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

Abstract

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 (\mathscr {R}_0) 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 \mathscr {R}_0<1, while for \mathscr {R}_0>1 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 \mathscr {R}_0=1 a forward bifurcation takes place. Numerical simulations, based on the anonymised insurance data, are also presented to illustrate theoretical results.