Abstract
In the paper we present a system of SIS type equations coupled by
impulses at fixed times that describe the transfer of patients in the
healthcare system represented by a graph of healthcare facilities and
corresponding communities. The first aim for this considerations is to
provide rigorous mathematical analysis of a general theoretical model,
which is then used to model transmission of hospital acquired
multidrug-resistant bacteria infections based on real patient hospital
records provided by German insurance company – AOK Lower Saxony.
Starting from the existence and the asymptotic behaviour, together with
specification of parameter R0, we propose
sufficient conditions guaranteeing network suppression of infection.
Furthermore, conditions derived analytically and proposed numerical
procedure are used to indicate healthcare facilities that are most prone
to the high prevalence bacteria spread in the healthcare system and to
ensure the stability of disease-free steady state of the system.