A discrete events delay differential system model for transmission of Vancomycin-resistant enterococcus (VRE) in hospitals

Abstract

Surveillance data from an oncology hospital unit on Vancomycin-resistant enterococcus (VRE), one of the most prevalent and dangerous pathogens involved in hospital infections, is used to motivate possibilities of modeling nosocomial infection dynamics. This is done in the context of hospital monitoring and isolation procedures as a prelude to the evaluation and improved design of control measures. A discrete event delay differential equation model in conjunction with statistical computational methods is formulated to estimate key population-level nosocomial transmission parameters and isolation procedures. This framework is used to test the surveillance data's usefulness in model validation. In the process of model calibration we discovered significant irregularities in the available surveillance data; these irregularities are most likely the result of the data observational recording-process as well as those in the isolation procedures. Efforts to fit data within our highly flexible dynamic-modeling framework suggest that clinical-trial level surveillance data is needed if one is to successfully develop quantitative models for disease transmission and intervention. It is concluded that typical "cold" data sets typically encountered in biological/sociological quantitative modeling efforts may be inadequate for support of serious model development.

A Deterministic Methodology for Estimation of Parameters in Dynamic Markov Chain Models

“…We note that this is not a particularly encouraging fit of models to the experimental data, perhaps suggesting unaccounted for modeling error which is discussed below and is addressed in a technical report 19 and a forthcoming manuscript. 33…”

“…These are reported elsewhere. 19,33 G, Fenimore PW, Castillo-Garsow MA, Castillo-Chavez C, SARS outbreaks in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism, J Theor Biol 224:1-8, 2003.…”

Modelling the transmission of healthcare associated infections: a systematic review

“…Moreover, as the majority of patients can carry HCAI such as MRSA and C. difficile asymptomatically, many mathematical models simulate the epidemiology of colonisation, however for brevity we have referred to all models as concerning the epidemiology of HCAI in the text. Figure 3 shows that MRSA was the most common bacterial species studied (34%; 33 studies) , followed by Vancomycin-resistant Enterococcus (VRE) (or glycopeptide-resistant enterococci) (16%; 15 studies) [12,18,28,31,[47][48][49][50][51][52][53][54][55][56][57] whereas C. difficile has rarely been the subject of a model (3%; 3 studies) [58][59][60]. As several studies investigated the dynamics of more than one pathogen, the total number of infection agents (N=102) listed in Figure 3 exceeds the total number of studies (N=96).…”

“…Several studies use new statistical methods to overcome such difficulties [31,36,48] and to allow for estimation of important epidemiological parameters (e.g. transmission rates) from different data sources, varying from routinely collected hospital data [56,57] to strain typing [63] or genotype data [64]. Others use modelling techniques to determine the relative importance of potential transmission reservoirs or acquisition routes (of C. difficile [58,60], VRE [50,53], cephalosporin-resistant Enterobacteriaceae (CRE) [65] and SARS [66].…”

“…As Figure 5b shows, although only 35% (34 studies) of HCAIs models have incorporated some sort of calibration process to empirical data, this proportion has increased over time. Metrics used to quantify goodness of fit include the least square criterion (minimisation of sums of squares between the observed data and the model predictions) [21,56,57,75], maximum likelihood estimation (identification of the parameter value(s) that makes the observed data most likely) [18,22,24,35,53,63,65,66] and since 2007, Bayesian methods; frequently using Markov Chain Monte Carlo (MCMC) approaches [19,32,40,41,50,58,64,76] or a combination of MCMC and maximum likelihood estimation [36,59]. A further seven studies reported fitting their models by comparing model predictions to observed epidemiological data but did not apply any formal quantitative approach [17,29,43,60,81,101,104].…”