Email:    monika(at)

Phone: +48 22 55 44 456
Fax:     +48 22 55 44 300

University of Warsaw,
Faculty of Mathematics, Informatics and Mechanics,
Institute of Applied Mathematics and Mechanics

ul. Banacha 2
02-097 Warsaw

Project information:

Type: Excellence Initiative -- Research University, University of Warsaw, New Ideas in Priority Research Area III.
Title: Analysis of coordinated countermeasures against the spread of hospital-acquired infections within healthcare systems by numerical simulations based on mathematical models
Keywords: hospital-acquired infections, prevention strategies, mathematical modelling, analysis of deterministic models, ordinary differential equations, directed graphs, numerical simulations
Realisation period: Jul. 2022 - Sep. 2023 (extended till Dec. 2023)

Short description:

The project aims to develop and analyse in silico the effectiveness of prevention strategies for hospital-acquired bacterial infections, acting on the whole health systems at the regional or national level. The primary used method in these studies will be mathematical modelling supported by numerical simulations. This project is a continuation of the research carried out as a part of the international EMerGE-NeT consortium. At that time, we developed mathematical models for the spread of hospital-acquired drug-resistant bacteria in the healthcare systems, taking into account the transmission of infection as a result of hospital transfers and readmissions of people still colonised by the bacteria. Based on data from German insurance companies, we estimated the parameters used to describe the movement of patients in the inter-hospital network. We also proposed strategies for choosing healthcare units that should implement additional prevention measures. As shown by numerical simulations, despite operating only on the hospital level, the introduced methods allowed for a significant reduction in the number of infected people in the whole system.

Some of the challenges in this type of research are the verification of data for used models, running efficient simulations and high costs of real-world implementation of considered prevention strategies. Prior to this project, these strategies were analysed only for the much more simplified model of the real system. Hence, in the proposed project we would like to pursue further development of the previous models, focusing on ideas such as dividing hospitals into parts instead of simulating monolithic hospitals or dividing patients into groups by their susceptibility to infection. These modifications affect the structure of the developed models and the indicators we examine. The most important aspect would be to check whether the trends observed in elementary models will also be present in more complex models accounting for additional phenomena. Thus, it will be necessary to estimate the additional parameters of models, either based on the available literature or the insurance data. Previously, we analysed this kind of data within the EMerGE-NeT project. Taking the structure of hospitals or patient groups into consideration enables the new significant modifications to the proposed intervention strategies, such as additional preventive measures in intensive care wards, where patients are particularly vulnerable to pathogens.

An important part of our research is the mathematical analysis of proposed models. It improves understanding of the model results and allows us to set achievable goals when planning new strategies or modifying existing ones. By mathematical properties of models, we mean aspects such as the existence of stationary states and their stability, the value of the basic reproduction number, and the classification of bifurcations, either concerning the whole network or its parts.

UW team members:


As a part of the IDUB NI 2B project, we have extended the previously developed the EMerGE-NeT Package.

The developed code may be used for simulating the pathogen spread in the system of healthcare facilities. In addition to the previous functionality, i.e. the code (release 2.3) contains additional modules for
Those additional modules are designed for deterministic models. The typical usage of this software is supposed to be as follows. A healthcare admission data set should be provided in the standardised database format, as required by the module. Then, inter-hospital and corresponding intra-hospital models must be chosen. The models require an initial network state to be specified, determining the initial susceptible/infectious patient distribution, etc. Then, the simulations can be performed. The inter-hospital module provides parallelisation by MPI library. It is assumed that the number of healthcare facilities in the considered systems is high so that the distribution of the facilities between processors and then executing serial intra-hospital models is enough to provide adequate speedup. Finally, simulation results may be processed with the aid of the auxiliary utilities provided by this module. Please note that this code has a form of library, so there is no GUI application provided for the management of the tasks described above. Access to algorithms provided by this code is through the provided Python API.

For the description of the inter-hospital models provided by this library, please refer to submodule emergenet.inter. On the other hand, intra-hospital models are implemented in submodule emergenet.intra.


Hardware requirements: any decent desktop computer; RAM usage may vary depending on input database size and the number of healthcare facilities in simulations.
Software requirements:
  • Python 3 (version 3.6.7 or later)
  • Python modules: argparse, attrdict, base64, colander, collections, csv, datetime, dateutil, enum, io, itertools, json, ksiterate, math, matplotlib, mpi4py, msgpack, networkx, numpy, os, pandas, pint, pprint, pygraphviz, random, scipy, shutil, sqlalchemy, sys, time, types.

  • Extended EMerGE-NeT Package Code and Documentation

    To download the code and documentation (release 2.3) please fill out the details in the form. Then the link to the download page will be provided.