Modeling methicillin-resistant Staphylococcus aureus in hospitals: transmission dynamics, antibiotic usage and its history

Abstract

Background: Methicillin-resistant Staphylococcus aureus (MRSA) is endemic in many hospital settings, posing substantial threats and economic burdens worldwide.

Methods: We propose mathematical models to investigate the transmission dynamics of MRSA and determine factors that influence the prevalence of MRSA infection when antibiotics are given to patients to treat or prevent infections with either MRSA itself or other bacterial pathogens.

Results: Our results suggest that: (i) MRSA always persists in the hospital when colonized and infected patients are admitted; (ii) the longer the duration of treatment of infected patients and the lower the probability of successful treatment will increase the prevalence of MRSA infection; (iii) the longer the duration of contamination of health care workers (HCWs) and the more their contacts with patients may increase the prevalence of MRSA infection; (iv) possible ways to control the prevalence of MRSA infection include treating patients with antibiotic history as quickly and efficiently as possible, screening and isolating colonized and infected patients at admission, and compliance with strict hand-washing rules by HCWs.

Conclusion: Our modeling studies offer an approach to investigating MRSA infection in hospital settings and the impact of antibiotic history on the incidence of infection. Our findings suggest important influences on the prevalence of MRSA infection which may be useful in designing control policies.

Figure 1

A flow diagram for the baseline model. The diagram shows the baseline model to describe transmission dynamics of MRSA in hospitals and the inflows and outflows of uncolonized, colonized and infectious patients (U, C and I), and uncontaminated and contaminated HCWs (H,H_c).

Figure 2

A flow diagram for the extended model with history of antibiotic usage in patients. The diagram shows the inflows and outflows of two groups of patients, with and without history of antibiotic usage, and HCWs.

Figure 3

Prevalence of MRSA infection. Numerical solutions: (a) the number of infectious patients when R₀ = 0.3 that MRSA is endemic when admission of colonized and infectious patients is present (dashed trace) and it dies out when there is no admission of colonized and infectious patients (solid trace): (b) the endemic number of infectious patients when R₀ = 1.7 while admission of colonized and infectious patients is present and absent (dashed and solid traces, respectively): (c) the prevalence of MRSA infection in the hospital when duration of treatment and probability of a successful treatment vary: and (d) the prevalence of MRSA infection when duration of contamination in HCWs and the number of required contacts from patients vary.

Figure 4

Prevalence of MRSA infection when history of antibiotic usage is taken into account. Numerical solutions: (a) the proportions of infectious patients with and without history of antibiotic exposure (dashed and solid traces, respectively): (b) the prevalence of MRSA infection in the hospital when duration of treatment in patients with and without antibiotics vary: (c) the prevalence of MRSA infection in the hospital when probability of a successful treatment in patients with and without antibiotics vary: and (d) the number of infectious patients according to the probability of treatment failure in the first therapy ( ${\lambda }_u=0.62,{\lambda }_{\mathit{\text{uA}}}=0.349,{\lambda }_c=0.01,{\lambda }_{\mathit{\text{cA}}}=0.03,{\lambda }_i=0,{\lambda }_{\mathit{\text{iA}}}=0.001,{\gamma }_u={\gamma }_{\mathit{\text{uA}}}=1/5,\kappa =1/7,m_1=0.2,m_{1A}=0.3,m_2=0.01,m_{2A}=0.005,\varphi =m_1\kappa ,{\varphi }_A=m_{1A}\kappa ,\omega =m_2\kappa ,\omega =m_{2A}\kappa ,{\gamma }_c=(1-m_1-m_2)\kappa ,{\gamma }_{\mathit{\text{cA}}}=(1-m_{1A}-m_{2A})\kappa ,{\rho }^s=0.5,{\rho }^u=0.15,\tau =1/10,{\tau }_A=1/14,{\gamma }_i=(1-{\rho }^s-{\rho }^u)\tau ,{\gamma }_{\mathit{\text{iA}}}=(1-{\rho }_A){\tau }_A,a=8,b_p=0.015,b_{\mathit{\text{pA}}}=0.025,b_{\mathit{\text{hc}}}=0.1,b_{\mathit{\text{hcA}}}=0.15,b_{\mathit{\text{hi}}}=0.25,b_{\mathit{\text{hiA}}}=0.3,\mu =1/(1/24)$).

Figure 5

Optimal control. Numerical studies of optimal control strategies and solutions (A = 1 or 1555,B = 1 or 3000, E = 1/2, F = 1/2): (a) the optimal treatment rates for the baseline model when admission of colonized and infectious patients is present or absent (solid and dashed traces, respectively): (b) the number of infectious patients corresponding to the optimal treatment rates: (c) the optimal treatment rates for patients with and without antibiotic exposure when admission of colonized or infectious patients is present or absent (solid trace=without antibiotic exposure but with admission of colonized or infectious patients, dotted trace=with antibiotic exposure and admission of colonized or infectious patients, dashed trace=without antibiotic exposure and admission of colonized or infectious patients, dashed-dotted trace=with antibiotic exposure but without admission of colonized or infectious patients): (d) the number of infectious patients corresponding to the optimal treatment rates (lines are defined in (c)).