Modeling Nosocomial Infections of Methicillin-Resistant Staphylococcus aureus with Environment Contamination<sup/>

Abstract

In this work, we investigate the role of environmental contamination on the clinical epidemiology of antibiotic-resistant bacteria in hospitals. Methicillin-resistant Staphylococcus aureus (MRSA) is a bacterium that causes infections in different parts of the body. It is tougher to treat than most strains of Staphylococcus aureus or staph, because it is resistant to some commonly used antibiotics. Both deterministic and stochastic models are constructed to describe the transmission characteristics of MRSA in hospital setting. The deterministic epidemic model includes five compartments: colonized and uncolonized patients, contaminated and uncontaminated health care workers (HCWs), and bacterial load in environment. The basic reproduction number R ₀ is calculated, and its numerical and sensitivity analysis has been performed to study the asymptotic behavior of the model, and to help identify factors responsible for observed patterns of infections. A stochastic epidemic model with stochastic simulations is also presented to supply a comprehensive analysis of its behavior. Data collected from Beijing Tongren Hospital will be used in the numerical simulations of our model. The results can be used to provide theoretical guidance for designing efficient control measures, such as increasing the hand hygiene compliance of HCWs and disinfection rate of environment, and decreasing the transmission rate between environment and patients and HCWs.

Figure 1

A compartmental model of transmission dynamics of meticillin-resistant Staphylococcus aureus among patients and healthcare workers (HCWs) with environmental contamination.

Figure 2

Solutions of colonized (P _c(t)) and uncolonized (P _u(t)) patients of the deterministic epidemic model (1) with initial values $(P_u^0,P_c^0,H_u^0,H_c^0,B_e^0)=(10,13,17,6,1000)$.

Figure 3

(a) R ₀ vs hand hygiene compliance η, and (b) R ₀ vs disinfection rate γ _b.

Figure 4

R ₀ vs hand hygiene compliance η and disinfection rate γ _b, compared with the baseline plane of R ₀ = 1.

Figure 5

(a) R ₀ vs contamination rate of the environment by colonized patients ν _p, and (b) R ₀ vs contamination rate of the environment by contaminated HCWs ν _h.

Figure 6

R ₀ vs contamination rate of the environment by colonized patients ν _p and contamination rate of the environment by contaminated HCWs ν _h, compared with the baseline plane of R ₀ = 1.

Figure 7

(a) R ₀ vs contamination rate from the environment to uncolonized patients k _p, and (b) R ₀ vs contamination rate from the environment to uncontaminated HCWs k _h.

Figure 8

R ₀ vs colonization rate from the environment to uncolonized patients k _p and colonization rate from the environment to uncontaminated HCWs k _h, compared with the baseline plane of R ₀ = 1.

Figure 9

Ten sample paths of the bacterial load in environment in nosocomial infection model with environment infection are graphed with the deterministic solution (black curve). The parameter values are Δt = 0.01, N _p = 23, N _h = 23, θ = 0.067, α _p = 0.0435, β _p = 0.72, β _h = 0.20, η = 0.4, γ _u = 0.067, γ _c = 0.046, γ _b = 0.7, k _p = 0.000004, k _h = 0.00001, (1 − η) = 0.6, μ _c = 24, v _p = 235, v _h = 235, time = 365, $P_c^0=13,H_c^0=6,B_e^0=1000$.

Figure 10

Ten sample paths of the number of colonized patients in nosocomial infection model with environment infection are graphed with the deterministic solution (black curve). The parameter values are Δt = 0.01, N _p = 23, N _h = 23, θ = 0.067, α _p = 0.0435, β _p = 0.72, β _h = 0.20, η = 0.4, γ _u = 0.067, γ _c = 0.046, γ _b = 0.7, k _p = 0.000004, k _h = 0.00001, (1 − η) = 0.6, μ _c = 24, v _p = 235, v _h = 235, time = 365, $P_c^0=13,H_c^0=6,B_e^0=1000$.

Figure 11

Ten sample paths of the number of contaminated HCWs in nosocomial infection model with environment infection are graphed with the deterministic solution (black curve). The parameter values are Δt = 0.01, N _p = 23, N _h = 23, θ = 0.067, α _p = 0.0435, β _p = 0.72, β _h = 0.20, η = 0.4, γ _u = 0.067, γ _c = 0.046, γ _b = 0.7, k _p = 0.000004, k _h = 0.00001, (1 − η) = 0.6, μ _c = 24, v _p = 235, v _h = 235, time = 365, $P_c^0=13,H_c^0=6,B_e^0=1000$