Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland.
Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht University, Utrecht, The Netherlands.
Sci Rep. 2023 Oct 30;13(1):18593. doi: 10.1038/s41598-023-45248-3.
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 ([Formula: see text]) 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 [Formula: see text], while for [Formula: see text] 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 [Formula: see text] a forward bifurcation takes place. Numerical simulations, based on the anonymised insurance data, are also presented to illustrate theoretical results.
本文提出了一种易感-感染-易感染（SIS）模型，用于模拟医院内和相关社区获得性感染的传播。该模型考虑了将住院患者分层为两个基于易感性的风险组。该模型被构造成具有适当初始条件的一阶常微分方程（ODE）系统。对该系统进行了数学分析。结果表明，该系统具有唯一的全局解，这些解是有界的且非负的。推导出了所考虑模型的基本再生数（[Formula: see text]）。分析了定态解的存在性和稳定性。无病定态解总是存在的，并且对于[Formula: see text]是全局渐近稳定的，而对于[Formula: see text]则是不稳定的。地方病定态解的存在取决于模型参数，并且当它存在时，它是全局渐近稳定的。地方病状态包括两个风险组。仅一个组中的地方病状态是不可能的。此外，对于[Formula: see text]，发生了正向分歧。还基于匿名保险数据进行了数值模拟，以说明理论结果。
