Optimal control applied to community-acquired methicillin-resistant Staphylococcus aureus in hospitals

Figures & data

Figure 1. CA-MRSA schematic.

Table 1. Parameter values [4].

Symbol	Description	Baseline Value
N	Total number of patients in the hospital	400
Λ	Total admissions per day	70
${\lambda }_{CC}$	Fraction of colonized CA-MRSA admissions	0.03
${\lambda }_{CH}$	Fraction of colonized HA-MRSA admissions	0.07
${\lambda }_{IC}$	Fraction of infected CA-MRSA admissions	0.005
${\lambda }_{IH}$	Fraction of infected HA-MRSA admissions	0.0017
$1/{\gamma }_S$	Average LOS of susceptible patients	5 days
$1/{\gamma }_{CC}$	Average LOS of colonized CA-MRSA patients	5 days
$1/{\gamma }_{CH}$	Average LOS of colonized HA-MRSA patients	7 days
$1/{\gamma }_{IC}$	Average LOS of infected CA-MRSA patients	10 days
$1/{\gamma }_{IH}$	Average LOS of infected HA-MRSA patients	18 days
η	Hand hygiene compliance fraction (0 to 1)	0.6
${\beta }_{CC}$	Colonized /colonized CA-MRSA transmission rate	0.36
${\beta }_{CH}$	Colonized /colonized HA-MRSA transmission rate	0.27
${\beta }_{IC}$	Infected /colonized CA-MRSA transmission rate	0.09
${\beta }_{IH}$	Infected /colonized HA-MRSA transmission rate	0.07
${\delta }_C$	Infected CA-MRSA patient death rate	0.033
${\delta }_H$	Infected HA-MRSA patient death rate	0.2
${\phi }_C$	Colonized CA-MRSA patient infection rate	0.1
${\phi }_H$	Colonized HA-MRSA patient infection rate	0.1
${\tau }_C$	Infected CA-MRSA patient cure rate	0.967
${\tau }_H$	Infected HA-MRSA patient cure rate	0.8
${\alpha }_{CC}$	Decolonization rate of infected CA-MRSA patient	0
${\alpha }_{CH}$	Decolonization rate of infected HA-MRSA patient	0

$\mathrm{LOS}=\mathrm{lengthofstay}$.

Figure 2. Patients: $S\left(t\right),CC\left(t\right),CH\left(t\right),IC\left(t\right),IH\left(t\right)$ without control, N=400. (a) Susceptible Patients w/o control (b) Patients colonized and infected with CA-MRSA, patients colonized and infected with HA-MRSA w/o control.

Figure 3. Patients: $S\left(t\right),CC\left(t\right),CH\left(t\right),IC\left(t\right),IH\left(t\right)$ with 3 controls, $D_1=D_2=D_3=5,D_4=1,N=400$. (a) Susceptible Patients with 3 Controls (b) Patients colonized and infected with CA-MRSA, patients colonized and infected with HA-MRSA with 3 controls.

Figure 4. Optimal Decolonization for patients colonized with CA-MRSA, $D_2=D_3=5,D_4=1,N=400$. (a) Optimal Decolonization for patients colonized with CA-MRSA, $D_1=5$ (b) Optimal Decolonization for patients colonized with CA-MRSA, $D_1=15$.

Figure 5. Optimal Screening for patients colonized and infected with CA-MRSA, $D_1=D_2=D_3=5,D_4=1,N=400$. (a) Optimal Screening for patients colonized with CA-MRSA (b) Optimal Screening for patients infected with CA-MRSA.

Figure 6. Patients: $S\left(t\right),CC\left(t\right),CH\left(t\right),IC\left(t\right),IH\left(t\right)$ with 3 controls, $D_1=15,D_2=D_3=5,D_4=1,N=400$. (a) Susceptible Patients with 3 Controls (b) Patients colonized and infected with CA-MRSA, patients colonized and infected with HA-MRSA with 3 controls.

Figure 7. Patients: $S\left(t\right),CC\left(t\right),CH\left(t\right),IC\left(t\right),IH\left(t\right)$ with 1 control, $D_1=5,D_2=D_3=0,D_4=1,N=400$. (a) Susceptible Patients with 1 Control (b) Patients colonized and infected with CA-MRSA, patients colonized and infected with HA-MRSA with 1 control.

Figure 8. Optimal Decolonization for patients colonized with CA-MRSA, $D_2=D_3=0,D_4=1,N=400$. (a) Optimal Decolonization for patients colonized with CA-MRSA, $D_1=5$ (b) Optimal Decolonization for patients colonized with CA-MRSA, $D_1=15$.

E.M.C. D'Agata, G.F. Webb, M.A. Horn, R.C. Moellering, and S. Ruan, Modeling the invasion of community-acquired methicillin-resistant Staphylococcus aureus into hospitals, Clin. Infect. Dis. 48 (2009), pp. 274–284.

 PubMed Web of Science ®Google Scholar