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• SIS-type system of equations coupled by impulses at fixed times is analyzed. • Dynamics and structure's interdependence constitute network damping of infection. • Network suppression of pathogen spread indicates units prone to high prevalence. • Based on analytical results a scheme for network R 0 reduction is proposed. • Theoretical results are illustrated by simulations for the patient hospital records. In the paper, we describe the transfer of patients in the healthcare system by SIS-type equations coupled by impulses at fixed times. The first aim for these considerations is to provide a rigorous mathematical analysis of a general theoretical model, which incorporates the structure of patients' transfers. Based on theoretical results, we disprove the intuitions taken from decoupled systems, showing a damping of infection in the case when the transmission rate is locally higher than the recovery rate. Observations on network suppression of pathogen spread allow us to indicate units prone to the high prevalence and propose, possibly low-cost, interventions reducing the infection spread in a whole system. Core results combine the dynamical and structural properties of a system. Finally, we consider a model of the transmission of hospital-acquired multidrug-resistant bacteriae infections, based on real patient hospital records provided by the German insurance company – AOK Lower Saxony, to ilustrate the theoretical considerations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to provide a rigorous mathematical analysis of an optimal control problem with SIR dynamics main feature of our study is the presence of state constraints (related to intensive care units ICU capacity) and strict target objectives (related to the immunity threshold). The first class of results provides a comprehensive description of different zones of interest using viability tools. The second achievement is a thorough mathematical analysis of Pontryagin extremals for the aforementioned problem allowing to obtain an explicit closed-loop feedback optimal control. All our theoretical results are numerically illustrated for a further understanding of the geometrical features and scenarios. [ABSTRACT FROM AUTHOR]