Modelling and inference for epidemic models featuring non-linear infection pressure

An epidemic model with short-lived mixing groups

Almost all epidemic models make the assumption that infection is driven by the interaction between pairs of individuals, one of whom is infectious and the other of whom is susceptible. However, in society individuals mix in groups of varying sizes, at varying times, allowing one or more infectives to be in close contact with one or more susceptible individuals at a given point in time. In this paper we study the effect of mixing groups beyond pairs on the transmission of an infectious disease in an SIR (susceptible [Formula: see text] infective [Formula: see text] recovered) model, both through a branching process approximation for the initial stages of an epidemic with few initial infectives and a functional central limit theorem for the trajectories of the numbers of infectives and susceptibles over time for epidemics with many initial infectives. We also derive central limit theorems for the final size of (i) an epidemic with many initial infectives and (ii) a major outbreak triggered by few initial infectives. We show that, for a given basic reproduction number [Formula: see text], the distribution of the size of mixing groups has a significant impact on the probability and final size of a major epidemic outbreak. Moreover, the standard pair-based homogeneously mixing epidemic model is shown to represent the worst case scenario, with both the highest probability and the largest final size of a major epidemic.

Evaluating hospital infection control measures for antimicrobial-resistant pathogens using stochastic transmission models: Application to vancomycin-resistant enterococci in intensive care units

Nosocomial pathogens such as methicillin-resistant Staphylococcus aureus (MRSA) and vancomycin-resistant Enterococci (VRE) are the cause of significant morbidity and mortality among hospital patients. It is important to be able to assess the efficacy of control measures using data on patient outcomes. In this paper, we describe methods for analysing such data using patient-level stochastic models which seek to describe the underlying unobserved process of transmission. The methods are applied to detailed longitudinal patient-level data on vancomycin-resistant Enterococci from a study in a US hospital with eight intensive care units (ICUs). The data comprise admission and discharge dates, dates and results of screening tests, and dates during which precautionary measures were in place for each patient during the study period. Results include estimates of the efficacy of the control measures, the proportion of unobserved patients colonized with vancomycin-resistant Enterococci, and the proportion of patients colonized on admission.