The effect of re-directed patient flow in combination with targeted infection control measures on the spread of multi-drug-resistant Enterobacteriaceae in the German health-care system: a mathematical modelling approach

Regional patient transfer patterns matter for the spread of hospital-acquired pathogens

Pathogens typically responsible for hospital-acquired infections (HAIs) constitute a major threat to healthcare systems worldwide. They spread via hospital (or hospital-community) networks by readmissions or patient transfers. Therefore, knowledge of these networks is essential to develop and test strategies to mitigate and control the HAI spread. Until now, no methods for comparing healthcare networks across different systems were proposed. Based on healthcare insurance data from four German federal states (Bavaria, Lower Saxony, Saxony and Thuringia), we constructed hospital networks and compared them in a systematic approach regarding population, hospital characteristics, and patient transfer patterns. Direct patient transfers between hospitals had only a limited impact on HAI spread. Whereas, with low colonization clearance rates, readmissions to the same hospitals posed the biggest transmission risk of all inter-hospital transfers. We then generated hospital-community networks, in which patients either stay in communities or in hospitals. We found that network characteristics affect the final prevalence and the time to reach it. However, depending on the characteristics of the pathogen (colonization clearance rate and transmission rate or even the relationship between transmission rate in hospitals and in the community), the studied networks performed differently. The differences were not large, but justify further studies.

Transmission of drug-resistant bacteria in a hospital-community model stratified by patient risk

A susceptible-infectious-susceptible (SIS) model for simulating healthcare-acquired infection spread within a hospital and associated community is proposed. The model accounts for the stratification of in-patients into two susceptibility-based risk groups. The model is formulated as a system of first-order ordinary differential equations (ODEs) with appropriate initial conditions. The mathematical analysis of this system is demonstrated. It is shown that the system has unique global solutions, which are bounded and non-negative. The basic reproduction number ([Formula: see text]) for the considered model is derived. The existence and the stability of the stationary solutions are analysed. The disease-free stationary solution is always present and is globally asymptotically stable for [Formula: see text], while for [Formula: see text] it is unstable. The presence of an endemic stationary solution depends on the model parameters and when it exists, it is globally asymptotically stable. The endemic state encompasses both risk groups. The endemic state within only one group only is not possible. In addition, for [Formula: see text] a forward bifurcation takes place. Numerical simulations, based on the anonymised insurance data, are also presented to illustrate theoretical results.