Modeling the impact of interventions against Acinetobacter baumannii transmission in intensive care units

Figures & data

Figure 1. A compartmental model describing the transmission dynamics of A. baumannii in an intensive care unit. The solid arrows represent entry to and exit from the 5 compartments: C, colonized without antibiotic exposure; C_A, colonized with antibiotic exposure; I, infected; U, uncolonized without antibiotic exposure; U_A, uncolonized with antibiotic exposure. The broken arrows represent the shed of bacteria into the environment (E) from colonized and infected patients, and the transmission from free-living bacteria in the environment to susceptible (uncolonized) patients.

Table 1. Baseline input values of model variables

Variable	Definition (unit)	Baseline value	Reference
ϵ	Antibiotic prescribing rate (/day)^a	0.12	23,24
λ	Recovery rate of intestinal microbiota (/day)	0.03	25
β	Cross-transmission coefficient (/colonized/susceptible/day)	50 × 10^−4	4
ζ	Environment-patient transmission coefficient (/CFU/susceptible/day)	4 × 10^−6	30
Ω1	Infectivity of CA relative to C	1.67	29
Ω2	Infectivity of I relative to C	2	29
θA	Rate of CA becoming infected (symptom development rate) (/day)	0.11	5
θ	Rate of C becoming infected (symptom development rate) (/day)	θA/5	32
τ	Treatment of A. baumannii infection (/day) (1/antibiotic treatment duration of infected patients)	0.08	33,34
σ	Treatment success rate of A. baumannii infection (/treated patient)	0.76	34
η	Rate of self-resolution of symptoms (/day)^b	0.018	35
f	Fatality rate of infected patients (/day)^c	0.016	36
r	Environmental cleaning rate (/day)	0.70	30
α	Efficacy of environmental cleaning (/CFU)	0.55	31
h	Compliance with hand hygiene	0.82	27
γU, γUA	Discharge rate of U and UA (/day)	0.18	19,20
γC, γCA	Discharge rate of C and CA (/day)	0.06	21,22
Λ	Admission rate (/day)	Rate of leaving the ICU^d
μU, μUA	Proportion of U and UA on admission	57.6%; 36.8%	16
μC, μCA, μI	Proportion of C, CA and I on admission	0.3%; 5.3%; 0%	16,17
Φ1, Φ2, Φ3	Bacterial density shed into the environment by C, CA and I (CFU/patient/day)	281; 470; 563	30

^a Calibrates to 59.5% of patients receiving antibiotics any time during their ICU stay.

^b Calibrates to 15% of infected patients having symptoms that self-resolve.

^c Calibrates to 14% attributable mortality rate.

^d Admission rate, ${\displaystyle \text{Λ}={\gamma }_{\text{U}}U+{\gamma }_{\text{A}}{U}_{\text{A}}+{\gamma }_{\text{C}}C+{\gamma }_{\text{CA}}{C}_{\text{A}}+fI}$

C, colonized without antibiotic exposure; C_A, colonized with antibiotic exposure; CFU, colony-forming unit; I, infected; ICU, intensive care unit; U, uncolonized without antibiotic exposure; U_A, uncolonized with antibiotic exposure.

Table 2. Variation range for variables evaluated in sensitivity analysis

Variable	Symbol	Range	Reference
Treatment success rate of A. baumannii infection	σ	0.6–0.9	34
Rate of self-resolution of symptoms	η	0.018–0.022	±10%
Cross-transmission coefficient	β	39–71 × 10^−4	4
Environment-patient transmission coefficient	ζ	3.4–4.6 × 10^−6	30
Fatality rate of infected patients^a	f	0.006– 0.020	36,55
LoS of colonized patients	${\displaystyle {\gamma }_{\text{C}}^{-\text{1}}}$	7–25	4,43

^a Calibrates to 6% and 17% attributable mortality rate, respectively.

LoS, length of stay.

Figure 2. Prevalence of patients colonized and infected with A. baumannii at baseline.

Figure 3. Effects of individual interventions on the prevalence of colonization (long-dashed lines), infection (short-dashed lines), total colonization and infection (solid lines), and the basic reproduction ratio, R₀ (dotted lines). The following interventions were investigated: compliance with hand hygiene (A), environmental cleaning rate (B), environmental cleaning efficacy (C), length of stay of colonized patients (D), antibiotic prescribing rate (E), treatment duration of infected patients (F), and recovery of intestinal microbiota (G).

Figure 4. Relative effects of different interventions on the total prevalence of colonized and infected patients (A), and the basic reproduction ratio, R₀ (B).

Figure 5. Prevalence of A. baumannii when the basic reproduction ratio, R₀ < 1 (A) and R₀ > 1 (B). When R₀ <1, A. baumannii persists when colonized and infected patients are admitted (solid lines), and will die out if there is no admission of colonized and infected patients (broken lines). When R₀ >1, A. baumannii always persists, once it has been introduced into the ward, irrespective of whether colonized and infected patients are admitted.

Figure 6. Effects of different combinations of interventions on the total prevalence of colonization and infection (A, C, E), and the basic reproduction ratio, R₀ (B, D, F).

Figure 7. Effects of varying cross-transmission coefficient (β) and environment-transmission coefficient (ζ) on the prevalence of colonization and infection (A), and the basic reproduction ratio, R₀ (B). β and ζ were set at 50 × 10⁻⁴ and 4 × 10⁻⁶ at baseline, respectively.

Figure 8. Sensitivity analysis.

Table 3. Correlation coefficients

	Correlation coefficients
Variable	Prevalence of colonized patients	Prevalence of infected patients	R0
Treatment success rate of A. baumannii infection (σ)	−0.85	−0.93	−0.94
Rate of self-resolution of symptoms (η)	0.15	−0.29	0.00
Cross-transmission coefficient (β)	0.13	0.16	0.26
Environment-patient transmission coefficient (ζ)	0.93	0.96	0.98
Fatality rate of infected patients (f)	−0.37	−0.93	−0.86
LoS of colonized patients ${\displaystyle \text{(}{\gamma }_{\text{C}}^{-\text{1}}\text{)}}$	1	0.60	0.99

LoS, length of stay; R₀, basic reproduction ratio.