Dynamics of extended-spectrum β-lactamases in Escherichia coli and Klebsiella pneumoniae: A mathematical model

Objectives: The prevalence of infections caused by extended-spectrum β-lactamases (ESBL) producing bacteria, associated with increased mortality, length of stay and costs, is rapidly increasing. Here we aim 1) to elucidate the dynamics of spread of ESBL and 2) to estimate the expected equilibrium prevalence of ESBL+ Escherichia coli (EC) and Klebsiella pneumoniae (KP) in a single hospital and its catchment area. Methods: We use a deterministic mathematical model with 3 hospital compartments distinguished by the risk for patients to acquire ESBL: Intensive Care Units (ICUs), high-risk non-ICU wards (e.g., haematology) and low-risk wards. Outside the hospital 3 patient groups are distinguished based upon their hospitalisation rates (data University Medical Center Utrecht (UMCU)). EC and KP can be ESBL + or -. Assuming each individual carries EC, we distinguish 6 intestinal colonisation states, EC-, EC-/KP-, EC-/KP+, EC+, EC+/KP-, EC+/KP+. Within the hospital, patients can acquire ESBL bacteria by cross transmission or by conjugation, when a patient is already colonised with a ESBL+ KP or EC. Within the hospital patients remain ESBL+ and after discharge lose ESBL+ strains after a mean of 90 days and do not acquire ESBLs. The nosocomial ESBL prevalence data used are deduced from the Dutch EARSS data (2000-2008) and UMCU (1996-2008) with a percentage of ESBL+ blood cultures in 2007 of 7% and 4% for KP and EC. Results: Model simulation results fit well with observed prevalence rates in recent years. Inside and outside the hospital the prevalence of ESBL+ carriership is for 2008 estimated to be 7% and 2.5%, respectively, for KP and 4.5% and 0.3%, respectively, for EC. Without changes in infection control measures, an equilibrium prevalence will be reached after 7 years. Equilibrium prevalence in ICUs will be 11% for patients colonised with EC+ and 8% for those colonised with both“KP+ and EC+”, respectively. The equilibrium prevalence will be highest (19%) for both ESBL+ species in the high risk wards, because of the highest readmission rates of chronically ill patients. Conjugation between EC and KP contributes to 14% of the acquisition of KP+. Conclusions: A multi-compartment deterministic model fitted to the observed increase in ESBL prevalence in the last 10 years, predicts that, in the absence of interventions, the number of patients per year with KP+ and EC+ will increase 116% and 67%, respectively, within the next 7 years.