A singularly perturbed delay differential equation modeling nosocomial infections

Abstract

In this article, we consider a model describing hospital acquired infections. The model derived is a system of delay differential equations. The state variable is formed by the patients and the health care workers components. The system is a slow-fast system where the fast equation corresponds to the health care workers equation. The question addressed in this paper is the convergence to the so-called reduced equations which is a single equation for patients. We investigate both finite time convergence and infinite time convergence (uniformly for all positive time) of the original system to the reduced equation.