Multigroup SIS type model with fixed time impulses

In the talk we present a system of SIS models coupled by impulses at fixed times in the way that it can describe the transfer of patients between healthcare facilities. The first aim for his considerations is to provide analytical background for numerical simulation of multidrug-resistant bacteria spread based on admission/discharge data from insurance provider for Saxony and Thuringia (Germany) for years 2010 - 2016 considered in [1]. Dynamical properties developed at possibly high level of generality can be easily applied for other settings.

Except from strictly applied results I give also the first thought on a relation between impulsive multigroup dynamical systems and the concept of a combinatoric/metric graphs.

References:
[1] A. Lonc, M. J. Piotrowska and K. Sakowski, Analysis of the AOK Plus data and derived hospital network (2017) Mathematica Applicanda, vol. 47 2019, 127 -- 139, doi: 10.14708/ma.v47i1.6497