EF45 – Multi-Agent Social Systems



Modeling Infection Spreading and Counter-Measures in a Pandemic Situation Using Coupled Models

Project Heads

Tim Conrad, Kai Nagel, Christof Schütte

Project Members

Kristina Maier (ZIB)

Project Duration

01.01.2022 – 31.12.2023

Located at



Agent-based models have been proposed for modelling the spread of Covid-19 under implemented and candidate counter-measures. Since they are computationally very expensive, we propose a faster approach based on a coupled system of full ABMs and reduced sub-models that still allows to sample quantities of interest. Currently, we are working on a reduced hybrid PDE-ODE model that allows to approximate the dynamics of an ABM. Using this approach would allow to model larger regions, e.g., Berlin-Brandenburg or parts of Italy.


Motivated by [1], our initial focus is on modeling Lombardy, Italy, where we simulate the dynamics using a partial differential equation (PDE) model as a foundational reference to the hybrid model. The first results can be seen in Figures A and B. We choose the densely populated province of Milan to be represented by an ordinary differential equation (ODE) model, as this mirrors the dynamics of the corresponding PDE model more closely than other provinces.


The coupling of these two models is achieved through boundary conditions. This coupling results in infectious individuals from the PDE model coming into contact with susceptibles in the ODE model. Specifically, we introduce the infectious individuals from the PDE model into the ODE model by integrating over the boundary. This results in infectious individuals from the PDE model coming into contact with susceptibles in the ODE model. Conversely, infectious individuals from the ODE model can infect susceptibles in the PDE model at a specified rate. These interactions are captured through the use of Robin boundary conditions, creating a bridge between the two modeling approaches.


[1] A. Viguerie, G. Lorenzo, F. Auricchio, D. Baroli, T.J.R. Hughes, A. Patton, A. Reali, T.E. Yankeelov, A. Veneziani. (2021) “Simulating the spread of COVID-19 via a spatially-resolved susceptible–exposed–infected–recovered–deceased (SEIRD) model with heterogeneous diffusion”. Applied Mathematics Letters, Volume 111, 106617, ISSN 0893-9659. DOI: 10.1016/j.aml.2020.106617.

Project Webpages

Selected Publications

  1. S. Müller, S. Paltra, J. Rehmann, K. Nagel, T. O. F. Conrad. (2023) “Explicit Modelling of Antibody Levels for Infectious Disease Simulations in the Context of SARS-CoV-2.” iScience, 26 (9). DOI: 10.1016/j.isci.2023.107554.
  2. K. Sherratt, A. Srivastava, T. O. F. Conrad, C. Schuette, K. Nagel, Grah et al. (2023) “Characterising information loss due to aggregating epidemic model outputs.” DOI: 10.1101/2023.07.05.23292245. (Under Review)
  3. S. Paltra, T. O. F. Conrad. (2023) “Effectiveness of Paxlovid – A Review.” DOI: 10.1101/2023.01.13.23284506. (Under Review)
  4. P. Dönges, J. Wagner, S. Contreras, E. N. Iftekhar, S. Bauer, S. B. Mohr, J. Dehning, A. C. Valdez, M. Kretzschmar, M. Mäs, K. Nagel, V. Priesemann. (2022) “Interplay between risk perception, behavior, and COVID-19 spread.” Front. Phys. 10:842180. DOI: 10.3389/fphy.2022.842180.
  5. K. Nagel, C. Rakow, S. A. Müller. (2021) “Realistic agent-based simulation of infection dynamics and percolation.” Physica A: Statistical Mechanics and its Applications, Volume 584, 126322, ISSN 0378-4371. DOI: 10.1016/j.physa.2021.126322.

Selected Pictures




A: Number of infectious people in each province (simulated and real 7-day average data).

B: Exposed density in Lombardy for different times t in {0,7,11,18,23,49}.

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