other pathogens (Zimlich-

man et al., 2013). HAIs prove most deadly

among older adults and those with immune sys-

tem suppression. Deeming such infections pre-

ventable, the Centers for Medicare and

Medicaid Services have begun withholding pay-

ments for certain infections (Center for Medicare

and Medicaid Service Hospital-Acquired Condi-

tion Reduction Program, 2018). It has been found

that when including indirect costs, HAIs cost

American society US$96 billion to US$147 bil-

lion each year (Marchetti & Rossiter, 2013).

Infections caused by three multidrug-resistantorganisms (MDROs). MDROs, sometimes referred

to as superbugs, are dreaded because they are the

most difficult to treat. In this investigation, three

groups of these MDROs were evaluated:

methicillin-resistant Staphylococcus aureus

(MRSA), carbapenem-resistant

Enterobacteriaceae (CRE), and vancomycin-

resistant Enterococci (VRE).

The first strains of MRSA were discovered in

1961 by a British investigator (Barber, 1961). The

resistance of Staphylococcus aureus to methicil-

lin has expanded to additional antibiotics

(Nichols, 2017). In 1986, vancomycin-resistant

Enterococcus spread rapidly throughout Europe

and the United States (O’Driscoll & Crank, 2015;

Uttley, Collins, Naidoo, & George, 1988). VRE

infects vulnerable patients via surgical wounds

and urinary tract catheters. It also causes colitis

and endocarditis (Cerrud-Rodriguez, Alcaraz-

Alvarez, Chiong, & Ahmed, 2017; Stevens &

Edmond, 2005). Carbapenem-resistant species

in the family, Enterobacteriaceae, CRE were first

identified in November 2012 (Deen & Debbie,

2014). During the course of just 2 years, CRE

spread across 42 states and 200 hospitals in the

United States (Deen & Debbie, 2014).

Benchmark for infection control. Biocontainment

labs and biocontainment units are the gold stan-

dard in infection control against “nightmare

pathogens” such as the Ebola virus. Evaluation

of hospital infection control within the context of

these types of facilities provides an important

frame of reference. Levels 3 and 4 biosafety labs

(i.e., biocontainment labs) and treatment facilities

for highly infectious patients (i.e., biocontainment

units) have rigorous controls and expensive infra-

structure. This infrastructure includes specialized

HVAC systems, water decontamination, and

chemical decontamination of personnel and equip-

ment exiting hot (highly infectious) regions.

There is a spectrum of infection control effi-

cacy, in which biocontainment units lie at the

cost-prohibitive upper limit. Healthcare facilities

must determine where on the spectrum they

should position themselves and evaluate their

infection control measures accordingly.

Three alterations of the built environment intended toreduce HAIs. While many efforts for infection

148 Health Environments Research & Design Journal 12(2)

control have focused on hand hygiene, our inter-

est is in the trade-offs between multiple candidate

interventions; we considered the impact of pairs

of the following three alterations in the built envi-

ronment: handwashing stations (HW), controlled

indoor air hydration (i.e., relative humidity con-

trol or RH), and negatively pressured treatment

rooms (NP). Architects and engineers acknowl-

edge the need for greater insight into the impact

of infrastructure on patient safety (Eames, Tang,

Li, Wilson, 2009; Hamilton, 2013). Close inter-

actions between microbiologists, infection con-

trol experts, engineers, architects, and

healthcare providers are critical to improve hos-

pital design and thereby decrease HAIs (Eames

et al., 2009).

Therefore, our article seeks to answer the fol-

lowing research questions:

1. What is the optimum resource allocation

for implementation of the three candidate

alterations in the built environment among

healthcare facilities of varying sizes and

budgets?

2. How effective is a pair of alterations at

minimizing infections, when compared to

another feasible pair for a specific sce-

nario? The best case for each pair is used

for these comparisons, in which resources

are optimally allocated between the altera-

tions in the pair.

How effective is a pair of alterations at

minimizing infections, when compared to

another feasible pair for a specific

scenario? The best case for each pair is

used for these comparisons, in which

resources are optimally allocated between

the alterations in the pair.

Specifically, we investigated the cost–benefit

analysis for each intervention (i.e., for each pair

of alterations). The contribution of our study is a

first-of-its-kind toolset that enables evidence-

based decisions for the allocation of budgets to

minimize HAIs. Furthermore, the toolset can be

used to analyze multiple budgets, hospital sizes,

and pathogens.

Alteration #1: Handwashing measures. In 1846,

Ignaz Semmelweis first observed the relation-

ship between infection and healthcare workers’

(HCW) failure to wash their hands (Davis,

2015). Even today, microorganisms may be

transported by the unwashed hands of HCW and

travel from one patient to another. Therefore,

compliance with hand hygiene protocols

remains a critical preventative measure in the

avoidance of HAIs (Beggs, Shepherd, & Kerr,

2009).

Evidence to date shows that handwashing

compliance is increased with convenient place-

ment of hand gel dispensers (Cure & Van Enk,

2015). For example, a paper towel dispenser

which automatically presents a paper towel to

passers-by significantly increased handwashing

compliance from 61.8% to 75.9% (Ford, Boyer,

Menachemi, & Huerta, 2014).

Boyce, Potter-Bynoe, Chenevert, and King

(1997) demonstrated that when treating MRSA

patients, 65% of nurses’ scrubs and uniforms

became contaminated with MRSA. This occurs

during contact with colonized or MRSA-

infected patients. Even without physical contact

with MRSA-infected patients, 42% of nurses

became contaminated from contact with contami-

nated surfaces in MRSA patients’ rooms (Boyce,

Potter-Bynoe, Chenevert, & King, 1997). Fre-

quent handwashing reduces person-to-person and

environment-to-person transmission of MRSA

and other bacteria.

Alteration #2: Control of indoor air hydration inhealthcare facilities. Whereas handwashing is

important for HAIs that are spread by direct con-

tact, RH is important because it affects disper-

sion of bacteria-containing droplets that are

aerosolized by coughing. Investigators found

that CRE can be spread by direct contact with

sinks (Crespo et al., 2004). VRE spreads by

direct contact and through contact with contami-

nated surfaces. MRSA is spread by both of these

routes and airborne transmission (Boswell &

Fox, 2006; Shiomori, Miyamoto, & Makishima,

2001).

Flugge in 1897 evaluated the spread of infection

via aerosols. He determined that droplets emitted

from the nose and mouth contained bacteria (Eames

Squire et al. 149

et al., 2009). Wells showed in 1934 that droplet

movement is dependent on droplet size (Wells,

1934; Tang, Li, Eames, Chan & Ridgway, 2006).

In addition, Arundel, Sterling, Biggin, and Sterling

(1986) demonstrated the control of indoor air

hydration/relative humidity between 40% and

60% is effective at mitigating the transmission of

pathogens through the air. Relative humidity (vapor

equilibrium) impacts the droplet size and therefore

the viability of the infectious microorganism. The

mechanism is further described below.

During a cough, about 3,000 droplets are

expelled from the airways at velocities up to 50

miles per hour (American Lung Association,

2018). Sneezes can reach speeds up to 100 miles

per hour and can include up to 100,000 droplets

(American Lung Association, 2018). MRSA’s

diameter ranges in size from 0.5 to 0.7 mm (Had-

dadin, Fappiano, & Lipsett, 2002). The largest

droplets, comprised of saliva and bacteria, settle

quickly and are deposited on surfaces. The bac-

teria are then released as the droplets evaporate.

Larger droplets settle on surfaces at shorter dis-

tances from the source, thereby reducing the area

of the infectious zone (Tang et al., 2006).

Once the infectious droplet has settled, it can

be effectively removed via surface cleaning. An

RH between 40% and 60% is the optimum level

both to reduce transmission of infection and to

prevent mold formation (Arundel, Sterling, Big-

gin, & Sterling, 1986).

In 1948, Dunklin demonstrated that relative

humidity in the “vicinity of 50%” also impacts

the viability of airborne organisms. This provides

a second mechanism by which relative humidity

affects the airborne transmission of bacteria

(Dunklin & Puck, 1948).

In 1959, Kingdon’s work supported the first

explanation. He showed that high humidities

retard droplet evaporation, hastening their fall

and removal from the atmosphere (Kingdon,

1960). In 1986, Arundel’s review corroborated

Dunklin’s research. Arundel et al. (1986) reported

multiple studies that showed mid-range humid-

ities (40-60%) were more lethal than low or high

humidities to nonpathogenic Escherichia coli,

were effective “with showed” the lethality of

intermediate humidities to Escherichia coli

(40% to 60%), effectiveness at preventing fungi

formation, and that these humidity ranges are the

optimum levels to reduce transmission of infec-

tion (Arundel et al., 1986). For these reasons, we

use this range of RH (i.e., 40–60%) in our models.

Alteration #3: Negatively pressured, high efficiencyparticulate air (HEPA) filtered treatment rooms.Additional built environment controls create a

containment barrier between highly infectious

patients and patients susceptible to infection.

Containment barriers such as negative pressure

and HEPA-filtration, decrease the risk of genetic

recombination between infectious species (Bos-

well & Fox, 2006). Private rooms with negative

pressure and HEPA filtration are likely to protect

both patients and hospital staff.

The Department of Energy requires HEPA-

filtration units to filter particulates greater than

or equal to 0.3 mm (Biosafety in Microbiological

and Biomedical Laboratories, 2009). HEPA fil-

tration is known to trap particles down to at least

0.1 mm; MRSA droplets measure 0.5 mm (Biosaf-

ety in Microbiological and Biomedical Labora-

tories, 2009).

Negative pressure rooms exist to block the air-

borne egress of pathogens. During the 2003 Cana-

dian outbreak of severe acute respiratory

syndrome, 46 patients were successfully isolated

using negative pressure rooms. The deployment

of these isolation measures required augmented

staffing, intense ancillary activity, and wide-

spread collaboration within the facility (Loutfy

et al., 2004).

Two years later, in 2006, the work by Boswell

and Fox further supported the effectiveness of

these measures, by demonstrating that HEPA-

filtration blocked the airborne transmission of

MRSA. Boswell and Fox (2006) demonstrated

that HEPA filtration greatly and significantly

reduces the prevalence of pathogenic bacterial

infections within the rooms of highly infectious

patients. These investigators placed agar plates in

three private intensive care unit (ICU) rooms

occupied by three patients with MRSA infections.

Two of the three patients, considered to be “heavy

shedders,” aerosolized enough MRSA to produce

5.0 colony-forming units per 10 hr of exposure.

Placement of portable HEPA-filtration units in

each room reduced contamination by 75%,

150 Health Environments Research & Design Journal 12(2)

90%, and 96% (Boswell & Fox, 2006). In a 2007

review, Li’s conclusions also supported the effec-

tiveness of negative pressure rooms as he identi-

fied multiple studies that demonstrated how

ventilation in the built environment may be

responsible for airborne transmission (Li et al.,

2007).

Proposed tool to facilitate informed decision-making.The principal goal of this investigation was to

quantify the relative effectiveness of multiple

interventions (each consisting of a pair of altera-

tions). The secondary goal was to optimize cost

and effect for these interventions in various sce-

narios. Total cost consists of both the cost of the

intervention and the cost of infection.

As far as we are aware, this is the first technique toanalyze budget, pathogen virulence, and facility sizeconcurrently. By using these models, hospital

administrators can assess cost savings that occur

as a by-product of implementing infection control

measures. Informed decision-making bolsters

patient safety, thereby facilitating an improved

environment of care.

Method

Study Design and Facility Size

We considered three facility sizes with the fol-

lowing bed counts, for the treatment region of

each facility: a 134-bed census count for large

hospitals, a 56-bed count for medium hospitals,

and a 13-bed count for small hospitals. Facility

bed count is distributed between private, two-bed,

three-bed, and six-bed rooms (see Supplement).

We assumed the beds in the treatment region of

this investigation are filled by highly immuno-

compromised patients, without time gaps.

Models. This investigation is based on Chamchod

and Ruan’s (2012) baseline model of hospital

infection rates. This model was expanded into

cost-optimization models for each of the three

alterations, HW, RH, and NP. The cost-

optimization models simultaneously account for

budgets, cost of infections, virulence of pathogen,

and cost of the respective alterations. Given a

limited budget, the investigation determines out-

comes for each facility size.

We initially obtained 24 scenarios, which are

summarized in Table 1. We used three virulence

levels (VRE ¼ 0.4, CRE ¼ 0.22, MRSA ¼ 0.08).

We produced 6 scenarios for large hospitals with

3 virulence levels and 1 budgetary level

($600,000), 12 scenarios for medium hospitals

(budgetary level of $180,000 and $250,000), and

6 scenarios for small hospitals (budgetary levels

of $60,000).

Data. We used the longitudinal data from the

MDRO Repository and Surveillance Network

(MRSN) to model the virulence factors, f(Table 1, column C). These longitudinal data

consist of 6 years of MRSA, CRE, and VRE

infections in one representative hospital pro-

vided by the Walter Reed Army Institute of

Research (WRAIR) MRSN. The virulence fac-

tors are derived from the MRSN’s original data,

based upon the highest increase in the rate of a

specific infection, in 2 consecutive years, over a

6-year period (MRSN, 2017). The virulence fac-

tors (f, an input into the models) measure the

rate of progression from colonization to infec-

tion. Direct costs of infections were determined

from Zimlichman et al. (2013). Associated liti-

gation costs (i.e., indirect costs) were also esti-

mated and incorporated. Indirect costs

incorporate decreased productivity, reduction

of wages, premature death, and burden upon

family members who become caretakers

(Marchetti & Rossiter, 2013). Costs of infection

include indirect and direct costs.

Costs for commercial off-the-shelf items used

in the interventions were determined from these

vendors: Johnson & Johnson, Medline Industries

Inc., Purell (HW intervention), Biological Con-

trols, and Qualitair (RH and NP interventions).

This investigation was conducted from a

healthcare-system perspective. Costs are in

2017 US dollars.

The number of contacts per HCW with possi-

bly unwashed hands is eight, based on the litera-

ture supporting the high efficacy of the HW

alteration (Boyce, 2013). The costs for reducing

these contacts with unwashed hands to zero with

Squire et al. 151

Tab

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Outp

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From

Optim

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ention.C

olu

mn

Jis

mea

sure

dby

the

reduce

dnum

ber

ofin

fect

ions

per

$1,0

00

spen

t.T

he

most

effic

ient

inte

rven

tion

has

the

low

est

valu

ein

Colu

mn

J.C

olu

mns

Kan

dL

repre

sent

the

optim

ized

per

cent

ofbudge

tal

loca

tions

for

Scen

ario

#2

(HW

and

NP).

Colu

mn

Mre

pre

sents

the

num

ber

ofi

nfe

ctio

ns

inSc

enar

io#

2th

atocc

ur

without

this

inte

rven

tion.C

olu

mn

Nan

nota

tes

the

num

ber

ofi

nfe

ctio

ns

inSc

enar

io#

2af

ter

the

use

oft

he

resp

ective

inte

rven

tion.C

olu

mn

Oal

so

repre

sents

the

effic

iency

oft

he

inte

rven

tion

ofS

cenar

io#

2(H

Wan

dN

P),

whic

his

quan

tifie

das

the

reduce

dnum

ber

ofi

nfe

ctio

ns

per

$1,0

00

spen

t.O

ptim

um

dis

trib

ution

off

unds

that

resu

ltin

min

imiz

atio

nofi

nfe

ctio

ns

and

inte

rven

tion

cost

sca

nocc

ur

without

use

of100%

ofth

ebudge

t.Pat

hoge

ns:

MR

SA¼

met

hic

illin

-res

ista

nt

Stap

hylo

cocc

usau

reus

;H

W¼

han

dw

ashin

gst

atio

ns;

CR

E¼

carb

apen

em-r

esis

tant

Ent

erob

acte

riac

eae;

VR

E¼

vanco

myc

in-r

esis

tant

Ent

eroc

occi

.In

fect

ion

num

ber

sth

atre

sulted

indec

imal

valu

esan

dar

ero

unded

up

toth

enea

rest

valu

e.a T

hes

etw

ova

lues

are

diff

eren

tw

hen

the

dec

imal

isac

counte

dfo

r.

152

the HW alteration were $143,300 (large facility),

$64,512 (medium), and $15,438 (small).

We assumed that without an RH alteration, 1%of those uninfected will be infected by each colo-

nized patient. The cost of reducing this infection

rate to zero for the RH alteration was $725,254

(large facility), $304,216 (medium), and

$89,387 (small). We assumed that without an

NP alteration, 1% of uninfected patients will

be infected by each colonized patient via aero-

solization. The cost of reducing this to zero for

the NP alteration is $4,178,408 (large facility),

$1,462,200 (medium), and $208,920 (small).

Multiple studies demonstrate the effectiveness

of negatively pressured, HEPA-filtered rooms

(Boswell & Fox, 2006).

The investigation determines p values using a

one-way Analysis of Variance (ANOVA); p val-

ues less than .05 were considered to be a sta-

tistically significant. This alteration was

conducted for medical facilities that previously

did not have hand sanitizers placed outside

patient treatment rooms. More details on the

costs incorporated into the alteration costs are

available in the Supplemental Section.

Simulation method. We used MATLAB to analyze

the ordinary differential equations (ODEs) of the

model using the Runge–Kutta technique. Cham-

chod and Ruan’s (2012) baseline differential

equations represent the transmission of patho-

genic bacteria (MRSA, CRE, VRE; see Figure 2,

Supplemental Methods section). Additionally,

Chamchod and Ruan cite and utilize over 12 sci-

entific papers to determine the parameters used in

the baseline transmission model (ODEs). The

input variables (see Figure 2A and 2B; Supple-

mental Methods section) in these differential

equations are used to quantify factors that affect

transmission of infection.

This technique resembles a modified version

of the S-I-R-S (susceptible, infectious, recovered,

susceptible) model. This modeling technique cal-

culates theoretical rates of infection based on the

characteristics of the population at risk. We uti-

lized the MATLAB fmincon solver to determine

the optimal budget allocation for each alteration

in an intervention, to minimize overall cost.

Results

The scenario diagram (see Figure 1) summarizes

the key optimized resource allocation results.

Optimization Results Across Models

Table 1 lists the parameters for the multidrug-

resistant pathogen (Table 1, columns A–C), facil-

ity size (Table 1, column D), and respective budget

trade-off analysis (Table 1, columns F-J and K-O).

Costs of infection (Table 1, column B; Marchetti

& Rossiter, 2013, Zimlichman et al., 2013) were

determined based on literature and frequency of

infection over a 6-year time period (MRSN, 2017).

Our model determined the optimal allocation

of funding for three preventative measures. We

used the model to apportion funds between the

following two trade-off, design scenarios: (see

Table 1) Scenario #1: rooms with relative humid-

ity control and improved HW; Scenario #2:

installation and operation of negative pressure

rooms and improved HW.

Optimized solutions of Scenario #1 (RH and

HW) and Scenario #2 (HW and NP) are presented

in columns F–G, I–J, and K–L, N–O, respectively

(Table 1). Columns I and M in Table 1 calculate the

preintervention, annual number of infections.

Based on the results in Table 1 and Figure 1, we

can state the following general remarks: Relative

humidity control combined with improved HW pro-

vides the greatest reduction of infections. Cost-

effectiveness and efficiency of interventions are

reflected by a low value for the reduced infections

per $1,000 expended (Table 1, columns J and O).

The values in columns F and G do not always

sum to the values in column E. This is because the

intervention can sometimes achieve the optimum

result (i.e., the greatest reduction in number of

infections) without using all of the available bud-

get. For the same reason, the values in columns K

and L may not sum to the values in column E. The

two extreme examples, one in each scenario,

show that optimization of infection control is

achieved by spending only one quarter (25%) of

the available funds. This is because the cost of

increasing the intervention effort beyond the opti-

mal level was not offset by the associated cost

savings of reduced infections.

Squire et al. 153

RH HW

Budget$600K

HW NP

Highest % 2nd Highest Not Evaluated in Allocated Allocated Scenario

Budget$180K

RH HW

HW NP

Budget$250K

MediumHospital

RH HW

HW NP

Budget$250K

RH HW

RH HW

HW NP

HW NP

Budget$180K

RH HW

Budget$60K

HW NP

SmallHospital

#

#

^,*

^,*

LargeHospital

#, ^, *

#, ^, *

Figure 1. Scenarios run in optimization models. This figure depicts the decision tree processes involved in theinvestigation. RH¼ relative humidity alteration; HW¼ handwashing alteration; NP¼ negative pressure alteration;yellow ¼ large hospital scenarios; blue ¼ medium hospital scenarios; olive green ¼ small hospital scenarios; # ¼with respect to MRSA pathogen; ^ ¼ with respect to CRE pathogen; *¼ with respect to VRE pathogen; MRSA¼methicillin-resistant Staphylococcus aureus; CRE ¼ carbapenem-resistant Enterobacteriaceae; VRE ¼ vancomycin-resistant Enterococci.

154 Health Environments Research & Design Journal 12(2)

Infections

With the implementation of relative humidity

control and handwashing: In a large hospital,

there was a reduction of 12 infections in the case

of MRSA, 28 infections in the case of CRE, and

42 infections in the case of VRE. In a medium

hospital, there was a reduction of 3 infections

in the case of MRSA, 10 infections in the case

A. Ordinary Differential Equations from the Baseline Transmission Model (Chamchod & Ruan, 2012).U = Uncolonized Patient, C = Colonized Patient, I = Infected Patient, H = Uncontaminated Health Care Worker, Hc = Contaminated Health Care Worker

= (1 − − )Λ − − +

= Λ − − − ( + + )

= Λ + − ( + )

= − − +

= + + −

C. Objective (Goal) Function

( , ) = + +

. . ( , ) = + +

Where,

=

=

= 1 ( . . )

= 2 ( . . )

= decision variable/ budget allocation in % for alteration 1 (e.g. HW)

= decision variable/ budget allocation in % for alteration 2 (e.g. RH)

interventionalteration

B. Parameters for Ordinary Differential Equations from the Baseline Transmission Model

(Chamchod & Ruan, 2012).

Parameter DescriptionProbability that a patient is colonized upon admission into healthcare facility. Probability that a patient is infected upon admission into healthcare facility.Probability of colonization after a contact with a contaminated healthcare worker.Probability of contamination after a contact with a colonized patient.Probability of contamination after a contact with an infected patient. Rate of decolonization.

Probability of a successful treatment.

1/ Average duration of treatment of an infected patient.Rate of progression from colonization to infection.

1/ Average duration of contamination (days).

Death rate of an infected patient (for both diseases and related causes).Discharge rate of an infected patient (for both diseases and related causes).

1/ Average length of stay of an colonized patient (days). Total number of contacts patient requires per dayTotal number of healthcare workers

Λ Daily admission rate

D. Constraints for Objective (Goal) Function

( , ) = + ≤

( , ) = + ≤ 1

( , ) = ≥ 0

( , ) = ≥ 0

( , ) = ≤ 1

Figure 2. Mathematical equations for optimization models. (A, top left) Baseline transmission model, ordinarydifferential equations (Chamchod & Ruan, 2012). (B, top right) Parameter definitions (Chamchod & Ruan, 2012).(C, bottom left) Objective (goal) function for optimization of decision variables. (D, bottom right) Constraints forobjective (goal) function and associated dual variables.

Squire et al. 155

of CRE, and 16 infections in the case of VRE.

In a small hospital, there was a reduction of

two infections in the case of CRE and three

infections in the case of VRE (and no reduc-

tion in the case of MRSA).

With the implementation of negative pressure

and handwashing: In a large hospital, there was a

reduction of 10 infections in the case of MRSA,

22 infections in the case of CRE, and 31 infec-

tions in the case of VRE. In a medium hospital,

there was a reduction of 3 infections in the case of

MRSA, 9 infections in the case of CRE, and 15

infections in the case of VRE. In a small hospital,

there was a reduction of two infections in the case

of CRE and three infections in the case of VRE

(and no reduction in the case of MRSA).

Cost Savings From the Interventions

The high cost of these expensive strategies

(negative pressure rooms and relative humidity

control) is justified by the cost savings, as

detailed below:

Among the 12 trials in Scenario # 1 and in the

absence of either of these two alterations (RH and

HW), the model projected an average of 17 infec-

tions (rounded up to the next whole number).

Whereas in the presence of these alterations

(postintervention), the model projected an aver-

age of only five infections. Thus, the difference of

12 infections represents the number of infections

prevented. The distribution of funds between the

two alterations was optimized to maximize the

number of infections prevented. The model fur-

ther projected that spending $1,000 would pre-

vent an average of 0.0688 infections (Table 2,

column E). On average, spending $18,705 would

prevent one infection (total cost expended across

each scenario, divided by total infections

prevented).

Scenario #2: Among the 12 trials in Scenario #

2, without either of the two alterations, the model

again projected an average of 17 infections;

whereas in the presence of the HW and NP altera-

tions, the model projected an average of only 7

infections. Thus, 10 infections were prevented by

optimizing the distribution of funds between

these two alterations. The model further projected

that spending $1,000 would prevent an average of

0.0914 infections (Table 2, column I). On aver-

age, spending $18,406 would prevent one infec-

tion (total cost expended across each scenario,

divided by total infections prevented).

Associations

Certain trends were evident across the three spe-

cies of pathogenic bacteria. The models gener-

ally demonstrated an inverse relationship

between the budget and HW resource allocation,

that is, as the budget decreases, the resource

allocation to HW increases. The budget and

NP resources are directly proportional to one

another, that is, as the budget decreases, NP

resource allocation also decreases.

The models generally demonstrated an

inverse relationship between the budget

and HW resource allocation.

The budget and NP resources are directly

proportional to one another . . .

Another association is that within the

$180,000–$250,000 budget range, increased RH

resource allocation will optimally protect against

increasingly virulent species of bacteria.

Bed Count (i.e., Facility Size)

As the bed count increases, NP resourcing also

increases. Therefore, NP resource allocation is

directly proportional to the bed count.

This investigation determined the prioritiza-

tion order of pairs of alterations, to minimize

infection and cost. Specific examples of unanti-

cipated results are discussed below.

Specific Examples

MRSA and large and medium hospitals. When eval-

uating alterations for MRSA infections in large

and medium hospitals, as the available budget

decreases, RH resource allocation decreases. Spe-

cifically, when a budget of $600 K is used, RH

has priority (see Table 1, column F).

CRE and large hospitals. As the budget decreases

from $600,000, RH resourcing decreases. At

156 Health Environments Research & Design Journal 12(2)

Tab

le2.

Anal

ysis

and

Sign

ifica

nce

ofT

rade-

Offs

Bet

wee

nT

hre

eIn

terv

entions.

Scen

ario

sSc

enar

io#

1,R

elat

ive

Hum

idity

Contr

olan

dH

andw

ashin

gSt

atio

ns

Scen

ario

#2,H

andw

ashin

gSt

atio

ns

and

Neg

ativ

ePre

ssure

Tri

al#

Rel

ativ

eH

um

idH

and

Was

hIn

fect

ion

With

Inte

rven

tion

Red

uce

dIn

fect

ion

per

$1,0

00

Han

dW

ash

Neg

ativ

ePre

ssure

Infe

ctio

nW

ith

Inte

rven

tion

Red

uce

dIn

fect

ion

per

$1,0

00

AB

CD

EF

GH

I

1to

266%

25%

3in

fect

ions

0.0

21

29%

61%

5in

fect

ions

0.0

17

3to

472%

28%

8in

fect

ions

0.0

46

31%

69%

14

infe

ctio

ns

0.0

37

5to

671%

29%

15

infe

ctio

ns

0.0

69

33%

67%

26

infe

ctio

ns

0.0

51

7to

818%

38%

2in

fect

ions

0.0

34

39%

0%

2in

fect

ions

0.0

48

9to

10

13%

27%

2in

fect

ions

0.0

34

28%

0%

2in

fect

ions

0.0

48

11

to12

54%

44%

3in

fect

ions

0.0

56

47%

0%

4in

fect

ions

0.1

11

13

to14

39%

32%

3in

fect

ions

0.0

56

34%

0%

4in

fect

ions

0.1

11

15

to16

54%

46%

6in

fect

ionsa

0.0

90

50%

0%

7in

fect

ions

0.1

67

17

to18

48%

35%

6in

fect

ionsa

0.0

80

36%

0%

7in

fect

ions

0.1

67

19

to20

0%

25%

1in

fect

ion

0.0

46

25%

0%

1in

fect

ion

0.0

46

21

to22

0%

31%

1in

fect

ion

0.1

13

31%

0%

1in

fect

ion

0.1

13

23

to24

0%

34%

2in

fect

ions

0.1

81

34%

0%

2in

fect

ions

0.1

81

Mea

ns,

stan

dar

ddev

iations

36.2

%(+

28.5

%)

32.8

%(+

6.9

%)

4.3

infe

ctio

ns

(+4.0

infe

ctio

ns)

0.0

688

(+0.0

439)

34.7

%(+

7.4

%)

16.4

%(+

29.7

%)

6.2

infe

ctio

ns

(+7.2

infe

ctio

ns)

0.0

914

(+0.0

58)

Diff

eren

cein

mea

ns,

pva

lues

3.4

%p¼

.000135

bp¼

.000291

b18.3

%p¼

.001219

bp¼

.004359

b

Not

e.T

able

dep

icts

the

stat

istica

lan

alys

isfo

rT

rial

s1–24:m

eans

and

stan

dar

ddev

iations

(Colu

mns

B,C

,D

,E,F,

G,H

,an

dI)

,diff

eren

cein

mea

ns

(colu

mns

Can

dG

),an

das

soci

ated

pva

lues

(colu

mns

D,E,H

,an

dI)

.p

Val

ues

wer

eca

lcula

ted

usi

ng

aone-

way

AN

OV

Ast

atis

tica

lte

st.T

he

pva

lue,

p¼

.000135,dem

onst

rate

sst

atis

tica

lsi

gnifi

cance

bet

wee

nth

ebudge

tper

centa

geal

loca

tions

(Sce

nar

io#

1,c

olu

mns

Ban

dC

)an

dth

enum

ber

sofin

fect

ions

post

inte

rven

tion

(Sce

nar

io#

1,c

olu

mn

D).

The

pva

lue,

p¼

.000291,d

emonst

rate

sst

atis

tica

lsig

nifi

cance

bet

wee

nth

ebudge

tper

centa

geal

loca

tions

(Sce

nar

io#

1,co

lum

ns

Ban

dC

)an

dth

enum

ber

ofre

duce

din

fect

ions

per

$1,0

00

expen

ded

(Sce

nar

io#

1,co

lum

nE).

The

pva

lue,

p¼

.00129,dem

onst

rate

sst

atis

tica

lsi

gnifi

cance

bet

wee

nth

ebudge

tper

centa

geal

loca

tions

(Sce

nar

io#

2,co

lum

ns

Fan

dG

)an

dth

enum

ber

sofin

fect

ions

post

inte

rven

tion

(Sce

nar

io#

2,co

lum

nH

).T

he

pva

lue,

p¼

.004359,d

emonst

rate

sst

atis

tica

lsig

nifi

cance

bet

wee

nm

easu

res

(acr

oss

the

valu

es)

for

the

budge

tper

centa

geal

loca

tions

(Sce

nar

io#

2,c

olu

mns

Fan

dG

)an

dth

enum

ber

ofre

duce

din

fect

ions

per

$1,0

00

expen

ded

(Sce

nar

io#

2,co

lum

nI)

.p

Val

ues

less

than

.05

wer

edet

erm

ined

tohav

ea

stat

istica

llysi

gnifi

cant

diff

eren

ce.

a Rep

rese

nts

diff

eren

tva

lues

when

acco

unting

for

dec

imal

s.bSt

atis

tica

llysi

gnifi

cant

bas

edon

aone-

way

AN

OV

Ate

st.

157

$600,000, RH is at 72% (in Scenario #1) and NP

is at 69% (in Scenario #2); thus, the delta

between NP and RH, between the scenarios,

is 3% (see Table 1, columns F and L). In these

instances, delta designates an absolute differ-

ence; more specifically, it is the absolute per-

centage difference in allocated funds between

any two alterations.

Statistical analysis. In Table 2, we provide a brief

statistical analysis of all of our design scenarios to

identify global trends in our results. Columns B,

C, D, and E show a summary of the model results

for Scenario #1. Averaging over all trials, our

model proposed investing 36.2% in relative

humidity control and 32.8% in improved HW,

which produced a mean difference of 3.4%. The

average number of infections postintervention,

across the 24 trials of Scenario #1, was 5 infec-

tions (rounded up from 4.3), with a p ¼ .000135.

Using a one-way ANOVA across the budget allo-

cation percentages (Table 1, columns F and G)

and the reduced infections per $1,000 (Table 1,

column J) results in p ¼ .000291.

Similarly, Table 2, columns F, G, H, and I

show a summary of model results for Scenario

#2. The model proposed investing an average of

16.4% of the allocated budget in negative pres-

sure rooms and 34.7% in improved HW, which

produced a mean difference of 18.3%. The aver-

age reduction of infections across the trials of

Scenario #2 was seven infections (rounded up

from 6.2), with p ¼ .00122. Using a one-way

ANOVA statistical analysis across the budget

allocation percentages (Table 1, columns K and

L) and the reduced infections per $1,000 (Table 1,

column O) results in p ¼ .00436.

Discussion

Our research questions focus on optimizing cost

and effectiveness of these interventions in various

scenarios (see Figures 2; Supplemental Results)

and on comparing the combined effectiveness of

a pair of alterations to another feasible pair. The

overall reduction of infections is greater in Sce-

nario #1 (RH and HW) than in Scenario #2 (HW

and NP).

The overall reduction of infections is

greater in Scenario #1 (RH and HW) than

in Scenario #2 (HW and NP).

The results demonstrate an inverse relation-

ship between the budget and handwashing

alterations, with the exception of the small hos-

pital MRSA scenario (see Table 1). As the

budget increased, handwashing resourcing

decreased. The benefit of HW is significant,

but maximum benefit can be obtained with a

relatively small investment. This effect is sup-

ported by a study undertaken in ICU environ-

ments (Jayaraman et al., 2014), which

demonstrates that when handwashing compli-

ance is at an extremely high level, the benefits

plateau.

The benefit of HW is significant, but

maximum benefit can be obtained with a

relatively small investment.

For any of the three bacterial species, and

within the $180,000 to $250,000 budget range,

there is an inverse relationship between the

budget and resource allocation for the relative

humidity alteration (see Table 1). The NP

alteration is directly proportional to the budget.

These findings are likely due to the expense of

these alterations as well as their impact on

mitigating transmission of pathogenic bacteria

from a colonized to an uncolonized patient.

The RH and HW scenarios best contain

multidrug-resistant bacteria. The HW and NP

alterations generally had the largest allocation

of resources for the larger sized healthcare

facilities (see Figure 1).

These results can be generalized to facilities

(or sections thereof) of various sizes by simply

modifying the bed count in the model. The

associated up-front costs can also be adjusted

in the models as needed. Methods described in

this article can be used to allocate resources in

the face of epidemics or facility outbreaks.

Finally, these methods can be used to inform

decision-making when unexpected funding

becomes available.

158 Health Environments Research & Design Journal 12(2)

Limitations

The infectious disease data derive from a

single, representative, medium-sized hospital.

Incorporation of data from multiple healthcare

facilities would likely improve the ability to

apply these determinations to a diversity of facil-

ities. This investigation only evaluated three

multidrug-resistant pathogenic bacteria and does

not include other causes of HAIs that may not

necessarily be due to an MDRO, such as C. dif-

ficile. An additional limitation is that the impact

of the bacterial infection by age-group is not

evaluated.

Conclusion

In this study, we developed a novel mathematical

approach that integrates hospital design and

infection control within a budget framework.

We used original longitudinal data, representing

6 years of observation in a single facility. The

budget allocations are representative of funding

that a facility, based on its size, would likely

receive for annual repairs and renovations. In this

research, we have determined how cost-effective

resource allocation enhances the built environ-

ment to provide effective infection control to

reduce the transmission of three bacterial patho-

gens from one human host to another.

We have conducted this analysis for 24 sce-

narios. Each scenario represents a unique combi-

nation of facility size, facility budget, pathogen

virulence, and alteration pairing. Each of these

pairs is derived from combinations of HW, neg-

ative pressure rooms, and control of relative

humidity between 40% and 60%.

Determinations from these models can inform

infection control strategies as architects, owners,

engineers, and medical providers plan, design,

and renew healthcare facilities. With this infor-

mation, designers and planners can exercise

novel insights as to the interactions between the

built environment, expenditure of resources, and

HAIs. In doing so, they are better prepared to

address the containment of multidrug-resistant

pathogens that are endemic in healthcare facili-

ties today.

With this information, designers and

planners can exercise novel insights as to

the interactions between the built

environment, expenditure of resources,

and HAIs. In doing so, they are better

prepared to address the containment of

multidrug-resistant pathogens that are

endemic in healthcare facilities today.

Implications for Practice

� This knowledge better prepares healthcare

facilities for the containment of multidrug-

resistant pathogens.

� These mathematical optimization tools can

better inform design decisions made by

healthcare executives and project delivery

teams, helping bolster patient safety and

enhance environments of care.

� These findings contribute to knowledge that

can shape best practices among hospital

design, including better use of RH control

and negatively pressured patient rooms, as

well as greater compliance of existing HW

practices.

Authors’ Note

The article has been reviewed by the Walter Reed

Army Institute of Research. There are no objec-

tions to its presentation. The opinions or asser-

tions contained herein are the private views of the

authors and are not to be construed as official or

reflecting the views of the Department of the

Army or the Department of Defense.

Acknowledgment

The Walter Reed Army Institute of Research

Multidrug-Resistant Organism Repository and

Surveillance Network provided the 6-year period,

original, longitudinal, infectious disease data.

The authors would like to thank Major Anthony

Jones and Lieutenant Colonel Mary Hinkle of the

Walter Reed Army Institute of Research, for their

feedback and collaboration throughout the inves-

tigation. Alexandros Moissiadis and Ramyani

Sengupta contributed extensively in the model

Squire et al. 159

development and data collection phase. Eili

Klein, assistant professor of Emergency Medi-

cine, Johns Hopkins, contributed helpful feed-

back to the investigation.

Declaration of Conflicting Interests

The authors declared no potential conflicts of

interest with respect to the research, authorship,

and/or publication of this article.

Funding

The authors disclosed receipt of the following

financial support for the research, authorship,

and/or publication of this article: This study was

funded by the U.S. Army Medical Command,

U.S. Army Medical Department Center and

Schools and Johns Hopkins University.

Supplemental Material

Supplemental material for this article is available

online.

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